ECFA 84/85 CERN 84-10 5 September 1984

LARGE HADRON COLLIDER IN THE LEP TUNNEL

Vol. II

PROCEEDINGS OF THE ECFA-CERN WORKSHOP

held at Lausanne and Geneva, 21-27 March 1984 ©Copyright CERN, Genève, 1984

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CERN - Service d'Information scientifique - RD/650 - 3000- novembre 1984 - iii -

ABSTRACT

A Workshop, jointly organized by ECFA and CERN, took place at Lausanne and at CERN in March 1984 to study various options for a pp (or pp) collider which might be installed at a later data alongside LEP in the LEP tunnel. Following the exploration of e+e" physics up to the highest energy now foreseeable, this would open up the opportunity to investigate hadron collisions in the new energy range of 10 to 20 TeV in the centre of mass.

These proceedings put together the documents prepared in connection with this Workshop. They cover possible options for a Large Hadron Collider (LHC) in the LEP tunnel, the physics case as it stands at present, and studies of experimental possibilities in this energy range with luminosities as now considered. - iv -

Organizing Committee

G. Brianti, CERN; W. Hoogland, NIKHEF M. Jacob, CERN; C. Joseph, Lausanne J. Mulvey, Oxford; C. Rubbia, CERN J. Sacton, Brussels

Workshop Secretariat Ch. Petit-Jean-Genaz CERN/LEP - v -

FOREWORD

The first part of the Workshop on the Feasibility of Hadron Colliders in the LEP Tunnel took place at the Dorigny Campus of the University of Lausanne. It lasted four days and brought together close to 150 participants. The second part was a one-and-a-half day meeting held at CERN, immediately following upon the Lausanne meeting, and during which the conclu• sions were presented to and debated by a very large audience of physicists and engineers.

The installation of a hadron collider in the LEP tunnel, using superconducting magnets, has always been foreseen as the natural long-range extension of the CERN facilities beyond LEP. The recent successes of the CERN pp Collider now give us confidence that such a large hadron collider would be an ideal machine for exploring physics in the few TeV range at the constituent (quarks and gluons) level — an energy domain which the very success of the Standard Model, based on the SU(2) x U(l) x SU(3) gauge symmetry of the electroweak and strong interactions, leads us to consider as being crucial for a deeper understanding.

Whilst the installation of a large hadron collider in the LEP tunnel may at present be considered as a rather remote possibility, the design of the high-performance magnets which we would like to use for such a machine still demands a great amount of research and deve• lopment; this indeed appears as a prerequisite for the definition of the parameters of such a project. A Workshop bringing together theorists, experimentalists, accelerator physicists, and also experts in superconducting magnets was thus deemed timely.

Although the Workshop proper was rather short, it was actively prepared by different Working Groups dealing with various facets of the whole scheme. A large amount of work was thus invested in the Workshop, and its outcome can be seen in these Proceedings, which are presented in two volumes.

This two-volume structure was adopted in order to make at least part of the material available at the earliest possible date — rather than, as initially planned, to put into the first volume the texts of the talks presented during the open meeting at CERN, which in fact concluded the Workshop. The table of contents now covers both Volume I and Volume II. At the beginning of Volume II we find the part of the proceedings of the CERN meeting which were not available for inclusion in Volume I and, in particular, the reports of the Working Groups on Electron-Photon Identification and on Data Acquisition. However, in order to strike the right key note, we actually start Volume II with the concluding remarks presented by C. Rubbia at the end of the CERN meeting.

Next to the two reports from experimental working groups, which logically should have followed Chapter IV and Chapter VI, respectively, we find a series of theoretical contribu• tions which were presented at Lausanne. This starts with the report of J. Ellis, G. Gelmini and H. Kowalski, 'New particles and their experimental signatures', which served as a general - vi - introduction to collider physics at Lausanne and is thus singled out as Chapter XII. These theoretical contributions altogether review in great detail the topical questions and expec• tations concerning collider physics in the multi-TeV range, which were summarized by Ch. Llewellyn Smith in his report at CERN (Chapter I). Two of the reports presented at Lausanne were already included in Volume I. These are in Chapter IX, which reviews Composite Models. (Logically, Chapter IX should be combined with Chapter XIII.)

We then move to physics issues which are potentially very interesting but which take us away from hadron-hadron interactions in the collider mode. The potential of ep collisions, as in principle accessible with LEP and a hadron collider in the same tunnel, is reviewed by G. Altarelli, B. Meie, and R. Riickl. The rather intense, very high energy neutrino beams, which one could obtain (for free) from the abundant production of charmed particles, open up very interesting possibilities, as discussed by A. De RÚjula and R. Rückl.

With the material thus put together, one finds a thorough discussion of collider physics in the multi-TeV range, as it is foreseen today.

We conclude these proceedings with the brilliant address of G. 't Hooft, 'Prospects of theoretical particle physics', which concluded the CERN meeting.

The Organizing Committee would like to express its thanks to those people in various sections of the CERN Documentation Department, whose conscientious work brought these Proceedings to their present form.

M. Jacob, CERN Editor - vii -

CONTENTS

Volume I

Page

FOREWORD vii

SUMMARY REPORT, The Organizing Committee 1

WELCOME ADDRESS, H. Schopper 19

INTRODUCTION, J. Sacton 21

CHAPTER I: THE PHYSICS CASE 25 Physics with a multi-TeV hadron collider, C.H. Llewellyn Smith 27

CHAPTER II: A FEASIBILITY STUDY OF POSSIBLE MACHINE OPTIONS, A. Asner et al. 49 11.1 Review of possible options 51 11.2 The pp option 53 11.3 The pp option 116 11.4 Final remarks and conclusions 117 CHAPTER III: THE SUPERCONDUCTING SUPER COLLIDER 143 Status report on the SSC, H. Gründer 145

CHAPTER IV: JET DETECTION 165 Jets at the Large Hadron Collider, The LHC Jet Study Group 167

CHAPTER V: MUON DETECTION 209 V.l Muon Group report, A. Ali et al. 211 V.2 Unconventional methods for muon momentum measurements, C. Goessling and C. ZuparièiG 223 V.3 Muon momentum measurement in magnetized iron spectrometers, R. Voss and C. Zupanaic 228 V.4 Muon identification and muon trigger, K. Eggert et al. 238

CHAPTER VI: TRIGGERING 243 Status report, The Trigger Working Group 245

CHAPTER VII: TRACKING CHAMBERS AND VERTEX DETECTION 265 VI1.1 Tracking detectors for a Large Hadron Collider, A. Wagner 267 VI 1.2 Report of the Vertex Detector Working Group, G. Bellini and P.G. Rancoita 282 VII.3 Low-noise electronics for experiments at LHC. Design suggestions, P.F. Manfredi 292 VI 1.4 Superconducting tunnel junctions as radiation detectors, A. Barone et al. 298 - vin -

CHAPTER VIII: FORWARD PHYSICS VIII. 1 Total cross-section and diffractive processes at the Large Hadron Collider, M. Eagv.enav.ev and G. Mattiae VIII.2 Production of masses in the forward cone — The "angle of archeology", T. Ekelöf VIII.3 Theoretical predictions for pp and pp elastic scattering in the TeV energy domain, C. Bourrely and A. Martin

CHAPTER IX: TWO THEORETICAL TALKS IX.1 Compositeness: the supercollider frontier, R.D. Peaaei IX.2 Lepton and quark substructure at a multi-TeV collider, H. Fritzsch

LIST OF PARTICIPANTS

Volume II

FOREWORD

CONCLUDING REMARKS, C. Rubbia

CHAPTER X: IDENTIFICATION OF ELECTRONS AND PHOTONS X.l Electron and photon identification, The Electron-Photon Group, presented by P. Bloch X.2 Electron identification using transition radiation, D. Froidevaux X.3 Identification of single photons, L. Camilleri

CHAPTER XI: DATA ACQUISITION AND PROCESSING (Should be read next to Chapter VI) Summary report of the Working Group, D. Linglin et al.

CHAPTER XII: NEW PARTICLES AND THEIR EXPERIMENTAL SIGNATURES, J. Ellis et al.

CHAPTER XIII: COLLIDER PHYSICS IN THE MULTI-TeV RANGE — THEORETICAL TALKS (Should be read next to Chapter IX) XIII.1 Why is this energy range so interesting, R. Barbieri XIII.2 Hard hadronic collisions — Extrapolation of standard effects, A. Ali et al. XIII.3 Soft physics with a supercollider, B. Andersson XIII.4 Heavy vector bosons and super colliders, CR. Llewellyn Smith et al.

CHAPTER XIV: PHYSICS OF ep COLLISIONS IN THE TeV ENERGY RANGE, G. Altarelli et al

CHAPTER XV: NEUTRINO AND MUON PHYSICS IN THE COLLIDER MODE OF FUTURE ACCELERATORS A. De Rújula and R. Rückt

CHAPTER XVI: PROSPECTS OF THEORETICAL PARTICLE PHYSICS, G. 't Roo ft - 363 -

CONCLUDING REMARKS

C. Rubbia CERN, Geneva, Switzerland

From the discussions during the last several days it appears very clearly that large hadron collider (LHC) physics is indeed very interesting. New physics thresholds seem almost inevitable. The observation of the W particles opens up the problem of infinities in the W-W scattering channel. Weak interactions between fermions have been kept finite by the presence of a W propagator (Fig. la), and the relatively low mass of the Intermediate Vector Bosons (IVBs) ensures that fermion-fermion interaction does not grow strong. A parallel

Fig. 1

argument is now in effect for W-W interaction, where a scalar (the Higgs) takes over the role of the IVB (Fig. lb). In essence, two possible alternatives can be visualized in the energy range of the hadron collider, both of them rich in new physics: i) The Higgs mass is smaller than the unitary limit (-0.5 TeV), and W-W interaction remains weak, as in the case of the fermions. The Higgs will then be directly produced at the LHC. ii) If the Higgs mass is much larger than 1 TeV, the W-W interaction becomes strong. Then, in analogy with old-fashioned pion physics, we expect bound states (p-like) and a new rich structure in the W-W scattering. Likewise, new particles stemming from supersymmetry or compositeness may appear in our search for higher-energy phenomena. Any 'surprise' born of the present generation of collider experiments or of experiments at LEP and the SLC will encourage a new race to even higher energies. We have already some preliminary evidence of 'anomalies' not easily explained by the Standard Model, and of some 'exotic' decays of IVBs, such as Z° ->• e+ + e" + y, X + W + + jets, etc., which are whetting our appetites. Although energy is, so to speak, 'the name of the game', and it should of course be as high as possible, there appears to be operationally a relatively small difference between collisions at, say, 18 TeV or at 40 TeV in the centre of mass. The main reason can be traced to the fact that truly high energy phenomena, which for instance could not be reached by an 18 TeV machine, at 40 TeV have such small cross-sections that they become extremely difficult to study. This is due both to the softening of the quark and gluon distributions and to the - 364 - over-all 1/E2 factor in the cross-sections. For instance, interesting effects which were studied at the CERN Collider at /s = 540 GeV have typical cross-sections of - 10~3L> cm2. They will translate into corresponding higher mass effects at /s = 50 TeV, with a cross- section lO1* times smaller, namely 10~38 cm2¡ John Ellis has shown that for a large set of different phenomena the 'useful' energy grows approximately like the /E^ rather than E . Furthermore, a 20 TeV pp collider is roughly equivalent to a 2 TeV e+e" machine. We are witnessing a sort of fundamental satura• tion of the ultimate energies which can be explored by hadron colliders. The maximum rate of events that can be studied in a practical detector sets a ceiling to the useful luminosity of the collider at about 1032-1033 cm-2 s"1. Phenomena at very high energies will eventually become inaccessible because of a lack of events, irrespective of the energy of the collider. The LEP tunnel represents a valid alternative, provided that high-field magnets will become available with the degree of reliability necessary for such a large-scale device (27 km!). Research and development are necessary for the development and production of cost- effective magnets of an adequate magnetic field. Some time ago, Europe played a leading role in the development of conductors (the Rutherford cable); however, in recent years the effort spent in the field of superconducting magnets has fallen to a level which is considerably less than in the USA and Japan. Fortunately, the approval of HERA represents a very important step in reducing the present technological gap. Cryogenic devices, new conductors, and cheap manufacturing techniques, developed in collaboration with European industry, will be amongst the beneficial spin-offs of the HERA project, and may become the basic foundations for the realization of the LHC project. There are no obvious 'major' unsolved accelerator development problems at the present moment, except perhaps that of the multibunch operation which is needed to achieve the lumi• nosity required at the high energies. One can express some concern about the viability of a proton-proton bunched scheme with two separate rings and a very large number (= 103) of bunches. Indeed, experience at DORIS has proved to be extremely negative; this may be very relevant, since the hadron collider can be visualized as a scaled-up version of DORIS in the ratios of proton to electron masses. It would seem possible to imagine electron-positron machines with two separate vacuum tubes where, following the ideas of the hadron collider, one could greatly profit from the luminosity increase permitted by the many bunches. Why have such schemes, a priori so inter- resting, failed miserably so far? Clearly the attractiveness of a hadron collider will become far less overwhelming if operation is limited to a few bunches. The CERN pp Collider is, to date, the only machine which could dissipate these fears. Formidable detector development problems are associated with the larger luminosity and the necessity of handling many collisions at each crossing. An equivalent effort in research and development is needed in order to ensure an economical and feasible solution to a 4TT uni• versal detector capable of operating at L = 1033 cm-2 s-1! I would like to close with a few personal remarks. The road to the LHC is very long, and LEP must come first. This is not necessarily a handicap since a large amount of research and development are needed in order to build the machine and the detectors. In the running phase there is complementarity between e+e~ and hadron-hadron collisions. Detectors are probably different. Perhaps a bypass solution for the experimental areas could permit simultaneous e+e~ and hadron-hadron operations. - 365 -

No machine of the magnitude of the LHC can be conceived, constructed, and operated without the support and the participation of the physics community as a whole. World-wide co-operation is necessary, and co-ordination with projects elsewhere is unavoidable. Our meeting has been extremely useful; however, it should not be overemphasized. Perhaps the time has come for us to pause, at least until the magnet, accelerator, and detector issues have made some significant progress. - 369 -

ELECTRON AND PHOTON IDENTIFICATION

P. Bloch, Convener of the Electron-Photon Group, CERN, Geneva, Switzerland

I. INTRODUCTION

The recent discovery of the W- and Z intermediate vector bosons (I.V.B.) at the CERN

SPS collider [1] as well as the previous observation of the heavy flavours (charm and beauty)

through their semileptonic decay, have well demonstrated the power of the lepton detection when searching for new particles.

Our group has therefore studied the possibility of detecting electrons and photons at the

Large Hadron Collider.

In order to study the experimental problems related to electron detection, we have consi•

dered as a test reaction the production of a heavy scalar Higgs particle : • p + p — H + anything (1)

o

Hopefully, if Mu < 2 Mw, the H meson will be discovered before the LHC comes into H o operation : we have therefore considered the case where M., >2 Mw. In this case, the H will

+ oo decay mostly into W W pairs (and Z Z pairs at approximately half the rate if M^_j > 2 M-,).

There are 3 possible mechanisms for reaction (1) [2]

i) - gluon fusion which proceeds via a closed loop of t quarks (or of the heaviest existing

quarks). o ii) - fusion of two virtual IVB radiated by the incident quarks or antiquarks : WW H 0 0 + _

or Z Z -*-H0 in a way similar to two-photon processes at e e colliders. 0 iii) - production of a virtual IVB which then decays into a real IVB and an H . In the three cases, the final state will contain at leat 2 IVB's ; the idea is to identify one of

0 + _

them by its decay into electron (VJ->-e — or Z V e e ), to detect the two jet decay of the other

IVB and to reconstruct the two IVB invariant mass.

We have performed simple Monte Carlo simulations of reaction (1) from which we found

the following properties :

a) Most of the electrons are centrally produced : for = 400 GeV, 70 % are contained

within - 2 units of rapidity. This is in fact a general characteristic of all processes

involving high mass objects.

b) The electron distribution is very broad extending up to ~ 200 GeV/c with an average

value of 80 GeV/c. Present experiences at the SPS collider suggest that there is no

problem to detect such electrons if they are isolated enough. Fig. 1 shows the distri•

bution of the angular separation 6J between the electron and the axis of the closest o jet in the final state. For ~ 94 % of the events, it is found that (x> > 12 , so there should be

no real problem to identify an electron in such events, provided that the granularity of the

calorimeter corresponds to a cell size of AO. A(j> =2 x 2 or smaller. - 370 -

c) The main background to these events is due to the production of IVB pairs which occurs

because of the three boson coupling. In this case, the invariant mass of the IVB pair

Q + _ OO shows a continuous distribution whereas the decay H W W or Z Z gives rise to

a peak. Good mass resolution will be therefore essential. 0

We must note however that the H width increases rapidly with Mu from 10 GeV at M M|_^ = 300 GeV to ~ 80 GeV at = 500 GeV. Hence good mass resolution will only

help for M,, < 400 GeV.

d) The electron detector must be associated with a powerful detector of high P jets

and missing transverse energy.

e) The expected event rates are very low. At = 20 TeV and M.. = 400 GeV/c , one 0 + - H expects one H -»- W W decay in a data sample corresponding to an integrated luminosity 36 -2 of 5 x 10 cm ; the requirement that one of the IVB's decays into electrons reduces

the rate by a factor of at least 7. The detector must therefore be able to work at

high luminosity

From all the previous considerations, we conclude that the electrons can only be detected via calorimetric methods, in a fine granularity central calorimeter. We will precise the requi• rements on the calorimeter in section III. II. PHOTONS AT THE LHC

Many reactions involve direct photons at the high energy of the LHC, giving rise to a

VI 71 ratio of the order of unity at very large P (P > 1 TeV). Among the most interesting processes involving V's let us mention :

- The production of gauge boson pairs Z + V or W + V [3] that could be enhanced in the case of compositness [4]

- The detection of excited quarks via their decay [5]

q — q + y

The problems related to the photon detection are reported separately in the contribution of L. Camilleri. From his report, one concludes that a detector with a good spatial resolution and granu- o larity is needed to distinguish the 2 photons ( 71 ) showers at low P , whereas a conversion .0 1 method may be used at larger P if the r In ratio is not too small.

III. THE ELECTROMAGNETIC CALORIMETER

Let us review the various requirements for the electromagnetic calorimeter.

1) Rapidity coverage

As mentionned previously, interesting processes involving high mass objects will produce central electrons. Taking into account the difficulty to detect electrons in the high rapidity regions, where jets are collimated, we found that a coverage of - 2 units of rapidity should be satisfactory. - 371 -

2) Energy resolution

The electrons to be detected having large energies (typically > 50 GeV/c), the energy

resolution appears not to be a real problem. Today's calorimeters ( 8 E/E = .16/ V E) will

give measurements at the percent level, already dominated by systematic effects such

as the cell to cell calibration.

3) Granularity

The granularity of the calorimeter is mainly dictated by background considerations.

The main background to electrons is due to jets which fragment into a single (usually • low energy) charged particle and one or several n 's which overlap in the same calorimeter

cell. To fight against this background, it is necessary to measure accurately the shower

position and to compare it with the extrapolation of the charged track measured in a

tracking device in front of the calorimeter.

An accurate measurement of the shower position requires a granularity of the order of

the radiation length. This fine granularity is only needed in the front part of the electro•

magnetic calorimeter : it has however been pointed out that a tower structure of this

granularity all along the electromagnetic calorimeter is very useful for the electron-hadron

separation [6].

If possible, one should aim for a granularity of the order of the minimal angle 0^ between

2 particles in a jet. For a 100 GeV/c P jet, this angle is ~ 0.5 degrees. This leads to

t Q G

a large number of cells, but one should not forget that cell granularity of 1 x 1 are

presently foreseen for LEP detectors [6].

Note that a dense (Uranium) calorimeter, with an effective radiation length of 1 to 1.5 cm

and an internal radius of 1 meter would fullfill all these requirements with a tower struc•

ture of (1.5 x 1.5) cm2. IV. BACKGROUND REJECTION

A rejection against jets of > 5 10 has been achieved in the UA2 detector for jets with

Pt > 20 GeV/c, asking for :

- A small shower size

- A small leakage in the back segments of the calorimeter

- A good agreement between the extrapolation of the charged track and the shower position

measured in a preshower counter of 3 mm resolution. o o Taking into account that the tower size of the UA2 calorimeter is (10 x 15 ), one may expect a better rejection in the case of the fine grain calorimeter described above (few 10^).

The QCD jet background has however very much increased compared to the SPS collider.

If one also wants to detect electrons close to jets, an additionnai rejection power is necessary.

We have considered the possibility to use :

- Transition radiation detectors

- A magnetic field for comparison of momentum and energy. - 372 -

i) - Transition radiation detectors (XTR)

XTR detectors are reviewed in a separate report by D. Froidevaux. His conclusion is

that, for isolated electrons in the 10-100 GeV range, an additionnai rejection of » 100

may be obtained with a Lithium radiator read out by Xenon chambers with a cluster coun•

ting technique.

Such a detector is going to be built for the D0 detector at Fermilab collider.

For non isolated tracks, the rejection will be worse, but a factor 10 is still easy to obtain.

ii) - Magnetic field

Since most of the background is due to the overlap of a slow charged particle with ener- 0 getic 71 's, the comparison of the energy in the calorimeter and the momentum measured by the magnetic field deflection helps to reduce the background. Using Monte Carlo simu•

lations, we estimated that a factor 10 may be gained if particles of momentum less than

20 GeV/c are clearly signed in the magnetic field.

Note that the sagitta of the trajectory of a 20 GeV particle is 500 microns in a low field

(.3 T), modest radius detector (1 meter). Such a low field could be obtained with a thin

Aluminium coil (-^ X0).

On the opposite, the background due to Dalitz decays or V conversions in the beam pipe

will increase in the presence of a magnetic field. In the absence of field, the 2 electrons

do not separate : a ^j=- detector or XTR detector will measure a signal corresponding to 2 minimum ionizing particles. In the case of a magnetic detector, the second branch of

asymétrie conversions has to be detected ; this implies a very efficient tracking device.

The magnetic field will be obviously useful for many physics topics, provided that the

charge measurements extend at high momenta (200 GeV/c), which seems to be possible

according to the tracking detector working group. We would like however to recall that :

- asymétries (for example in the case of a heavy W') will be small in the central region,

especially in pp interactions.

- flavour mixing (e.g. bb mixing) will be difficult to observe in the electron channel, since

the decay electrons will be close (if not inside) to the jets.

We then think that the choice between a magnetic and a non magnetic detector is still open.

V. LUMINOSITY

Concerning the luminosity, we asked the 3 following questions :

33 -2 i) Do we need a high luminosity such as C = 10 cm /sec ?

ii) Do we prefer a machine with many bunches and a small average number of collisions

per crossing (e.g. A t = 25 ns, < Ncol > = 1) or a machine with less bunches and more

collisions per crossing (e.g. At = 165 ns =10)

iii) Do we need a "superfast" calorimeter, where superfast means : with an integration

time smaller than the time At between bunches ? - 373 -

Taking into account the low cross section of the interesting processes, of the order of

1 pbarn, the answer to question 1 is certainly yes.

To answer question 2 and 3, we considered the fact that the additional events following

(or in coincidence with) an interesting event will be mainly minimum bias events which deposit in average only 6 GeV energy per unit of rapidity, uniformly distributed in azimuth. Assuming that a moderate P jet spread over a region Ay. A

15 GeV/c amounts to 2 % of the total cross section [7], we have estimated the probability that a jet from the next event overlaps the electron cluster of an interesting event ; we found it to be ~ 1.5 10 3. Therefore, the probability that the addi• tional events overlap in space in the calorimeter with an interesting event is at most a few percents.

We conclude that it is possible to pile up events : but, in order to disentangle the various

events, to study the topology and the missing Pt, it will be better to have these events at different times with a precise timing ( « 4 t) on each cell of the calorimeter.

The solution with many bunches is then our prefered solution. There is no obvious need for a superfast calorimeter ; the integration time of the order of a few At (e.g. 100 ns) is acceptable.

A possible electronics is schematically drawn on Figure 2. A 100 MHz fast ADC samples the signal twice per time slices At. The shape analysis of the signal allows to measure the signal timing and to remove signals occuring before or after the time of the trigger cells.

Note however that, to measure a signal ranging from 100 MeV (m. ionizing) to 1 TeV in the calorimeter, we need a fast 14 bits electronics.... which is not yet on the market .'

VI. TRIGGER

The electron trigger does not seem to be a problem at high energy (P > 50 GeV/c) if

it is based on small size clusters.

For P > 50 GeV/c, the jet rate is 5104/sec at C = 1033 cm~2/sec. A rejection of 10 at the trigger level was obtained in UA2 with large clusters • a (4 (10 x 15 ) cells) and without check on the hadron leakage.

We estimate that a factor 100 will be obtained with a fine grain calorimeter, bringing

down the first level trigger to a rate of 500/sec.

Other triggers (e.g. association with XTR detectors or tracking detector) will be used

at the 2nd level.

VII. CONCLUSION

Even if we did not have the possibility to fully design an electromagnetic calorimeter

during the short time of the workshop, our group was convinced that it is possible to detect electrons at the Large Hadron Collider, at least in the case of isolated electrons as we expect

in the decay of intermediate vector bosons or heavy flavors.

A fine grain calorimeter with good spatial resolution is needed.

High P isolated photons may also be statistically detected with a conversion method.

Additional devices to improve the electron hadron discrimination such as transition radia•

tion detectors are necessary if one wants to detect electrons near jets. - 374 -

We believe that a granular calorimeter can stand the pile up problem up to a luminosity 33 -2 -1 of 10 cm s , with a preference for a machine with many bunches and a small number of collisions per bunch crossing.

Acknowledgements

As convener of the group, I would like to thank all the physicists who participated to the workshop and to the preparation meetings. I am very grateful to L. Camilleri, L. Dillela and D. Froidevaux for their contribution to the proceedings.

References

[1] G. Arnison et al. Physics Letters 122B (1983) 103

Physics Letters 129B (1983) 273

Physics Letters 126B (1983) 398

M. Banner et al. Physics Letters 122B (1983) 476

P. Bagnaia et al. Physics Letters 129B (1983) 130

CERN EP 84/39

[2] John Ellis, invited talk at this workshop

[3] B. Humpert, Physics Letters 135B (1984) 179

[4] M. Leurer, H. Harari and R. Barbieri

Physics Letters 141B (1984) 455

[5] A. de Rujula, L. Maiani and R. Petronzio

CERN TH3779 (1983)

[6] ALEPH technical proposal CERN LEPC/83-2

[7] B. Humpert Physics Letters 140B (1984) 105 - 375 -

ru p p —" H + anything

CO (degrees)

Fig. 1 : Angular distance between the electron and the closest jet axis in the 0 + - pp--H —-WW reaction. L_ e+V

decision time Good event time

* good signal

late signal (next crossing)

50 va 150 time (ns)

^ bunch crossings

Fig. 2 : Schematic principle of a proposed readout electronics for the calorimeter Fast ADC's allow to reject signals due to early or late collisions. - 376 -

ELECTRON IDENTIFICATION USING TRANSITION RADIATION

D. Froidevaux LAL, Orsay, France

I. Motivation

Previous sections have shown that electrons from heavy Higgs decay are expected in the

central region (\rj\ <" 2) and in the PT range between 50 to 200 GeV/c. /— Because of the fast rise in the jet production cross-section as a function of \ s, the ratio

electron to jet at fixed P-p will be considerably smaller at the LHC than at the present SppS

collider. Background sources to electrons will therefore arise from pathological jet fragmen•

tation, where most of the jet energy goes into neutral pions, and a small fraction to a charged

pion which, at some level, will generate a charged track matching the energy deposition in

the calorimeter. This type of background has in fact been observed by both UA1 and UA2.

Transition radiation techniques using lithium radiators and xenon chambers have been shown

[1,2] to provide good additional independent electron-hadron discrimination, once the full power

of calorimetry has been used. More recently [3] cluster counting techniques have been shown

to provide significantly better electron-hadron discrimination than the standard method using

the total energy deposited in the chamber.

This study was therefore performed to find out what transition radiation would bring in

the difficult environment of the LHC.

II. Standard XTR performance

For obvious reasons of detector compactness, we considered an optimized XTR detector of fixed total length L (L = 50 cm). The total number N of sets (radiator + chamber) was also

fixed to N = 4. In fact the optimum was found to be N = 6, assuming partial recovery of X-rays

produced in a given radiator but not absorbed in the chamber immediately behind it, which sometimes would be absorbed in the following chambers. Mechanical considerations (in the

case of a cylindrical detector mostly) tend to suppress this partial recovery of the X-ray signal,

and the corresponding loss in electron-hadron discrimination is roughly a factor 2.

II. 1 Radiator

It is well known that low Z materials are best in order to minimize reabsorption of the

X-rays produced. We have chosen lithium for this study, ignoring, for the moment, problems

of mechanics, construction and safety.

After optimization (see reference [4] for an overwiew of cluster counting XTR detector

optimization), the radiator has the following parameters :

- number of foils : 550 (per radiator)

- foil thickness : 30 \i - spacing between foils : 150 p. - 377 -

11.2 Chamber characteristics and simulation

We have used a sophisticated program developed by Gavrilenko, Dolgoshein et al. (Lebedev

Institute, Moscow) to define a realistic chamber performance. We included such effects as absorption of X-rays in radiator and chamber windows, merging of nearly primary clusters as a function of chosen drift velocity (typically 10 |i/ns for 80/20 Xe-CO^ gas mixture), expo• nential absorption of X-rays in the chamber as compared to flat production of 8 -rays, and losses of absorbed X-rays due to Auger effect.

11.3 Results

Fig. 1 shows the total number of X-rays above 2 keV absorbed in the 4 chambers, for electrons and pions, as a function of energy.

Electrons saturate below 5 GeV, whereas pions become a problem around 100 GeV (in fact the pion curve is just the electron curve shifted by the ratio of pion to electron mass as expected for transition radiation).

The electron-pion discrimination using cluster counting was found to be optimum for a cluster energy threshold of 5 keV.

The average number of clusters above 5 keV from XTR is about 10, whereas it is about

0.7 from 8 -rays.

For a fixed electron efficiency of 90 %, Fig. 2 shows how the rejection against single pions varies as a function of pion energy. Such a standard XTR set-up provides a rejection of 10 against pions below 50 GeV, and is therefore a powerful tool against overlap background from jet fragmentation, where the charged pion is at low energy. However the rejection against single pions above 100 GeV is 100 times worse, due to the rapidly rising XTR production from pions themselves.

In a non-isolated environment, the XTR performance would be much worse, since additional tracks produce on average 0.7 clusters above 5 keV. Typically one additional track would bring the rejection down from 1Q"3 to 50, two additional tracks from 10 to 20. Finally, the XTR set-up, in an experiment without magnetic field, provides rejection against electron pairs from conversions or Dalitz-decays.

III. Possible new developments

Following recent developments on the use of low pressure gaseous detectors [5], devices, which are sensitive to UV photons from Cerenkov light, but not to minimum ionizing particles, are being developed (for LEP experiments in particular).

The advantages of such a detector for the LHC are immense :

a) The low pressure chambers have extremely good timing resolution (100ps) and can be

gated in 20 ns, e.g. less than the time between two bunch crossings.

b) The very low sensitivity of these chambers to minimum ionizing particles provides

even higher rejections against hadron background, which would be most useful in a

search for non-isolated electrons.

Tests are currently under way at CERN (Charpak, Majewski) using a thin (1u.) gold layer to generate photoelectrons from a Fe X-ray source. Preliminary results are encouraging and development work is clearly needed in this field. - 378 -

References

[1] W. Willis, Yerevan Conference on Transition Radiation, 1977.

[2] M. Bourquin et al., RL-82-0U2.

[3] T. Ludlam et al., NIM 180 (1981) 413-418.

[4] C. Fabjan et al., NIM 216 (1983) 105-111.

[5] A. Breskin, WIS-15/81, Invited Talk at the INS International Conference on Nuclear Radiation Detectors, 1981. - 379 -

Fig. 1 : Number of X-rays above 2 keV absorbed in the Xenon chambers.

Pion energy (GeV)

100

Rejection against pions

Fig. 2 : Pion rejection as function of pion energy. - 380 -

IDENTIFICATION OF SINGLE PHOTONS

Leslie Camilleri CERN, Geneva, Switzerland

Several processes are expected to yield high energy single photons at the LHC. Basically they fall into two categories:

a) Resonances decaying into one or more photons.

b) Standard QCD processes yielding a photon or photon pair continuum.

In both cases the background comes mainly from tr°'s and n's decaying

into two photons. The problem then reduces to determining whether a shower

observed in an electromagnetic calorimeter originates from one or two

photons. There are two ways to go about this

1. The Shower Separation Method.

It requires an active converter interleaved with or followed by a

detector with very good spatial resolution such that one can distinguish a

shower with two distinct conversion points from one with a single conversion

point. For very high energy *°'s when the two conversion points are very

close the method reduces to separating IR°'s from y's on the basis of the

broader shower size of IR°'s due to the presence of two y's. The method

provides a clean separation between y's and IR°'s on an event by event

basis. However it can only be applied up to a maximum p^, which is apparatus

dependent, beyond which the two showers from a IR° are so close as to be

completely indistinguishable.

The minimum separation between two y's from a «° decay is shown in Fig. 1 as a function of p^ for a detector located at 3 metres from the interaction point (general purpose detector) and for a detector at 10 metres (small solid angle dedicated single photon detector).

12 3) Several groups ' ' have studied the problem of shower localization and 2 two-shower separation. In particular V. Aretemiev et al. have used a lead

proportional tube calorimeter. The tubes have a 7.7 mm pitch and the planes

of tubes are separated by lead sheets 0.8 radiation length thick. A sample of

single showers was obtained in an electron beam. Two-shower events were

"constructed" by overlapping two uncorrelated single showers. They fit to an

exponential the shower shape observed in the last two layers of tubes after 8

radiation lengths. Cutting on a value of x* of the fit that accepts 90% - 381 - of the single showers they plot the percentage of two-shower events that pass the cut as a function of the separation of the two showers (Fig. 2). For 1 cm separation only 15% of two-shower events survive as one shower.

3) Another method which is still under development involves the use of BaF^ crystals (2.5 cm thick) interleaved with low pressure wire chambers containing 18 torr of isobutane and TMAE which are sensitive to the scintillation light of the BaF^. A position resolution of 3 mm has been measured by the authors. A simulation of the detector taking into account the scintillation light emission and propagation in the detector shows, Fig. 3, that separating showers down to about 1 cm should be possible.

The shower separation method is therefore capable of distinguishing one from two shower events down to two-shower separation distances of the order of 1 cm. This in turn means that a general purpose detector at 3 metres from the production point could separate photons from ir°'s up to 100 GeV/c.

2. The Conversion Method.

This again requires a converter interleaved with a detector which however need only have a modest spatial resolution. The basis of the method is that ir°'s consisting of two Y'S on average will convert earlier than a single photon. For a given sample of events one therefore measures the fraction that converts as a function of depth into the converter. The method 4) has been used in an experiment at the ISR and is described in detail in the LAPDOG proposal ' for the Tevatron. A plot taken from ref. 5 is shown in Fig. 4. It shows the number of conversions divided by the number of conversions expected from pure ir°'s for samples of events containing different y/n° ratios. The larger the fraction of Y'S in the sample, the larger the fraction of events converting deep into the detector. The advantage of this method is that there is no upper limit to the p at which it is applicable. However it only determines the y/v ratio on a statistical basis and does not separate Y'S from if°'s on an event by event basis. The method is particularly useful for large y/n ratios. 7,8) Table I summarizes some cross-sections and rates for the production of Y'S, jets and ir°*s (assuming ir°/jet ~ 10 3) from standard QCD 40 -2 processes. At /s = 18 TeV and for an integrated luminosity of 10 cm the rate for the production of photons is substantial even up to 1 TeV/c. The Y/ir ratio there is expected to be of order 1. However to explore these extremely high transverse momenta it is clear that only the conversion method will be useful. Table I

The production of photons and jets at /s = 18 TeV.

PT da1' (cm2 GeV/c 1) dojet (cm2 GeV/c"1) Y/jet Y/TT° Events/100 GeV

(GeV/c) dpTdy 40 -2 dpT

•35 •31 100 10 10 10 0.1 10

•37 •33 200 6.3 x 10 3.5 x 10 -4 2 x 10 0.2 6.3 x 10

•39 •35 500 9.4 x 10 2.5 x 10 3.8 x 10 0.4 10000

•40 •36 800 8 x 10 10 8 x 10 0.8 800 - 383 -

REFERENCES

1. R. Rame ika et al.. Measurement of electromagnetic shower position and size

with a saturated avalanche tube hodoscope and a fine grained scintillation

hodoscope.

FERMILAB - Conf. - 8A/22-E.

2. V. Aretemiev et al., Performance of a Fine grained photon position

detector using proportional tubes, to be published in Nucl. Instrum.

Methods.

3. D.F. Anderson et al., Recent Developments in BaF^ coupled to a

low-pressure wire chamber, CERN-EP/83-200, to be published in Nucl.

Instrum. Methods.

4. A. Angelis et al., Phys. Lett. 94B (1980) 106.

5. The LAPDOG Tevatron proposal and Note 6 on Photon/ir° separation

attached to this proposal.

6. Contribution by B. Humpert and R. Riickl to this workshop.

Figure captions

1. Minimum separation between the two photons from ir° decay as a function o

of pT of the ir for a detector located at a) 3 m and b) 10 m from

the interaction point.

2. The fraction of two-shower events accepted as single showers as a function

of the separation of the two showers.

3. Simulation of the light intensity on the surface of a 2.54 cm thick BaF

crystal a) for one particle and b) for two particles separated by 1.5 cm.

4. The Total Number of conversions divided by the number of conversions

expected from ir°'s only as a function of the point of conversion in the

detector. - 384 -

<

Ao >*0 CoO %o too

Fig. 1

Totol Conversions Conversions Expected from TT" Only

Number of Radiation Lengths

12 3 4 5

Fig. 3 Fig. 4 - 385 -

CHAPTER XI

DATA ACQUISITION AND PROCESSING

(should be read next to Chapter VI)

Data acquisition and data processing, Summary report of the working Group (D. Linglin, P. Charpentier, S. Cittolin, A. Clark, M. Demoulin, D. Jacobs, L. Mapelli, B. Nielsen, J.-P. Porte and A. Rothenberg)

Presented by D. Ling!in - 387 -

DATA ACQUISITION AND DATA PROCESSING

Working Group summary report

1) INTRODUCTION

The major task of the DACQ/processing group was to examine the possibility of Data Acquisition systems which could sustain very high transfer rates along with a maximum of high level trigger intelligence and flexibility. In addition, it had to investigate practical ways of processing the large amounts of data that will finally come out of detectors at the LHC (Juratron).

This chapter should be regarded as a continuation of the summary provided by the trigger group. There were extensive discussions with that group, and our group assumed as input their estimates of level-1 and level-2 trigger rates. The reader can refer to their report for an overview of the various trigger signatures, possible problems, and expected rates.

Our approach was the following : first, we examined the trends in the present large detectors, especially those installed at colliders, and then we tried to define by extrapolation a scheme that could reasonably operate at higher energies, with higher event rates, sizes and complexity, in 10-15 years from now.

This short report is divided into 3 general parts :

Section 2 gives an overview of our proposal for a DACQ system. Section 3 describes in more detail the various components of such a system : Level 2, Data Acquisition Bus, Level 3, recording media. Section 4 deals shortly with the problems of data processing and analysis.

2) DACQ system - Overview of a proposal

"The UPSTREAM MOVE" :

In the past two decades, one has observed a general move to instal computer "intelligence" as early as possible in the data taking system, in parallel with growing detector complexity and event rates, and also in parallel with the rapid development of the electronics and computer industries. Not so long ago, recorded data were only looked at in off-line computer centres (eg. the so-called "Bicycle On-Line" or BOL activities). We observe now that more and more decision tasks, monitoring or calibration tasks, and even partial reconstruction tasks are performed locally, either near the detector or in the control room, on the on-line computer(s) of the experiment or in dedicated microprocessors. This "upstream move" will certainly continue in the years ahead, given its many advantages (for example avoiding BOL or large numbers of recorded tapes, improving response time, etc.).

FLEXIBILITY :

On the other hand, flexibility is an absolute must. Large 4rr detectors at LHC, built to observe physics in a new energy domain, must be ready to adapt to many scenarios, whether it be the existence of surprising event topologies, the demand of increasing luminosity, etc. . - 388 -

Everyone knows the few basic triggers on "elementary" constituents that one plans to deal with. For example :

- Jet trigger (quark or gluon), - Localised EM shower (electron or photon, depending upon charged track trigger), - Missing Et (neutrino, ...), - Penetrating particle (Muon), - other triggers such as Total (transverse) Energy.

However other triggers may be needed (eg. new types of particles) and, above all, any type of combination of the above triggers is a-priori desirable. Hence implementation of trigger algorithms resulting from the observation of new topologies, or from an improving understanding of the data must be easy to do. A flexible trigger solution is to have the same software running off-line (when developing new algorithms) and on-line (in the high level trigger processors).

Also, the CPU capacity of the high level triggers must be flexible, to cope with increasing luminosity and/or level-2 trigger rates.

PROPOSAL :

Our proposal, which solves these trends reasonably well, is based on 3 main ideas :

- A high speed DACQ Bus (between the detector area and the control room, that is also between level-2 and level-3 triggers, a distance of =50 to 100m.) - A single system with very large CPU capacity (up to 1000 processors, each one equivalent in speed and memory to a present large mainframe). This system is used for high level ("level 3") trigger decisions. - Data storage and processing mainly at the experiment.

3) DACQ system - Description

Let us now describe in more detail a possible scheme (Figs 1 & 2) and its main consequences :

LEVEL 2 TRIGGER :

The so-called level-2 trigger has been described in the report of the trigger group. It can use digitized data from the calorimeters and the muon chambers, and also from central tracking chambers. Transition radiation detector signals seem to be too slow to be used at this level. However, at level 2, the events remain split into several branches and the full event information is not available to a single processor.

Talking about the level-2 DACQ system (the readout), it is proposed to hold there, in sequence, the digitizers (10-100 us), FIFO multi event buffer memories (to derandomize the event arrival time), data formatting tasks, reduction tasks, and finally data concentration tasks to put together the many parallel event pieces into a small number of branches that form the DACQ bus. Details of the digitization of the calorimeter cell pulse heights are described in the report of the trigger group, where they considered a level-2 trigger description based on calorimeter signals alone.

Canonical numbers usually quoted are a maximum rate of 1 KHz, for an event size of 1 Mbyte at the exit of level 2, to enter the DACQ bus.

DATA ACQUISITION BUS :

This bus should be able to sustain a rate of 1 Gbyte/sec (IKHz ® 1Mbyte) over a distance of 50-100m, that is from the detector area to the control room. Presumably this - 389 - will only be feasible with several (between, say, 10 and 25) parallel branches and possibly with optical fibres.

For comparison, VME can reach =10 Mbytes/s. FASTBUS can theoretically reach a maximum transfer rate of ^20 to 40 Mbytes/s over short distances. The 1-Gbyte/s quoted above represents 25 parallel branches with a speed not so different from today's maximum value for Fastbus, apart from the larger distance involved and N-branch coordination problems. Although the goal of 1 Gbyte/s does not seem unrealistic, we feel that Research and Development will be desired in this field.

LEVEL 3 TRIGGER :

The event information is still in N separate pieces when it arrives in the control room at the end of the DACQ bus. Only here, at level 3, does a single processor has access to the full event information, ready for recording.

It is proposed to install at this stage a "stack" made of a large (50—1000) number of processor units (as for the 3081E emulator of today), as shown on fig. 2. Each unit of this stack has a typical CPU speed of 10 Mflops with 10-16 Mbytes of central memory. This is roughly the speed and memory sizes of the large computers we are using today in our computer centres. We assume that the computer industry will be able to deliver such processors in a volume equivalent to one (or a few) CAMAC units, at a price of one to a few KSF. This means one rack could hold 5 crates with 5 to 20 processors each, plus its (optical disk) recording unit. A 1000 processor system would then be accomodated in 10 to 40 racks, at a price of a few MSF.

Each incoming event selects the first unit available and, depending upon the bits set by lower level triggers, starts one of the fast filter programs. This can be, for instance, a refined level-2 trigger, with the final calibration constants, or an elaborate jet finding algorithm, with for example an improved Et cut or a multi-jet effective mass selection. If the event passes the test, one starts a second, more elaborate, selection program. Thanks to CPU power, this can even be the reconstruction of tracks from the central detector for additional rejection power. Other selection programs may follow, increasingly elaborate as the remaining events decrease, with consequently more CPU time available per event. Possibly, selected events can be fully reconstructed before being recorded. With enough memory, each unit can hold all the filter and reconstruction programs and play the role of "several-in-one" high level triggers.

Moreover, the scheme allows : - a flexible number of microprocessor units, to match increasing luminosity, level 2 rates or decreasing costs per unit, - an easy implementation of new algorithms (the development of which depends mainly on the off-line analysis of previous data). It is very important that algorithms run with the most up-to-date information and calibration constants.

RECORDING :

The best choice foreseen as a recording medium seems to be the optical disk (although magtapes may have not yet given their last word). 12" optical disks are now arriving on the market, with reasonable prices, although one must admit that none has been delivered yet to customers. Advertisements already propose 2-Gbytes capacity disks (1 Gbyte per side), that is more than 10 6250bpi tapes, with typical writing speeds of 0.4 Mbytes/s, only limited by laser power. Capacity and recording speeds should increase, and prices should decrease, in the next few years. With rather cheap disk systems available in 10 years from now, one can choose between a good "juke-box", or a disk pack system, or 5-20 independent disk drives as shown on fig. 2.

Although it would be possible to record rates as high as 10-50 Hz (eg. with 20 independent disk drives), we feel that one should aim at a standard rate of =1 Hz, with - 390 -

peak values of -5 Hz. Otherwise, the high level trigger programs in the stack would not be fully efficient. For an average 1 Hz trigger rate of events, with a typical 1 Mbyte length, we would need to change a 1 Gbyte side of a disk every 15-20'.

4) DATA PROCESSING AND ANALYSIS

PROCESSING :

Since the full experimental data base is available in the control room, and having in addition a large CPU capacity there, the reconstruction and data reduction tasks should be made with the multiprocessor stack. This can be performed off-line or even on-line when one has enough confidence in the programs. This would ease all the administrative aspects such as bookkeeping, calibration constant base, etc., and also the present tape handling bottleneck, which presently afflict large experiments. Also, the random access facility of the optical disks must ease many of the data processing activities.

With the large filtering power of the stack, every recorded event should be interesting enough for further analysis. Each 1000-hours period of useful data taking should then yield, for 1 Hz average recording speed, 3.6 10s events of 1 Mbyte each, stored for instance on 360 10-Gbyte disks. Assuming 20 to 50" CPU time to fully process an event in any given processor of the stack, this means between 20 and 1000 hours for 50->1000 processor units. Such computing power allows for several complete processings of the same events, whenever wanted.

ANALYSIS :

Analysis (and analysis development) should be done on private workstations or on large mainframes because of the niceties which are not available with the multiprocessor stack. To provide data information to any external laboratory, disks can be copied and shipped. Individual events can also flow from the control room through inter-computer networks. However, for bulk analysis, the best scheme would be to connect private workstations to the on-line computer ("supervisor") and from there, use the stack and the data base.

5) CONCLUSION

- The above scheme follows the present trends and is flexible enough to adapt to many scenarios. - The computer industry should deliver by LHC turn-on time, at a reasonable cost, all the elements. - Some R&D however might be needed on fast data bus development. - 391 - iiiiiiuiiiiuimmiiíiiiiiiiiimmiiiiiiiiiiiiiMiiiiiiii Z^^^^^E^^^Ez~^^^^^=z^^^=^==^^ rfJLTT EVENT BJFFER/FIFO

Fig. 1

Fig. 2 - 393 -

CHAPTER XII

NEW PARTICLES AND THEIR EXPERIMENTAL SIGNATURES

J. Ellis, G. Gelmini and H. Kowalski - 395 -

NEW PARTICLES AND THEIR EXPERIMENTAL SIGNATURES

J. Ellis and G. Gelmini CERN, Geneva, Switzerland

H. Kowalski DESY, Hamburg, Fed. Rep. Germany

1. Introduction

The most exciting experiments with a new accelerator are those which discover new particles. One of the main motivations for a Large Hadron Collider in the LEP tunnel is the opportunity it offers for exploring a new energy range, and perhaps discovering new particles with masses up to 0(1) TeV. This report summarizes work done by our theoretical working group on exotic particles before, during and since the Lausanne meeting. We discuss the motivations, rates and experimental signatures for new physics and new particles in the 1 TeV mass range. Section 2 reviews some of the motivations for expecting new physics in this range. Of particular interest is the physics of gauge symmetry breaking. From where do the W* and Z° acquire their masses? From spontaneous symmetry breaking? Via the Higgs mechanism with elementary Higgs particles? Are Higgs masses protected by supersymmetry? Or are they composite? Other ideas for new physics which might be detectable in the 1 TeV range include the possibility that the W* and Z° may be composite - is this why they are massive, whilst the photon y and gluon g are massless? - or that quarks and leptons may be composite - is this why there are so many flavours of apparently "fundamental" fermions? In the case of spontaneous gauge symmetry breaking it is possible to give firm arguments why new physics should be expected in the 1 TeV range. Such may also be the case in models with composite W1 and Z°. It is not so obvious why quarks and leptons should appear composite at an energy scale 0(1) TeV, although some theorists have been inspired by 2 3 4 5 6 recent UAn collider data ' ' ' ' to speculate about this possibility. More motivations for new physics in the 1 TeV range are provided by Riccardo Barbieri 7 in his talk at this Q meeting, while Roberto Peccei discusses composite models in his talk. One possibility g (discussed at this meeting by Chris Llewellyn Smith ) is an extension beyond SU(2)^ x

U(l)y of the electroweak gauge group, perhaps to SU(2)L x SU(2)R x U(l), which some theorists expect to yield new gauge bosons with masses below 1 TeV. In section 3 we discuss the rates and experimental signatures of new particles predicted by theoretical models of gauge symmetry breaking, notably the Higgs boson, + supersymmetry and technicolour. Among the signatures we discuss are multiple W and/or Z° events (for the Higgs), missing transverse energy (for supersymmetry) and multiple t~t events - 396 -

(for the Higgs and technicolour). We provide many examples of final state differential distributions in rapidity and p-p particularly for Higgses and for supersymmetry. We also analyse some physics backgrounds to the new particle production processes which interest us. Examples include W+W", Z°Z°, W(tTt) and (tt)("tt) production as backgrounds to Higgs production. However, we do not consider in detail non-physics backgrounds such as the jet fluctuation background to missing energy signals for supersymmetry production. Many calculations of conventional physics processes which may provide backgrounds to new particle production are presented in the talks by Ali ^ and by Andersson ^. The 12 production of new particles in ep collisions is discussed in the talk by Altarelli Section 4 summarizes our preliminary conclusions on the observability at a high 13 energy hadron collider of the new particles studied in this report

2. New Physics in the 1 TeV Range?

Unfortunately for our sense of progress, the Standard SU(3) x SU(2) x U(l) Model continues to work very well. Fortunately, the veneer of experimental success may be beginning to crack. In recent months a variety of funny events have been reported from the — 4 6 CERN pp Collider. Among these are monojet "zen" events ' , electron + jet + missing 3 + - 2 energy-momentum events , anomalous Z° + 1 1 y decays , a possible bump in the multijet 5 invariant mass distribution around 150 GeV in mass , and a number of dimuon events, particularly three with like signs. Many physicists believe that some of these events may be inexplicable within the Standard Model. Perhaps all these phenomena will eventually turn out to be explicable within the Standard Model, but we hope one or more of them may lead us beyond it. Theorists have been proclaiming for some time the inadequacies of the Standard Model, and proposing myriad solutions to the mysteries it leaves unsolved. What are the origins of particle masses? Are they due to the spontaneous breakdown

of SU(2). x U(l)v? Why is there such a proliferation of "fundamental" quark and lepton ± flavours? Are they composite? Are the W and Z° composite? Are the spin-zero fields related to gauge symmetry breaking composite? Since they offer the best motivations for the existence of new physics in the 1 TeV range, we will concentrate here on the possible mechanism of weak gauge symmetry breaking, including the possibility of composite spin-zero fields.

2.1 Gauge Symmetry Breaking

If weak gauge invariance were exact, the W* and Z° would be massless, in the same

way that the masslessness of the photon and gluon reflect exact U(l)gm and SU(3)C gauge invariance respectively. Similarly, the known quarks and leptons would have to be

massless, since their left- and right-handed components fL, fR are known from standard weak interaction phenomenology to have different isospins: I = j, 0 respectively leading to maximal parity violation in the charged current weak interactions. Fermion mass terms

m + f : ancl tnere re must couple left to right: f(fLfp, ^R lJ f° violate weak isospin invariance with AI= Hints on the nature of the new physics responsible for weak gauge symmetry breaking can be extracted from an analysis of perturbative unitarity and renormalizabili- ty14. - 397 -

To avoid unrenormalizable divergences in one-loop contributions (fig.l) to 2 +-»• 2

2 scattering processes, all tree level 2«->-2 scattering cross-sections must fall as 1/E M at high energies. The archetype is e+e" -* u u", which is well-known to have the point-like cross-section 4 TTCI2/3E2 in lowest order QED, consistent with the renormalizability of cm the theory. Non-abelian gauge theories almost succeed in having the same good behaviour, thanks to the cancellations due to the 3- and 4-gauge boson vertices (fig.2). However,

2 there are residual excesses over the 1/E m law, which are proportional to rry in the case of f7->-W+W~ annihilation, and proportional to m^ in W+W"->- W+W" scattering. To cancel these out we must introduce (fig.3) a new boson with couplings to fermions <*try, and to gauge bo• sons «m2. Such a boson should not have spin greater than 1, as the couplings of such par• ticles are well-known to be unrenormalizable. The hypothetical new boson cannot have spin 1, since the only such bosons allowed are gauge bosons, and they have universal couplings 14 to fermions, not couplings proportional to m^. The only solution is to postulate a new boson with spin zero - either the Higgs boson or something very much like it.

2.2 Elementary Higgses

We have already seen that generic Higgs couplings are proportional to rry for fermions and to for massive gauge bosons. In the minimal version of the Standard Model with one complex I = ij- Higgs doublet there is just one elementary neutral Higgs H° and no charged Higgs H* and we will stick to this minimal possibility in what follows. The 15 couplings of the unique H° are completely fixed :

gH?f = (/2"GF)5 mf , gHW+w- = 2(/2Gp)5 (2.1)

Thus the H° couples to the heaviest particles available. For example, decay rates to some fundamental quarks and leptons are in the ratios

r(H° - tt) : r(H° -bb) : r(H° - TV) : T(H° - u+u~) (2.2) » 3m? : 3m¿ : m2 : m2 t b T p

Thus any H° heavy enough to decay into (Tt ) would have a u+u~ branching ratio less than 10-5. Thus looking for H° •* u+u~ at a large hadron-hadron collider is unlikely to be very frui tful. While the couplings (2.1) of the minimal H° are completely determined, its mass is almost completely arbitrary. Fruitless nuclear physics searches ^ tell us that

mHo > 0(15) MeV (2.3)

while radiative corrections and conventional cosmology ^ suggest that

muo > 10 GeV (2.4) - 398 -

However, the radiative correction limit is not watertight, and can be evaded if the t quark mass is suitably chosen. At the upper end, if we want the Higgs self-coupling to be weak enough for perturbation theory to be applicable, then we need ^>19

mHo <0(1) TeV (2.5)

Of course, it is just this assumption of weak self-coupling which is jettisoned in techni- 20 colour models of strongly interacting composite Higgses. The range (2.3, 2.4, 2.5) is

21 rather wide. We take the point of view that if mH<, < 100 GeV, it will have been detected at LEP before our large hadron-hadron collider comes into operation. Let us assume also

that mt < 50 GeV. If 2mt < mHO < 2mw± we expect the dominant decay mode of the H° to be

+ into tt, whereas if muo > 2mw± or 2mzo we expect the decays into W W~ and Z°Z° to dominate

(their ratio is 2:1 for mH„ >> 2mzo). Heavy Higgses have a large total decay rate ^:

Gm2- 2i 1 2 G m 2 r{H°) = [ -O. i^-^il (3x - 4x±+ 4) + E W_ d - x°)'.(3x 0-4x0+4)] (2.6)

2 2 + where x+ 0 = 4m + z0/in 0, which means that T(H°) mHO as mH<3 * 1 TeV. The decay rates of

heavy Higgses are plotted in fig.4: we see how the tt decay mode is overwhelmed when muo >

2mw±. Also shown on fig.4 are lines corresponding to ?(r\°)/m^0 = 0.01 and 0.1. We see that

if mHo < 200 GeV it is worthwhile aiming for a 1% resolution in mHO, since the natural

width is smaller. However, if mHO > 400 GeV it is not even worthwhile trying to get a mass resolution of 10%, since the natural width of the H° is larger. This means that a massive H° will be more difficult to disentangle from background sources of W+W~ or Z°Z° production, for example from continuum qq -* W+W" or Z°Z° production. Another important source of background will be 2 simultaneous hard parton-parton collisions, either with both giving vector bosons, or with one giving a W* or Z° and the 22 other giving a dijet pair with m^ » 80 or 90 GeV . As we will see in section 3, typical cross-sections for H° production are 0(l)pb, and therefore the rates will not be so generous that we can afford the luxury of working only with leptonic decays of the W" and

+ Z°. Moreover, we lose all kinematic constraints when we look at (W l+v)(W -» 1 v). Therefore we will presumably have to try to work with at least one hadronic W* or Z° decay, and contend with QCD multijet backgrounds. As we will see in more detail in section 3, looking for heavy neutral Higgses in hadron-hadron collisions will not be very easy. Although we do not discuss them here, looking for the charged Higgses present in non- minimal models is probably comparably difficult.

2.3 The Trouble with Higgs

When one calculates loop corrections (fig.5a) to the mass of an elementary Higgs boson, one finds that they are quadratically divergent:

2 (2.7) 2 d*k YI - A 6mH oc - 399 -

Some might argue that these divergences are unimportant, because they are renormalizable and can be compensated by a suitable choice of the bare Higgs mass. However, these divergences, if not diseases in themselves, seem to be symptoms of a more grievous under•

2 lying malady of instability in mH . The difference between the Higgs mass divergence (2.7) and other renormalizable divergences is that the others are only logarithmic. The 24 quadratic form of the divergence (2.7) raises problems of naturalness : if the cutoff

2 2 A> 0(1) TeV then the corrections 6mH to the Higgs mass squared become larger than its physical value. On the other hand, logarithmically divergent loop corrections to other quantities such as fermion masses are numerically small even if A » 0(1) TeV. Large corrections (2.7).to m^ seem unnatural to many theorists, who therefore seek models with some effective cutoff A = 0(1) TeV. Related difficulties arise whenever one tries to construct theories containing two

o±1 or more very different mass scales, e.g. mw = mu x 0(10 ) and the Planck mass

15 nip = 0(1019 ) GeV or the grand unification scale m > 0(10 ) GeV. Hawking and 24 ~ collaborators claim that elementary Higgs bosons propagating (fig.5b) through the space- time foam expected in the quantum gravitational vacuum acquire large mass shifts:

2 2 19 6 mH = 0(mp ) = 0(10 GeV) (2.8)

25 Moreover, elementary Higgses propagating through a GUT vacuum acquire

2 2 15 2 Smu = 0(m ) > 0(10 GeV) (2.9) n X ~ 1 5

from their couplings to GUT Higgses with large vacuum expectation values 0(mx) > 0(10 GeV). Even if the large 6m2 (2.8, 2.9) are cancelled by some mechanism, radiative corrections involving transitions to heavy virtual particles with masses 0(m ) can upset 25 26

the delicate cancellation in mu ' . For example, loop corrections in GUT's give

2 n 2 6 m = 0(a mx ) (2.10)

and some miracle should be found to cancel these loop corrections through 0(0'^)! These examples illustrate the fact that it is difficult to construct theories with two or more

vastly different mass scales, e.g. m^ « mx or mp. The heavy scale tends to leak into the light scale via the Higgs. This is often termed the hierarchy problem: why is

20 17 mw/mp=0(10~ ) ? One possible solution to these instability problems is to dissolve the Higgs by making it a composite scalar bound state of new fermionic constituents called "technifermions" which have new "technicolour" interactions analogous to QCD, but becoming strong at a scale

AjC = 0(5*) = 0(1 TeV) (2.11)

whereas QCD becomes strong at A^ = 0(1 GeV). While it is easy to construct technicolour models giving masses to the W* and Z°, giving masses to quarks and leptons has proved to 27 be much more difficult. Early prescriptions for solving this problem involved extending the technicolour model in a way which predicted flavour-changing neutral interactions that - 400 - were too large , and light charged spin-zero bosons P which should have been detected 29 in experiments at PETRA and PEP . Technicolour is therefore out of theoretical favour at the moment. However, it has never been demonstrated that a phenomenologically acceptable 30 technicolour model cannot be constructed , so we retain technicolour as an interesting theory to test experimentally and as a yardstick for measuring the potential of a high energy hadron-hadron collider. An alternative solution to the instability problems of elementary Higgses is to protect their masses and cancel out large loop corrections by invoking supersymmetry (susy). Several miraculous cancellations ocur in susy theories. The quadratic divergences due to bosons and fermions in fig.5a have positive and negative signs respectively. Therefore, if one has pairs of bosons and fermions with identical couplings available to circulate in the loops, as in a susy theory, one has

ôm2 = 0(a)x |m| - m2 | (2.12) which can be less than the O(m^) required for m2 by perturbative unitarity if

2 2 I m| - mp |> 0(1) TeV (2.13) corresponding to a low effective cutoff: A2 = 0(1) TeV2. A second miracle is the absence of large A™!2 from propagation through space-time foam in a susy theory. Finally, if the GUT contribution (2.9) to m^ is cancelled in a susy theory, no contributions of the form (2.10) are generated by radiative corrections. This is thanks to certain miraculous 32 no-renormalization theorems in susy theories which guarantee that many logarithmic divergences are absent. Because of these miracles, is stabilized in a susy theory, and therefore m^ is also stabilized against the effects of radiative corrections. However, there is no fundamental understanding of the origin of the weak interaction scale, which means that the hierarchy problem is not really solved by susy. But at least some technical progress is made in alleviating the symptoms of the disease.

2.4 Supersymmetric Particles and their Signatures

Cancelling the unwanted loop diagrams required bosons and fermions with identical couplings and similar masses. These are provided in susy theories which contain particles 33 in the following supermultiplets :

l/ Z gauge: (^ , chiral: ( Q ) (2.14)

Unfortunately, no known particle is the spartner of any other known particle, which requires a doubling of the elementary spectrum and the invention of many new names as seen in Table 1. - 401 -

Table 1: Supersymmetric Spectrum

particle spin sparticle spin

1 1 quark qLjR squark ij^ R 0, 0 2' 2

1 1 lepton 1L R slepton R 0, 0 2' 2

1 photon y 1 photino Y 2

1 gluon g 1 gluino g 2

1 1 W 1 wino W* 2

1 Z° 1 zino Z° 2

1 Higgs H0'* 0 shiggs H°'* 2

The absence of any charged sparticle at PETRA and PEP means that

m~, nr|, ny*. mqfc> 0(20) GeV (2.15)

34 The absence of a signal in SPS and FNAL beam dump experiments mean that coloured sparticles must be massive and in particular

m~ >0(3) GeV (2.16)

4 — with the precise value dependent on the assumed squark mass. Experiments at the CERN pp 35 Collider can be used to argue that

m > 0(40) GeV (2.17) S > M ~

36 There is no particle physics bound on colourless neutral sparticles, but cosmology suggests that the lightest sneutral may be the photino, and

m~ >0(|) GeV (2.18) with the precise value dependent on the assumed masses of sleptons and squarks. The fact that in general particles and sparticles have different masses means that supersymmetry must be broken, just as rr^ means that flavour SU(3) had to be broken. It may well be that supersymmetry is broken spontaneously, as we believe to be the case with electroweak gauge symmetry. The precise mechanism of supersymmetry breaking need not - 402 -

concern us here: many models with broken supersymmetry also have the desired miraculous cancellations. By how much can supersymmetry be broken? or in other words, how heavy could the unseen sparticles be? In supersymmetric theories the self-couplings of the Higgs particles are specified to be 0(a), and the masses of the Higgs bosons are fixed to be

close to ny and m^0. Therefore we expect from equation (2.13) that the sparticles will have masses below 0(m,,//a ) = 1 TeV, and this is indeed the case in most though not all 37 models 37 In most models there is an exactly conserved multiplicative quantum number R = +1 for ordinary particles and R = -1 for sparticles. This means that sparticles can only be produced in pairs, that their decay products always contain another sparticle, and hence that the lightest sparticle is absolutely stable. In this case cosmology probably requires the lightest sparticle to be neutral and not strongly interacting, as was assumed in deriving the limit (2.18). In models where R-parity is conserved the signature of susy is 36 missing energy-momentum carried off by the missing sneutral, probably the photino: q+q+Y, 1 + 1 + y. 9 + W Y (2.19)

These are the susy signatures developed most extensively in section 3. However, it is 38 possible to construct models in which R-parity is violated in which case sparticles may decay into leptons such as the x or the v :

q-q+(^) , î-l+i^) , Y + (^ )+ e(*) (2.20)

This alternative is also discussed in section 3. Sparticle masses are very model-dependent, but typically <0(1) TeV because of the 39 cancellation argument (2.13). As discussed in more detail in section 3, rates for the production at high-energy hadron colliders with s = 0(20) TeV of coloured sparticles, q and g, are large enough for m^,~ > 0(1) TeV to be detected. There are no obvious physics backgrounds to the missing transverse energy signatures provided by the canonical decay patterns (2.19). While a detailed evaluation of instrumental backgrounds is not included in our brief 40, we do not believe that they are very troublesome. Therefore, as we will see in more detail in section 3, looking for heavy sparticles in high energy hadron-hadron collisions will be relatively easy.

2.5 The Technicolour Alternative

We also study in section 3 what the phenomenology of a realistic technicolour 20 41 41 theory ' might resemble. We assume that a realistic theory contains a complete new

technigeneration of fermions: (IL v B; DD v R, E, N). Since such a theory has a whole new K,I,DK,T,D ^,

set of strong interactions on a scale ATC = 0(1) TeV (2.11), one expects a rich spectroscopy of new states with masses in this range:

technip : mpT = 0(1) TeV , technibaryon : mR = 0(1) TeV, etc. (2.21) - 403 -

as illustrated in Table 2. Also shown in Table 2 are the many "low-mass" technipions with masses « 1 TeV which are anticipated in extended technicolour models which seek to under• stand quark and lepton masses. As already mentioned, all existing technicolour models are ± 29 unsatisfactory, in part because the P of Table 2 have not been discovered , and it may be that Table 2 is not a reliable guide to technispectroscopy. Nevertheless, it is the best we have. Of particular interest in high-energy hadron-hadron collisions are the colour octet states Pe , ps etc. One would expect the decay signatures

P°8 -*tt, Pi •*• g + VT , ps, ois +technipions (2.22)

Rates for production of Ps, Ps and the techni fermion continuum are large at /s = 0(20) TeV, and the signatures (2.22) are probably detectable as we will see in more detail in section 3.

Table 2: Techm'hadron masses

Particle Description Mass

T P°' e.m. neutral < 3 GeV ? e color singlet c

h P1 e.m. charged < 15 GeV ? n color singlet i

leptoquarks 150 GeV color triplet 0

n P°8' * color octet 250 GeV s

p color singlet / '4/fL x 900 GeV T octet

Ü color singlet /4/NTC x 900 GeV T octet

e.m. neutral v/4/NTC x 970 GeV RT color singlet

fy.etc color singlet, octet /4/NTC x 1500 GeV, etc.

B technibaryons /N TC/4 x 1500 GeV T

The number of technicolours is denoted by N - 404 -

3 - Production and Detection of New Particles

3.1 - General Comments on Rates and Distributions

We have seen in section 2 that extant models of gauge symmetry breaking (elementary Higgs bosons, supersymmetry, technicolour) all firmly expect some new physics in the 1 TeV range. The new particles that these models predict are the main foci of our studies in this section. Before getting into details, we first make a few general remarks for orientation purposes.

If the mass of a new particle system x is quite heavy (mx >> 1 GeV), and if its ratio to the total centre-of-mass energy is not too low (m^//s 0(10~2)?), its production cross-section at a hadron-hadron collider can be estimated quite reliably (to within a factor of a few ?) using the model illustrated in fig.6. The general approximate form of 42 the cross-section is given by the Drell-Yan formula:

o(x) =L J dx L B(T) Ô b(x) (3.1) a,b where 5 is the cross-section for a parton-parton subprocess a + b •*• x, e.g.

4™2eq 4m[

X for heavy-lepton pair production via a virtual photon of invariant mass m , and L |J(T) is the parton-parton luminosity function for ab collisions:

L (x) =J dx ab " a /

2 T = xaxBE m / s : xa = Zpj/S , xb = 2pb/A , /i = Ecm (3.4)

The parton fractional momentum distributions a(x 1 etc. should be evaluated at some a momentum scale Q = 0(m ), evolved from lower scales using the QCD Altarelli-Parisi 43 equations . The formalism (3.1, 3.2, 3.3) predicts correctly to within a factor of 2 the cross-sections for production of lepton pairs with m > 4 GeV in fixed target experiments + 12 and mx K or m^o in collider experiments ' . The discrepancies between experiment and the naive theory (3.1) have the same sign and order of magnitude as the computed higher order QCD corrections to equation (3.1), though these corrections are 0(1) and difficult 44 to estimate quantitatively. The same formalism (3.1, 3.2, 3.3) is applicable to large p-j. strong interaction cross-sections, and seems to work there also to within a factor of

2. Not all the next-to-leading order QCD contributions to large pT jet production have yet been calculated. Genérica!ly, one expects subprocess cross-sections to have geometrical values characteristic of the collisions of point-like particles: -, , 1 0( 10_1*) for electroweak processes (3.5a) x 0(1) for strong processes (3.5b) - 405 -

The Drell-Yan subprocess cross-section (3.2) exemplifies the general rule (3.5a). The rule (3.5b) is an effective upper bound on the possible cross-section for the point-like production of new particles. It tells us that even though a very high energy hadron-hadron

collider offers in principle the possibility of parton-parton collisions at mx up to/I, in practice the collision rates will be bounded above by the luminosity functions L^ÍT) (3.3), which are known to fall monotonically with increasing T. The precise forms of all the parton-parton luminosity functions are not well determined in fixed target experiments at Q2 < 0(100) GeV2. For example, it is difficult to measure parton distributions at x < 0(10 ~2), and gluon distributions may only be determined indirectly in lepton-hadron collisions, with the result that their shapes are strongly correlated with the fitted value of the QCD scale parameter A. However, these uncertainties tend to wash out at very

large £~ and mx, although it is always difficult to make reliable predictions for parton distributions at x < 0(10~2 ). Even if one knew precisely the low energy input structure functions, the logarithmic QCD extrapolation to higher energies is more uncertain here than at larger values of x. Shown in fig.7 are some of the effective parton- parton 45 luminosity functions that we use in our cross-section calculations. They are obtained 46 from CDHS structure functions evolved up to the appropriate energies using the 43 47 Altarelli-Parisi equations . Comparisons with other calculations lead us to believe that our parton-parton luminosities are not likely to mislead by more that a factor of 2 for x > 0(10~2), which is in any case within the inevitable range of uncertainty due to higher order corrections. We see from fig.7 that because of the general rules (3.5), one is unlikely to have observable cross-sections for new strongly interacting particles which weigh more than a few TeV, even if the available centre-of-mass energy is an order of magnitude higher. When comparing machines with different centre-of-mass energies but the same hadron-

2 hadron luminosity, the geometrical factors of l/mx (3.5) imply that any given parton- parton subprocess has an observably large cross-section only up to values of T which decrease as /"s increases. One must compensate for the lower values ofcr by going to lower values of T where L(T) is larger (fig.7). This effect is seen in fig.8, where we have plotted the luminosity (3.3) multiplied by the geometric factor 1/m2 (3.5). The horizontal

axis is taken to be mx, the vertical axis has the dimensions of a cross-section, and we have included horizontal lines corresponding to plausible limits of observability for hadron-hadron colliders with liminosities in the range 10 32 to 103 3cm~2sec_1. The curves plotted are for gg and uïï luminosities in pp and pp collisions at 7s = 10, 20 and 40 TeV.

As a rule of thumb in the region of interest, the effective range of mx in which one can probe for new physics increases like 3 6 mx « ( ^)°(1) <-)

It is easy to see from fig.7 how one loses physics reach at fixed /s if one decreases the available hadron-hadron luminosity L. As a rule of thumb in the region of interest, the

effective range of mx in which one can probe for new physics decreases like

,0(0-2) ,, 7, mx = L ' (3.7) - 406 -

The first rule (3.6) must be borne in mind when considering possible values of /s (10, 20 or 40 TeV?), and the second rule (3.7) must be borne in mind when considering the relative merits of pp and p~p colliders. It seems likely that pp colliders will be limited to luminosities at least one order of magnitude smaller than pp colliders, say 1032cm"2sec-1 for pp rather than 10 3 3cm~2sec_1 for pp. Comparing figs.8a and 8b, one then sees that the physics reaches for producing strongly interacting particles by uü" collisions, as indicated by the horizontal "limits of observability" lines, are very similar for pp and pp colliders having the same /"5. The assumed factor of 10 advantage in hadron-hadron luminosity of a pp machine is essentially cancelled by the pp" advantage in parton-parton luminosity at large values of T: compare the dotted horizontal line in fig.8a with the dashed horizontal line in fig.8b. On the other hand, it is clear from fig.8c that one loses physics reach for particle production by gg collisions if one decreases the hadron-hadron luminosity by a factor 10, as expected when comparing pp and pp collisions. Moreover, the pp advantage in hadron-hadron luminosity is also significant when considering a electroweak production mechanism. In such a case the subprocess cross-section a (3.5a) is likely to be OilO-1* ) of a strong cross-section at the same invariant mass. This means that the "limit of observability" occurs at a much lower value of T, where the difference between the uD parton-parton lumi• nosities in pp and pp" collisions is much less significant. Thus pp colliders with a hadron-hadron luminosity of 1032cm-2sec-1 generally give more events than pp colliders of the same Js with a hadron-hadron luminosity of 1032cm"2sec-1, with the limited exception of the production of very high mass strongly interacting particles via uu collisions. In most of the range of interest, luminosity functions in pp and pp collisions do not differ by more than a factor of 2, which therefore accords no great physics advantage to pp col• lisions. Indeed, the differences between the pp and pp" cross-sections are typically smaller than the likely theoretical errors in estimating the absolute values of these cross-sections. Nevertheless, in what follows we always state whether a given cross- section is calculated for a pp or a pp collider. Heavier particles which are produced with smaller cross-sections closer to the limit of observability are produced predominantly centrally, with rapidity |y| = 0(1). For example, Higgses of 200 GeV produced in association with a tt pair (see section 3.2) have i _ 2 = 1-1, while the q and q jets coming from pair-production of gluons weighing 1 TeV i (see section 3.3) have 5 = 1-2. By contrast, particles of smaller mass, which are generally produced with larger cross-sections, generally tend to be produced closer to the 49 r- + beam directions. For example, it has been estimated that at /s = 40 TeV W are produced in the rapidity range lyl < 0(5), with 2/3 going within 5° of the beam-pipes (fig.9). These are specific examples of an analogy between production angles and the depths of sedimentary strata in which archeologists search for ancient artefacts, illustrated in fig.10. At any given accelerator, the new physics of the day tends to be produced at large angles, while yesterday's physics is produced closer to the beams, and last week's physics passes down the beam pipes. At present, today's new physics is the W*, Z° and hadron jets

with pT = 0(100) GeV, all of which are currently produced at large angles. However, at the LHC the W and Z° will be swept forward and backward in the centre-of-mass, as we have seen. We hope they will be replaced at large angles by gluinos or Higgses or? - 407 -

In addition to the single-subprocess hard scattering cross-sections given by (3.1), 22 there can also be events featuring two hard parton-parton collisions in parallel, as illustrated in fig.11. As we will see later in Section 3, some of such multiple hard collisions could provide significant backgrounds to new particle searches. To estimate these double cross-sections, one needs two-parton distributions

a(x , x ) (3.8)

50 which are not known in general, although some model distributions have been proposed 22 The double distributions (3.8) do not in general factorize, but model studies indicate that factorization gives an approximation to the double subprocess total cross-section which may be correct to within a factor of order 2, if one is considering processes initiated by partons with low values of x. In what follows we therefore estimate these double subprocess cross-sections by

o(Xl, x2) = (fiili) (£li^l)xaot (3.9) atot CTtot zoz where ^ is the total pp cross-section * 100 mb.

3.2 - Higgs production and signatures

We consider several mechanism for Higgs production at hadron colliders in sections 3.2.1 to 3.2.5, as well as several sources of physics background in section 3.2.6.

3.2.1 - qq - H

This reaction proceeds via virtual quark diagrams as shown in fig.12. The total cross-section is

aa (3.10) Jgg->-H 64 TT 9 1 dx where N = £ N : q q

Nq = 3[2Xq + Xq(4Xq " ] (3-lla> with o 1 X2Í„„ , vi

2/2 fM , 2 (sm-^) forx >f

K 5 m /m f( = q q q H ' V + + (3.11b)

+ilTl |log(40 - V °9(J-) for Xq < \ and rf = \ ±\-\ (3.11c)

Total cross-sections (no rapidity cuts) are shown in fig.13 for /s = 10, 20, 40 TeV,

mt = 35, 70 or 100 GeV and a range of Higgs masses between 200 GeV and 1 TeV. - 408 -

The cross-sections can only be estimated approximately when 0(200) GeV. The cross- sections depend sensitively on the assumed masses of the quarks propagating round the loops, with

= 0(mVmi\ In (mf/mf,)) as m /mH - 0 (3.12) -»• 1 as "•q/f^ -»• =

We have only included one heavy quark in calculating fig.13, which we take to be the t quark, though there could be important contributions from representatives of a fourth generation. In fig.13 we have taken = 35, 70 and 100 GeV: the cross-sections increase

rapidly with as long as mt « mu, quantitatively as one expects from equation (3.12), although the analytic form 3.12 is not a good approximation throughout the interesting range of m^. Even if the t quark were soon found to have a mass 0(35) GeV, the cross-section for gg - H could be substantially increased if there is a fourth generation. The rapidity distribution of the Higgs decay products is shown in fig.14 for different values of m^. - We see that, as expected, the rapidity distribution is more central for larger m^. The Higgs will decay isotropically in into centre-of-mass frame, predominantly

+ into Tt if 2mt < m^ < 2mw, and into W W" or Z°Z° for mu> 2mw. Possible backgrounds are considered in section 3.2.5.

3.2.2 - qq ->• H, g + q- q + H

It is necessary to distinguish two contributions of this sort to Higgs production: via the annihilation of light quarks which are copions inside nucleous, and via heavy quarks which are rare. The coupling (2-1) of the standard model Higgs to ligh quarks is so small a m : m .«10 MeV, m,s200MeV) that they make a negligible contribution to Higgs 15 production . The dominant perturbative QCD contribution to Higgs production via heavy quarks is likely to be that discussed in the next subsection. However, it is à priori possible that there might be an important nonperturbative contribution due to an "intrinsic" component of heavy quarks in the proton. The existence of such an intrinsic 52 heavy quark component has been proposed in connection with the diffractive production of charm, and similar diffractive production of the t quark, due to "intrinsic top" in the proton, is now being looked for at the CERN pp Collider. The existence of an "intrinsic" 52 53 54 charm component at the proposed level does not conflict with EMC data on dimuon production. Production of light Higgs at lower energies via intrinsic charm has already 55 i— been considered . It is easy to scale the cross-sections found there up to higher fs

using the t quark - Higgs coupling am^ instead of a mc:

2 coit / da|c = 0(Jj|) x ( /s|c / /s~|t ) (3.13a) for similar values of m^/Zi and of the kinematic variables such as the rapidity y. In deriving the ratio (3.13) we have assumed similar distributions for intrinsic charm and 52 intrinsic top, but scaled by 0(l/m2) in each of the two colliding nucléons. Using - 409 -

equation (3.13) to compare H production at a collider with /s = 10 to 20 TeV with lighter

7- -5 Higgs production at /s = 10 to 20 GeV, we find a suppression factor of order 10 . Since previously quoted cross-sections for low /s collisions were at most 0(10"38cm2) this suggests that intrinsic "tt annihilation would not make a significant contribution to H production at the colliders of interest to us here. Potentially more interesting might be bremsstrahlung of Higgs from an "intrinsic" 56 heavy quark struck by a gluon: e.g. g + tH + t . Assuming intrinsic distributions independent of m^ apart from an overall normalization factor 0(l/m2), this cross-section scales as 2

da|t/da|c = 0(^-) (3.13b)

m for similar values of y, mq/mH and m^/Zs. Scaling from m^ = 10 GeV, /s = 800 GeV andc = 1-5 GeV to m^ = 250 GeV, /s = 20 TeV and « 38 GeV, the low-energy calculations of ref.56 yield an estimate of 10~3 pb. While giving a cross-section considerably larger than the tt annihilation mechanism estimated previously, this g + t •+ H + t mechanism does not seem to be competitive in terms of rate and event signature with other mechanisms. There• fore we have not studied it further.

3.2.3 - qq or gg •» ttH

The underlying mechanism in these reactions is Higgs bremsstrahlung from a heavy — — 57 quark as in fig.15. The subprocess cross-section for qq •+ ttH is known in analytic form:

3 3 3 a - - - c Gc rat d kt d kP d kh , , , „

where 2 2 a(qq - ttH) = 6-(p^-k^- (4mk ) |m M | + (3.14a) 32 r,_ x2„_ ._ , . ,2ri. t - ^Pq Pq> ^¿^J^J^+ 2 2 ] = (2k..kT+mH)(2kh-kt+mH) {(Pq Pq) ((Pq+Pq-)'P ) fl' (2kh-kt+m¿)(2\-k^m¿)

(3.14b)

2 k 4tI m + 2 r,, ,22 22 „ 22 x (Pq+Pq-)- h( it- H)ir(Pq Pa:) 22 w , M + [((pq+Pq) +n. -4m ) + ]í~f^- \ - 2(kt-Pq) (p^)] h t H

+ (kt~ kt) - ((Pq+P^)2+mH-4mt) [2(kt-PqHkTPq)+2(kt-Pq){krPq)-(Pq+Pq)2(kt-kt)^

The evaluation of gg -* ttH involves the interferences between several different diagrams obtained by permuting the external gluons and coupling the H to the different internal and external t quark lines. No complete analytic calculation is available, but we have used 57 58 the outputs of 2 different algebraic programs ' for the trace calculation. Results for m^ = 35 GeV and different choices of m^ and /s are shown in fig.16. We have not been able to confirm the large cross-sections or the shapes of the Higgs rapidity distributions reported in ref.57. Some final state distributions for a representative m^ = 200 GeV and /s~ = 20 TeV are shown in fig.17. Fig.17a gives the rapidity distribution of the Higgs, and fig.17b that of the accompanying t (or T) quark. Fig.17c shows the Py distribution of the Higgs, while fig.l7d shows that of the accompanying t (or t) quark. Finally, fig.17e show - 410 -

the distribution in invariant mass of the spectator (Tt) system. We see that the Higgs is

produced quite centrally, as previously advertized, and with an average pT = 0(100) GeV. The additional event signature of a spectator (Tt) pair in the final state may be used to reduce the backgrounds below those encountered in gg H production.

3.2.4 . WW -> H

59 + - This process is an electroweak analogue of yy scattering in e e annihilation, as seen in fig.18. The subprocess cross-sections for ud •+ duH, uïï •+ uüH, dd->ddH, üd-*üdH

and analogous processes involving strange quarks are all identical: the matrix elements squared are

2 2 Cl 2 2 + C 2 2 2 1 Ml = 64g [

In the expression (3.14b)

gVVH = 9 ' n,W for WW* H

mz (3.15b) 9' Hië^ for ZZ" H and

Cl = ÍRgR2 ' C2 = gL9R2+ 9R9L2 (3-15c) where

9L,R = l(g + 9A> (3,15d)

with

9v = "9A = 2^ f0r W±

3 15e *v = icier: (K - Q si"2^) 1 ( - )

W > for Z°

9A = _ cos0~

An approximate form for the subprocess cross-section (3.14a), integrating after all the final state variables, is:

5(qq + qqH via WW) = ^ (^) log^ * (3.16)

The total cross-section for WW H in pp collisions is shown in fig.19 for interesting

ranges of mu and /s. We see that the cross-sections are larger than those for gg •* H when

mu > 0(500) GeV. Unfortunately, when it is so heavy the Higgs is so wide that it may be difficult to pick out from the WW or Z°Z° continuum. The vector boson poles in (3.14a) tend to give sharp forward-backward peaking for the final state q (or ~q) and a flat rapidity distribution for the Higgs (hence the logarithm in equation (3.16). It is possible to compute ^ analytically from equations (3.15) the form of the Higgs distribution in the centre-of-mass frame of the parton-parton subprocess. It exhibits - 411 -

strong forward-backward peaking when s » m^:

2 4C 2 6 d ô igyVH /TT 13 uvf , . , {3 17) ^/s»%~VF~ - W , reflecting the kinematical similarity of this process to yy scattering. The rapidity distribution 60 of the Higgs in the parton-parton subprocess centre-of-mass is shown in fig.20. Because of the peaking (3.17) the scattered quarks or antiquarks in the final state do not get out to large enough Py to provide a distinctive signature, such as was provided by the (tt) pair in the previous reaction.

3.2.5 - gg + M*** W + H

The diagram for this subprocess is shown in fig.21. The subprocess cross-section for qq (W±*or Z°*) •+ (W or Z°) + H is 19'61

+ 9vvH 9v 9A Pv n ^ Pv > ,„ 1Q . avH = 24rT IRf 77 (1 + 3if;) <3-18a> V v S V

where gvv^, 9V and g^ were introduced in (3.15), and py is the final state momentum of the H in the subprocess centre-of-mass: ^

-2 4 it » 2 •> 2 2 2 —

(s +mv+mH-2smv-2smH-2mvmH) 2 (3.18b) pv = ¿71 ~~~ The total cross-section for these processes is not very large, falling below the limit(?)

of observability of 1/10 pb for mH = 0(200 to 400) GeV, as seen in fig.22. This process

has the distinctive final state event signature of 3 intermediate vector bosons if mu>2iriy. Unfortunately, the fall-off of the cross-section curves in fig.22 means the total cross- section is probably unolservably small in the region of large m^ (>400 GeV) where its natural width is too large for it to appear as a sharp resonance above the WW continuum.

3.2.6 - Observability

As stated in section 2, we assume that any Higgs with mass less than about 100 GeV 21 will have been detected by LEP before this large hadron-hadron collider starts operation. A compilation of cross-sections for heavy Higgs production in pp collisions at

/s = 20 TeV is shown in fig.23. Cross-sections for 100 GeV < mH < 200 GeV are tricky to estimate because there we get into regions of /r = 0(10~2) where we no longer have great confidence in the perturbative QCD extrapolation of the presently known parton distributions and the subprocess luminosity functions of fig.7. If 100 GeV < m^ < 2m^, we presume the dominant decay mode is H tt. In this mass range , the largest production cross-section is that for gg •* H, but in this case the absence of any other final state event signature leaves us prey to the relatively large gg or qq •* tt background shown in fig.24. If one assumes a plausible (?) mass resolution for (tt) pairs of order 10%, the (Tt) background overwhelms the H signal. One could hope that the situation would be better if one looks for processes with final state event signatures such as gg or qq -Î- Htt or - 412 -

qq - W+H. For the Htt case we have estimated the background in two different ways. One 5« uses a perturbative QCD calculation of the 2 to 4 subprocesses giving tttt final states. The cross-section for this raction is estimated to be very large (fig.25) and overwhelms the tt+(H -+ tt) signal. We have tried unsuccessfully to get out the signal by implementing

cuts on p-j-(H) or pT(t) or m(7t). Unfortunately, the final state distributions for (TtTt) production shown in fig.26 are very similar to those for (tt+H) production in fig.17. The background from the double-subprocess mechanism (gg or qq •+ Tt)(gg or qq - Tt) estimated using the Ansatz (3.9) is much smaller than that due to the 2 to 4 subprocess (see Table 3) and would by itself be menageable. Turning to the process qq ->• W+(H -* Tt), the backgrounds come from 2 to 3 reactions qq -*- Wtt and from the double-subprocess reaction (qq -W)(gg or qq •+ Tt). A recent calculation 58 of the cross-section for ud •+ W++Tt indi• cates that it is not uncontrollably larger than that for ud-W*+ - W++H. Taking /s=400GeV,

2 mw = 80 GeV and mH = 120 GeV one has ô(ud -* W+H) « 7 x Iff" pb, whereas the total subprocess cross-section for ud •* W++Tt is â(uïï - W+Tt) « 1-3 pb. However, if one assumes a 10% resolution so that one can take the background in a bin of width Am(Tt) = ± 5% of m(Tt) « 120 GeV, one only has to contend with Aô = dô/dm(Tt) x Am(Tt) « 7-5 x 10"2 pb. This ratio of signal tophysics background ô(W+H)/Aô(W+Tt) « 1 to 1 does not vary strongly with either s or m^. The background from the double-subprocess reaction (q"q- W) (gg or qq - Tt) seems to be manageably small, as seen in Table. 3.

Table 3: Double-subprocess backgrounds to Higgs searches at /s = 20 GeV

Signal Background Background Process cross-section (pb) process cross-section (pb)

tt+(H+Tt)120GeV 3-6 (gg or qq+Tt)(gg or qq+tt) 2-5

W+(H-tt)120GeV 0(10) (qVW)(gg or qq-Tt) 1-5

gg-(H-ww)200GeV 0(10) (qq->W)(qq->W) 0-9

WW-(H+WW)400GeV 1 (qq+WHqq+W) 0-9

Tt+(H-WW)200GeV 3 1 (qq-WW)(gg or qq-Tt) 1-5 x 10"

W+(H-WW)200GeV 3 (qq-WW)(qq-W) 9 x 10""

6 W+(H-WW)200GeV 3 (qq+W)(qVW)("qVW) 3 x 10"

+ If 2mw < mu < 400 GeV the dominant decays of the Higgs are into W W" or Z°Z°. Ncwthe dominant physics backgrounds come from qq -+ W+W~ or Z°Z0, and from the double process (qq - W+ or Z°)(qq W~ or Z°). The total cross-section^^ for qq W+W" and Z°Z° are shown in fig. 27 as functions of /s. We see from the Table that these are much larger than the double-subprocess cross-section estimated using the Ansatz (3.9), and therefore we have concentrated on the qq -> W+W" background to an H search. The encouraging - 413 - feature of this background is that it falls very rapidly with increasing m(W W"), as seen

in fig.28: this means that the background is smaller for heavier Higgses m^>> 2mw. Another encouraging feature is that the intermediate boson pairs have final state angular CO distributions which are sharply peaked forward and backward, as seen in fig.29. In contrast, Higgses decay isotropically in their centre-of-mass, which yields a Jacobian peak in the Pj of the final state W~ or Z°. The ratios between the qq* W W or Z°Z° cross- sections of fig.27 and the gg -+ H cross-section shown in fig.13 are so large that we do not expect gg -»• H to be observable, except possibly if one optimizes cuts on the final state W and Z° distributions. It is possible to enhence the signal to background ratios

by a factor 3(5)(7)(8) for mH = 4(6)(8)(10) by selecting events where WW pair emerge within 90° ± 30° in their centre-of-mass. We are more optimistic if one looks for the reactions gg or qq + Hit or "qq*-V+H. In both cases the double-subprocess backgrounds from (qq*VV)(gg or q"q*Tt) or (qq+V)(q"q* VV) are smaller than the signal, as seen in Table 3. While the total rates for Hit or V+H production are quite small, they may offer the best modes for H detection in this mass range. If m^ > 400 GeV the dominant Higgs cross-section is MM + H and the dominant background is (qq+VV). The (qq-»-V) (qq-* V) background is concentrated at small Pj << m^, and so cannot be confused with massive H decay which produces vector bosons V with py>>m^. Simply looking at the VV invariant mass distribution will not be enough, because such a heavy Higgs is a wide resonance (fig.4). However, the angular distributions of the vector boson pairs in their centre-of-mass are completely different: isotropic in the s-wave H VV decay but sharply peaked in qq->-VV. Therefore it may be possible to detect such a heavy Higgs by looking for deviations from the peaked angular distributions shown in fig.29. Since in looking for > 200 GeV we have to battle with low rates, it will be important to be able to detect a large fraction of H decays. This means being able to detect a large fraction of W* and Z° decays. In particular, when looking at W+W' and Z°Z° pairs, one should be able to detect at least one vector boson by its hadronic decays. The rates will be too low if one can only use leptonic W-+-lv or Z° -»-l+l" decays and the final states may be insufficiently constrained, if one must contend with the two missing neutrinos from 2W* lv decays. It is clear that there will be large backgrounds to the hadronic decay modes from QCD jet production We have not evaluated them because they are very detector-dependent, and we have prefered to concentrate on backgrounds due to readily quantifiable physics processes. It may be that one can obtain better jet energy resoTution and hence dijet mass resolution for heavier Higgses which decay into W's and hence jets with larger p-p also the QCD background will be smaller at larger Pj. Our preliminary analysis already makes it clear that looking for Higgses at a high-energy hadron-hadron collider will not be easy. However, there may be hope for detecting Higgses

by looking for V+H final states if mu < 400 GeV, (H VV) + tt if 200 GeV < mR < 400 GeV,

and wide angle (H+VV) final states if mH > 400 GeV. - 414 -

3.3 - Supersymmetric Particles

We concentrate on the production of strongly interacting supersymmetric particles, namely squarks cf and gluinos g, since they have the largest cross-sections (3.5) for a given mass, and seem likely to make the largest possible mass range accessible for any given cross-section sensitivity.

3.3.1 - gluino pairs

The dominant perturbative QCD mechanism for ~gg production is likely to be gg — 39 fusion, followed by qq annihilation. The subproces cross-section for gg -+ gg is f 2 2 2 2 2 2 qua2 |2(mg-t)(mq-û) (mq-t)(mñ-u)-2mq(mñ+t) da , —» ^ st a—5—a +r —a 3———2A—a +(t-*-*-u)

¿ y n di (gg-gg) = §2 L (m~ - t) 4S 2 2 , 29 2 (3.19)

, mq(s-4mg) (m-q-t)(nrg-Û)+mq(û-t) 1

Vg-t)(rég-û)"l- ^. + (t~u)Jj — — 39 S( t) while that for qq •* g g is

£ (**> • P-1 ! <£ Í • fr [ (i-t^-û)^]

q q 2 (3.20)

[ (tf^-t) + nt|s ] 3[ (m|-û) + m^s-j i ègï s(nr* - t) s(m^ - û) 3 (n^-tJin^-û) '

The total cross-section for gg production is only weakly sensitive to m~, as long as mq > mg ^see ^9-30) ar,d mg < 1 TeV. In what follows we generally present cross-sections calculated with m~ = m~. We see immediately from fig.24 that the total cross-section for gg" production is larger than 1/10 pb for

< 1 TeV /s = 10 TeV < 1.6 TeV A = 20 TeV (3.21) < 2.4 TeV /s = 40 TeV

This confirms our general observation (3.6) that the accessible range of new particle i masses increases roughly as /s1* . The results (3.21) mean that any collider with /s < lOTeV can probe all the expected (2.13) range of gluino masses: the next step is to figure out the signatures for'gg' production. As we mentioned in section 2, we expect g ->- qqy decays to dominate. Another 63 possibility is 'g -»• gy via quark and squark loops , but this is expected to be a

relatively unimportant decay mode2 :

q LGts+LU :ki R V « 1 (3.22)

r (g*qq7) 4TT (M¿ +M£ ) qL qR'

37 The presence in the final state of two photinos Y , which are expected in many models to have masses much less thant irr^, typically - 41S -

ÜÜ 8g m- - SsirfG^- (3.23) means that one expects a large missing transverse energy-momentum signature: ss pf - 0(0.4rrç) (3.24)

Fig. 31 shows the missing pT for different values of m~. We see that the expectation 9 54

(3.24) is borne out. A typicaljcalorimetric experiment such as UA1 has a resolution in

Pj which is proportional to Ejl:

a E ApT = 0.7 /ij (3.25) 4 Present collider extend up to Ej = 0(200) GeV, and events are selected as having a "interesting" missing Pj signature if Pj1ss > 4a. We apply a similar cut to our sparticle production cross-sections, where Ej is computed from the "visible" q and jet decay products. We see from fig.32 that the total gg cross-section is not greatly reduced by such a cut if nig > 0(100) GeV. We in any case expect the gluino to have been discovered before

iss the start-up of a Large Hadron Collider if nw < 0(100) GeV. The p™ > 4a cut has a negligible effect on the total gg cross-section for large m^ = 0(1) TeV, close to the limit of cross-section sensitivity. We have computed the final state distributions for the final state jets coming from _^ i g+qqy decay. Their rapidity distribution is shown in fig.33: it is central with ;=l.l, in accord with our general expectations (fig.10). Even the smallest of the 4 jets coming from gg production has sizeable p-p fig.34 shows the distribution in p^ of the minimum Pj jet. We find

Since most of the gluino pairs are produced quite centrally, and decay quite isotro- pically, we expect large angular separations Aa between the different q and q jets. Indeed we find

* 1.6 radians for m^ = 1 TeV (3.27)

Since the angular resolution for jets at these energies is expected to be a few degrees, there should be no difficulty in distinguishing the 4 final state jets. Thus ~gg final states should be quite distinctive: 4 widely separated final state

miss jets, each with > 0(100) GeV, and large p . - 416 -

3.3.2 - Squark pairs

The dominant mechanism for qq pair production are again gg fusion and qq annihilation. ~— 39 The total subprocess cross-section for gg -*• qq is

2 2 M~irrv -31 m? ; 2 m2s i ~ — Nn™'«i , \w niff -r , tf(gg>q (4 q) = -fr [(Ü + lff )C + + f ) f in (j^)] (3.28) where Ç 5 /T^4m^/s, and is the number of squark flavours available,

_ — 39 while the differential cross-section that for qq + qq is

a . I 1 r (m3,-t)(u-t)+s(n¿ + t)] (3.29) 3 L q q s(m.g-t)

2 2 + ^ [s(s-4mq )-(Û-t) ] }

— 39 if the q and q have the same flavours, and

§ (qq'- qV) = §(m|-t)-(^-t)«]} (3.30)

if they have different flavours. In most models the different flavours of q have almost the same mass. Therefore, in what follows we have added together all the cross-sections for different flavours of qq production. We see from fig.35 that the total cross-section for qq production is quite sensitive to the gluino mass. If we assume conservatively that m^ » m^, then we see from fig.35 that the total cross-section for qa, production is larger 1/10 pb for

900 GeV /s = 10 TeV m~ < 1.4 TeV /I = 20 TeV (3.31) q ~ 2 TeV /i = 40 TeV

in accord with the rule of thumb (3.6). Again we see from the results (3.31) that any collider with/s> 10 TeV can explore essentially all the expected (2.13) range of squark masses. If m^ < m^, we expect the dominant decay mode of the q to be q + g:

r(o>q+Y) "3a q

In this case we would expect the g to decay subsequently into qqY, and the Pj1SS signat• ure to be somewhat diluted by comparison with that (3.24) for gluinos:

ss = 0(0.3m^) (3.33) - 417 -

Fig.36a shows the missing pT distribution for different combinations of q and g masses. We see that the expectation (3.33) is indeed borne out, and that the pmiss > 4a cut ment• ioned earlier has a negligible effect on the interesting cross-section for large m~ (fig.37a). The final state missing Pj signature would be even more dramatic if m~ > m~, so that q ->-q + y decays dominate (fig.36b, 37b). In this case we would expect

= 0(lm~) (3.34) as seen in fig.36b. In the case of q->- q + g, g-* q + q + y decay we would expect 6 final state jets. The rapidity distribution for these jets in the case m~ = 1 TeV, m~ = 700 GeV is shown in fig.38. We find that

J = 1.2 (3.35) in accord with the expectation of fig.10. The p-^ of each jet is of course somewhat smaller than was the case in direct gg production. Fig.39 shows the Pj distribution for the minimum Pj jet, which has

« 90 GeV (3.36) in the case m~ = 1 TeV, m~ = 700 GeV. This should nevertheless be large enough to be detectable. As expected, the angular separation Aa between the pairs of jets in~q->- q + g, y-* q + q~ + Y decay is somewhat smaller

m~ = 1 TeV Aa = 1.4 radians for q (3.37) m~ = 700 GeV 9 than was the case (3.27) for direct g production and decay. The angular separation (3.37) is nevertheless large enough for all 6 final state jets to be separated, providing a distinctive event signature. In the cas m~ > m~ so that q ->q +Y decay dominates, we

expect the final state missing pT to be larger than in'q-s- q + g (see fig.36b). There will

be 2 jet final states,for m~ = 1 TeV. The average pT and angular separations of these two jets will surely be sufficient for them to be detected and separated easily.

Thus we expect qq production to produce distinctive 6 or 2-jet final states with

large missing pT> In addition, we note that a large fraction of the q produced will have heavy flavours (c, B or t), providing an additional final state event signature: c or b or f + (c or b or t) + fg or Y)• - 418 -

3.3.3 - Sparticles in the proton

In addition to the perturbative QCD sparticle production by gg or qq collisions that we have discussed so far, there are other possible sources of sparticles in hadron-hadron collisions. In particular, it is possible that protons may already appear to contain sparticles when they are observed on a sufficiently high momentum scale. As was already discussed in connection with heavy quarks, this component may either be generated perturbatively (flavour excitation) or may be present nonperturbatively (intrinsic). 65 Calculations have been made of the perturbative generation of a sparticle content in 2 the proton. They indicate that at infinite Q the momentum of the proton is shaved out in the following way between quarks, gluons, squarks and gluinos:

Table 4: Asymptotic perturbative sparticle momentum fractions in the proton

Pure QCD QCD + g QCD + q QCD + g + q

3N 3Ng 3Nq 3N, q + q 3- (0.53) (0.47) (0.39) 3- (0.36) 16+3N 20+3N 16+5N 20+5N V 16 0 35 42 (0.32) 2ÔW- (°- ) T6T5T;( - ) 20+5N

w^(o.ii) 2Ö75N- (°-08) q

2Nq 2N0 q + q (0.26) (0.24) 16+5N 20+5N

the total number of quark flavours is denoted by N^, the figures in parentheses are the

2 fractions obtained if Nq = 6. The perturbative QCD sparticles start from 0 at Q < m~, m~, and are always smaller at finite Q2 than the values in Table 4. Since " " 66 ~ cross-sections with initial state sparticles (e.g. g + g -g + g) are of the same order of magnitude as sparticle production cross-sections in collisions of normal partons (e.g. g+g ->-g+g~), we do not expect the production of heavy final state sparticles from initial perturbative sparticles in the proton to exceed the cross-sections we have presented in previous subsections. Indeed, since the initial sparticle distributions are small (i.e.

2 0(as)) at Q = 0(m~, m|), we expect the dominant contributions to heavy sparticle production to come from normal parton collisions: gg or qq- gg or~qq~. However, (g or q) + (g or q) •+ (g or q) + (g or q) subprocesses have interesting event signatures: one

sparticle at large PT and the other in one of the beam fragmentation regions. This type of reaction may, however, be interesting if m~ or m~ is just above the limit from present- day accelerators say m~ or m~ < 100 GeV. It is possible that there may be a large nonperturbative intrinsic sparticle 52 component in the proton, just as has been postulated for charm and heavier quarks. This picture may be either confirmed or refuted by searches for diffractive t quark - 419 -

production at the CERN pp Collider. In the absence of any better experimental guide, we 52 assume the form of diffractive cross-section postulated by theorists:

o(?, /s") = J- f (m,//s) (3.38)

We assume a universal scaling function f for heavy quarks, squarks and gluinos. Then we

can scale up from mc = 1.5 GeV,/~s(ISR) = 60 GeV,o (mc, 60 GeV) « 100 pb to deduce

a (m~ or m~ = I TeV, Ss = 20 TeV)= 0(l)nb (3.39)

n Even if this is a grotesque overestimate - perhaps cross-sections scale as m'7 =^ instead of n = 2 in equation (3.38)? - it suggests that there may be observable diffractive cross-sections for the production of sparticle pairs weighing up to 0(1) TeV. The signature for such events would be two sparticles moving forward in one hemisphere, while the other hemisphere is quiet. It has been proposed ^8 that one may estimate the t quark mass from diffractively produced T s (tq) meson decays into bq+u++ v final states by computing the minimum transverse mass (or cluster transverse mass)

m m + 2 ÍSS2+ + 1SS ] 3 4 * =[ vis PT Kis PT ^ ^ ( - °) which is theoretically expected to be sharply peaked at E, = m*/m^~ 1. In the case of

anc heavy quarks, one might expect the meson to have a smaller mean Xp = E/F-beam' ' thereby avoid any misidentification of meson and baryon decay products. The same might also be true for q hadrons: perhaps Xp(qqq) > Xp(qq)? but it might be that both gluino hadrons would have similar values of Xp. In this case, if one seeks to estimate m~ by looking for a peak in ç = m*/m~, where m* is computed from a pair of observed jets deemed to come from g~ qq'y decay, one must contend with a combinatorial background due to the misidenti• fication of which jets come from the decay of which gluino hadron. However, as seen in 69 fig.40, this may not be an overwhelming background , and one should still be able to see a nice peak in m* and thereby estimate m~ in diffractive events. Looking for evidence of diffractive squark production would be even easier if q* q + Y decays dominate. In this case there would be a Jacobian peak in the observed jet p^ in diffractive events with large missing Py.

3.3.4 - Observability

It is difficult to think of large physics backgrounds to the missing pT signature 3 4 of susy. Present-day collider data ' are already encouraging, in that it has been possible to extract a sample of events with significant missing p^ which have a cross- section no larger that that for pp -* W + x, W + lv, and are not overwhelmed by backgrounds due to physics or instrumental effects. As mentioned earlier, we do not discuss instrumental backgrounds (jet and calorimeter fluctuations, holes in the apparatus, etc.) 40 as they depend strongly on the detector characteristics assumed . The dominant physics background is likely to be from heavy flavour pair production and semileptonic decay: - 420 - c or b or t + v +1 +q, where the final state charged lepton is not detected and the + neutrino carries away a large amount of pT. While e can only be detected if they have +

relatively large pT (> 0(50) GeV?), it should be possible to detect u with pT above a few GeV. Thus a large part of the heavy flavour background (v + u + q) can be measured, and the rest ( vg + e + q, + T + q) will have a similar magnitude. Most of the back•

ground events will have 2 jets, and the missing pT vector will be aligned essentially parallel to one of the jet axes in the azimuthal angle plane. There will be some fraction of multiple jets due to gluon bremsstrahlung and other higher order QCD effects, but the

missing pT vector will always be essentially parallel to one of the jets. We have not studied the heavy flavour background itself, but have looked at the distribution in Pj1ss transverse to the observed jets in g decay. We see in fig.41 that the distribution in missing pT transverse to the nearest jet axis is relatively wide, certainly much wider QT b or t than the 0( ^— ) which one would expect from heavy flavour production. We therefore expect that the heavy flavour background can be dealt with, as it seems to be 4 at the present Collider . This expectation is supported by the analysis of an 40 experimental working group at this Workshop. We conclude that detecting supersymmetric particles weighing less than the expected upper limit of order 1 TeV should be relatively easy at any hadron-hadron collider with /s < 10 TeV. - 421 -

3.3.5 - Alternative supersymmetry phénoménologies

So far we have explored the conventional phenomenological supersymmetry scenario, in which the lightest sparticle is the photino y, and R-parity is conserved so that every sparticle must have a y among its decay products, e.g. q-q + Y.g^d + q + Y- In this subsection we explore two alternative phenomenological scenarios : either (I) the gluino is (almost) the lightest sparticle, R-parity is conserved as usual, and the gluino is (almost) stable70, or (II) R-parity is broken38'71'72'73. (I) In the context of a collider experiment, a new particle appears stable if it strikes the calorimeter before decaying. This requires ycx > 0(1) metre, or

x> 10"9 (Kf10) sec if Y= 3(30) (3.41)

For this to occur, the momentum release in g decay should probably be less than a GeV. This could well be the case if m~ is a few GeV, but seems unlikely if m~ > 0(10) GeV, and is excluded if the y and g masses are in the canonical ratio (3.23) which is smaller than about 1/7. It could well be that the canonical ratio (3.23) is incorrect, but even if it is, we find it unreasonable that m~ - m~ < 1 GeV if m~ > 0(10) GeV, though g y g this could be a possibility if m^ < 0(10) GeV. When m~ > 0(10) GeV, we believe that the only reasonable alternative to the conventional assumption is to postulate that the canonical ratio (3.23) is so wrong that the gluino is actually the lightest sparticle. We therefore retain as logical possibilities m~ < 0(10) GeV and either absolutely or almost stable, or m~ > 0(10) GeV and absolutely stable. If the gluino is absolutely stable, the lightest gluino hadron should be neutral, 29 otherwise there will be a conflict with upper limits on stable charged hadrons coming + 79 from e e annihilation (m± < 0(20) GeV) or from searches for exotic isotopes containing relic gluino hadrons left over from the Big Bang (m + < 0(1) TeV). Searches for exotic isotopes and mass, spectrometer experiments also exclude stable neutral gluino hadrons if they weigh more than about 3 GeV. Therefore stable gluinos should weigh less than about 3 GeV. The existence of such objects seems not to conflict with any present-day particle 70 75 65 physics experiment ' . The best place to look today for such stable gluinos may be in 65 the decay of P-wave states of bottomonium P^. These are expected to have a branching ratio of order 30% into pairs of such light gluinos. A systematic search of P^ decays could surely reveal whether such a large fraction of final states contained a pair of stable or almost stable gluino hadrons. We do not think that a very high energy hadron collider, or even the present CERN pp Collider, is the ideal place to look for light stable or almost stable gluinos (m~ < 0(10) GeV). It may nevertheless be interesting to point out a possible signature, namely

the production of a pair of large pT jets which each contain an energetic neutral particle that is undetectable in the central tracking detector, but deposits its energy in the hadronic (not electromagnetic) calorimeter, causing a mismatch between the energy-momentum measurements in the central detector and in the calorimeters. Of course, such events occur all the time, thanks to neutron and K° production. However, when one of these particles is produced in one jet, there is no reason to expect another one in the - 422 -

opposite large Pj jet, though this should occur inevitably in gg production events. More•

over, if m~ > 0(mc) ~ 1.5 GeV, one could expect the neutral gluino hadron to carry on average a half of each large Pj jet energy, whereas neutrons and K°'s are generally softer. A search for such anomalous calorimetry events at lower centre-of-mass energies might be valuable. (II) Two possible mechanisms for R-parity violation have been considered in the literature - explicit breaking through soft supersymmetry breaking or superpotential terms7*, and 72 spontaneous breaking through sneutrino vacuum expectation values . For reasons of elegance and simplicity we restrict ourselves to spontaneous R-parity breaking, which may come about

72 through vg = <0 [ vjco j= 0, v^s <01 v [ 0> j= 0 or vT E <0| Vt|0> j= 0. Model studies

indicate that vT ^ 0 whenever any other sneutrino develops a vacuum expectation value, and

that in general vT > > vg . Whenever a certain sneutrino acquires a vacuum expectation value, the corresponding lepton number L is also spontaneously violated, but the modified parity R = R(-l) 1 is conserved. The very stringent upper limits on violations of

electron-number Lg and of muon-number impose small upper limits on vg and v . The upper limits on violation of tau-number L are much less stringent, and v could be quite large. v = v = In what follows we assume that only v^ ? 0, while e u 0. In this case, although R-parity is violated, R = Ri-lj'r is conserved. The consequences of R-parity breaking for the production and decays of sparticles are quite dramatic ' . they need no longer be produced in pairs, they need not decay into other sparticles, and the lightest sparticle need not be stable. In general, sparticles can mix with particles having the same colour and electric charges. In the case considered here, R violation is always associated with violations, so sparticles may be produced in association with T or v , sparticles may decay intox or v , and colourless charged ~±T ~± ± sparticles such as the W and H can mix with the T , while colourless neutral sparticles

V can mix with the ^T . Examples of posssible novel phenomena are in principle Z° ~" Y + T , q~ ->-q + (T or v ) and Y •* T~e+v or v e+e" decays. In what follows we discuss briefly some 73 qualitative features of such phenomena, the details being discussed elsewhere . The T mix with the Wand rf through a ma trix of the form72'73

1 ~ \ + + (W , H , TO\ M2 g2v w"

E H" g2v 0 T (3.42)

T " 0 mT \\ 0

1 where M2 is the SU(2) gaugino mass, e is a term mixing the two Higgs multiplets H and H , v

and v' are their vacuum expectation values, Tq is the unmixed T and mro is its mass before

mixing with îï and H, and hT is the tau Yukawa coupling to the Higgs H. The physical tau mass eigenstate has mass

Mv2 - v?) (3.43) 2 2 /v + v - 423 - and the mixed components 2h vv , VT", - v ÎL"

+ We see from (3.44) that the physical has only a small mixing with the ííL , because

hT is small even though vT may not be much smaller than v, while the physical T~ may have large mixing with the H, " but not with the W. ". Since the H couplings to quarks and leptons 73 are small, this unfortunately means that taus are unlikely to be copiously produced in the decays of squarks and gluinos. An analogous study of the more complicated mixing matrix

V ? fer the T°, W , 2°, H° and H'° reveals that the physical^ might have substantial mixing with the W° and B° :

0 g2w° + g^ v = v° + 0(e T T m,,' / 2 ¿

w / g1 +-g2 + H°, H'° components, higher orders in — , etc. (3.45) mW

Therefore the v could in principle be copiously produced in q and g decays, but would give the same missing energy-momentum signature as that expected in conventional supersymmetric phenomenology. We find that mixing includes an off-diagonal neutral current coupling of the Z° to a H° and a v , which is proportional to T and hence small if v « v,v'. // + v,¿ Therefore in the model discussed here much of conventional supersymmetry phenomenology remains unchanged, except that the y can now decay. The lifetime of the y depends sensi•

tively on its mass, but the mixing between the y and the vT lifetime could well be long enough for its decay vertex to be separated from the interaction point. Disappointingly, we have not discovered a strong likelihood for copious x production in models with broken R-parity, though y decays may provide a signature for such models. This possibility should be borne in mind when planning searches for supersymmetric particles, though we still feel that the conventional sypersymmetric phenomenology discussed in previous sections is a more plausible scenario.

3.4 - Technicolour

As representative examples of technicolour particles, we have considered the production of coloured pseudoscalars Pg, octets Vg and the techniquark continuum.

3.4.1 - Technipions Pg

These are expected to have masses 0(250) GeV. The largest cross-section is ' for neutral P?, production via gg fusion : - 424 -

r a (P°) -4— (Pg - 99) TL (T) (3.46) m po " 99

Gc ML ,C< V 2 , NTr „ 2 where r (P| * gg) = § ^ ^8 (f >• (3.47)

We take the number of techni col ours = 4 as a representative example. The partial decay width (3.47)is much larger than that for decays into qq pairs, with the exception of tt : G MP°

r P + < 8 = 71 m?t (3.48)

Comparing the total decay widths (3.37, 3.48), we see that the dominant decay mode of Pg may be into tt. The Pg cannot be produced by gg fusion, but only by ud or du fusion, which has a far smaller coupling than (3.48). Therefore we only compute the cross-section for Pg production in hadron-hadron collisions, which is displayed in Fig. 42. The signature for Pg production would be Pg •+ tt decay.

3.4.2 - Technivectors Vg

Also shown in Fig. 42 are the cross-sections^ for Vg production :

a (V°) = [ r (V| * gg) TLgg(x) + ^ T (V| * üu) TLUG(T) mv° (3.49)

+ ^| r (V| * dd) xLda(T) ]

where 2TO2

r V F : F s2F : ( 8^") = "S v v ? FT«125GeV (3.50a) V8 2

2 F(V° + uü or dd) . * ^5- F (3.50b)

We take mvo = 900 GeV. The gg fusion mechanism dominates over uü and dd annihilation by an ordeP of magnitude. This means that Vg production, which proceeds via ud or ûd anni• hilation alone, is somewhat smaller than Vg production, as seen also in fig. 42. We would expect the Vg decay into g + Pg, by analogy with conventional QCD vector -> pseudoscalar + y decays, and also into g + (y or Z°), while the Vg could decay into W1 + g.

3.4.3 - Technicolour Continuum

In addition to the production of particular technifermion-antifermion QyQy bound states, one can also estimate the total cross-section for continuum QyQy production by analogy with conventional heavy quark production. We assume the existence of 2 techniquarks Uy and Dy, each coming in Ny^ = 4 technicolours, so that the production cross-section is 8 times larger than would naively be estimated by scaling up gg or qq •*• tt. - 425 -

The principal uncertainty of this estimate is the correct techniquark mass niq^to be used. One expects it to be generated dynamically by the strong technicolour interactions, and to be somewhere in the range 300 GeV to 1 TeV. In fig. 42 we have plotted total cross-sections for QJQJ continuum production for three possible values : 300 GeV, 500 GeV and 1 TeV. We guess that would lie in between the two lower values used : the highest value is a gesture to conservatism. In all cases the continuum production cross-section is likely to

be large enough to be detectable at Ecm >_ 10 TeV, though the cross-section becomes rapidly

more favourable for lower values of nig^ and larger values of Ecm. Presumably the final

state resulting from QTQT continuum production would contain many technipions, including ±o the Pg, other denizens of Table 2, and longitudinal components of the W and Z . We have not attempted to estimate these, as they must be very model-dependent and our competence does not in any case extend to calculating strong technicolour dynamics.

3.4.4 - Observability

The main physics background to a search for Pg ->• tt comes from QCD production of tt pairs via gg fusion or qq annihilation. At the centre-of-mass energies and (tt) invariant masses of interest to us, the dominant source of (tt) pairs is gg fusion. Since this is also the dominant source of PS production, the signal-to-background ratio is essentially 77

independent of E and y in the range of interest to us. Assuming mDO = 250 GeV and m+ = Gin r Q X 35 GeV we have calculated

o (gg + PS + it , * « : integrated over all e (3.51) a (gg - tt)

if one assumes 5% resolution in m(tt) and integrates over all the (tt) angular distrib• ution. However, the rate for Pg production is so large that one can afford to reduce it by making cuts in 8*. the (It) centre-of-mass angle relative to the beam axes. The Pg •+ tt decays are of course isotropic in this variable, while gg ->• tt is sharply peaked in the forward and backward directions, as seen in fig. 43. This means that one can improve the signal-to-background ratio by making cuts in 6* :

o (gg - PS * tt) f 0.9 for |e*-ï| < î 2 < (3.52)

1.5 v a (gg + tt) I for |e* T2T ' i - TT '

where the overall reduction in signal rate is by a factor of 0.7 or 0.4 respectively. We conclude that it should be possible to detect the Pg¡ if one can identify clearly (tt) jet pairs and get good invariant mass resolution around m(tt) « 250 GeV. One is helped at a Large Hadron Collider by the large rate relative to those at the present CERN pp Collider and the forthcoming Tevatron Collider projects. We have not looked in detail at the physics backgrounds to a search for Vg or Vg~, which we fear may be substantial. - 426 -

4. - Summary of important signatures

In this final section we catalogue some of the important signatures which experiments at large hadron colliders should be able to detect. We leave to our experimental colleagues the task of devising detectors which see them with high efficiency and low background. This will not be trivial in many cases, particulary those involving heavy particles which decay into hadronic jets. Any non-ideal detector would suffer from backgrounds additional to the "physics" backgrounds discussed in section 3.

(tt) : useful for hunting Higgs bosons and technipions.

Multiple W* Z° : Also useful for Higgs and technicolour searches. In view of the low rates for many Higgs production mechanisms, one should not rely solely on leptonic decay modes of the W ± and Z°, but should also have some efficiency for picking them out via their decays into hadronic jets. Experience from UA1 and UA2 indicates that this is not easy in events without an additional final state signature. It may be easier to pick out a second or third W1 or Z° + hadronic jet decay if the first W" or Z° is already identified through a leptonic decay mode. Paying the price of a second or third leptonic decay branching ratio might leave an unobservable small rate.

Missing Pj : This is very important for supersymmetry searches, and a hermetic detector on the UA1 model seems to be essential. As already mentioned in section 3.3, searching for

missing pT is likely to be easier at higher energy colliders, since calorimeters have

energy resolutions AE <* /E, whereas the missing pT signal being sought probably increases roughly linearly with E. jet-jet-mass bumps : Good dijet mass resolution is clearly important for the tt, W* and Z° searches previously mentioned, as well as for such signals as excited quark •* q + g decay.

Y-jet mass bumps : Are also potentially useful in the search for excited quarks. leptons, e, v.. T, ... : It goes without saying that a high capability to detect these is a sine qua non for many of the other particle searches.

Based on the analyses of section 3, and on the likely cleanliness of the above sig• natures, we reach the following tentative conclusions about the difficulty of observing different species of new particles at a large hadron-hadron collider.

Supersymmetry : relatively easy

Technicolour : possible

Conventional Higgs boson : relatively difficult.

In general we are quite optimistic that a large hadron collider wuld make an important contribution to the exploration of physics in the mass range up to 0(1) TeV where there is good reason to expect a rich harvest of new particles.

ACKNOWLEDGEMENTS

We would like to thank C. Jarlskog and Z. Kunszt for sharing with us their resutlts described in the paper. - 427 -

References 1 - UA1 Collaboration, G. Arnison et al. - Phys. Lett. 122B, 103 (1983); UA2 Collaboration, M. Banner et al. - Phys. Lett. 122B, 476 (1983).

2 - UA1 Collaboration, G. Arnison et al. - Phys. Lett. 126B, 398 (1983); UA2 Collaboration, P. Bagnaia et al. - Phys. Lett. 129B, 130 (1983).

3 - UA2 Collaboration, P. Bagnaia et al. _ pnvs. Lett. 139B, 105 (1984)

4 - UA1 Collaboration, G. Arnison et al. - Phys. Lett. 139B, 115 (1984)

5 - UA2 Collaboration, J.D. Hansen - Talk presented at the 4th Workshop on pp" Collider Physics, Bern (1984).

6 - UA1 Collaboration, C. Rubbia - Talk presented at the 4th Workshop on pp" Collider

Physics, Bern (1984).

7 - R. Barbieri - Talk presented at this meeting.

8 - R. Peccei - Talk presented at this meeting.

9 - C.H. Llewellyn Smith - Talk presented at this meeting.

10 - A. Ali - Talk presented at this meeting.

11 - B. Andersson - Talk presented at this meeting.

12 - G. Altarelli - Talk presented at this meeting.

13 - E.Eichten, I.Hinchliffe, K.D.Lane and C.Quigg - Fermilab-PUB-8417-T (1984).

14 - J.S. Bell - Nucl. Phys. B60, 427 (1973); C.H. Llewellyn Smith - Phys. Lett. 46B, 233 (1973); J. Cornwall, D.N. Levin and G. Tiktopoulos -.Phys. Rev. Lett. 30, 1268 (1973) and Phys. Rev. DIO, 1145 (1974).

15 - 0. Ellis, M.K. Gaillard and D.V. Nanopoulos - Nucl. Phys. B106, 292 (1976).

16 - S.O. Freedman, J. Napolitano, J. Camp and M. Kroupa - Phys. Rev. Lett. 52, 240 (1984).

17 - S. Coleman and E. Weinberg - Phys. Rev. D7, 788 (1973); S. Weinberg - Phys. Rev. Lett. 36, 294 (1976); A.D. Linde - Pis'ma Zh. Eksp. Teor. Fiz. 23, 73 (1976); E. Witten - Nucl. Phys. B177, 477 (1981).

18 - M. Veltman - Acta Phys. Pol. B8, 475 (1979);

CE. Vayonakis - Lett. Nuov. Cim. 17, 383 (1976) and Athens Univ. preprint (1978).

19 - B.W. Lee, C. Quigg and H. Thacker - Phys. Rev. D16, 1519 (1977).

20 - S. Weinberg - Phys. Rev. D13, 974 (1976) and D19, 1277 (1979); L. Susskind - Phys. Rev. 020, 2619 (1979). For a review, see E. Farhi and L. Susskind - Phys. Rep. 74C, 277 (1981).

21 - Exotic particles Study Group, G. Barbiellini et al. - DESY preprint 79/27 (1979). - 428 -

22 - B. Humpert - Phys. Lett. 131B, 461 (1983); B. Humpert and R. Odorico - Talk at the 4th Workshop on pp Collider Physics, Bern(1984) and talk at this meeting.

23 - G. 't Hooft - "Recent Developments in Gauge Theories", ed. G. 't Hooft et al. (Plenum Press, N.Y., 1980).

24 - S. Hawking, D.N. Page and C.N. Pope - Phys. Lett. 86B, 175 (1979) and Nucl. Phys. B170 (FS1), 283 (1980).

25 - E. Gildener and S. Weinberg - Phys. Rev. D13, 3333 (1976); E. Gildener - Phys. Rev. D14, 1667 (1976).

26 - A.J. Buras, J. Ellis, M.K. Gaillard and D.V. Nanopoulos - Nucl. Phys. B135, 66 (1978).

27 - S. Dimopoulos and L. Susskind - Nucl. Phys. B155, 237 (1979);

E. Eichten and K.D. Lane - Phys. Lett 90B, 125 (1980).

28 - S. Dimopoulos and J. Ellis - Nucl. Phys. B182, 505 (1981).

29 - S. Yamada - Proc. Int. Symposium on Lepton and Photon Interactions, Cornell 1983, ed. D.G. Cassel and D.L. Kreinick (Lab. of Nuclear Studies, Cornell, 1983), p. 529.

30 - For recent attempts, see M.A.B. Bég - Phys. Lett. 124B, 403 (1983); S. Dimopoulos, H. Georgi and S. Raby - Phys. Lett. 127B, 101 (1983).

31 - Y. Gel'fand and E.P. Likhtman - Pis'ma Zh. Eksp. Teor. Fiz. 13, 323 (1971); D. Volkov and V.P. Akulov - Phys. Lett. 46B, 109 (1973). J. Wess and B. Zumino - Nucl. Phys. B70, 39 (1974).

32 - J. Wess and B. Zumino - Phys. Lett. 49B, 52 (1974); J. Iliopoulos and B. Zumino - Nucl. Phys. B76, 310 (1974); S. Ferrara, J. Iliopoulos and B. Zumino - Nucl. Phys. B77, 413 (1974).

33 - For a review, see P. Fayet and S. Ferrara - Phys. Rep. 32C, 249 (1977).

34 - CHARM Collaboration, F. Bergsma et al. - Phys. Lett 121B, 429 (1983); E 613, R. Ball et al. - Univ. Michigan preprint UMHE 83/13/UWEX-83-234 (1983).

35 - J. Ellis and H. Kowalski - CERN preprint TH-3843 (1984) and DESY preprint 84-045 (1984).

36 - H. Goldberg - Phys. Rev. Lett. 50, 1419 (1983); J. Ellis, J.S: Hagelin, D.V. Nanopoulos, K.A. Olive and M. Srednicki Nucl. Phys. B238, 453 (1984)

37 - For a review, see J. Ellis - CERN preprint TH-3802 (1984).

38 - L.J. Hall and M. Suzuki - Nucl. Phys. B231, 419 (1984); G.G. Ross and J. Valle - Oxford preprint in preparation (1984).

39 - G. Kane and J.P. Léveillé - Phys. Lett. 112B, 227 (1982); P. Harrison and CH. Llewellyn Smith - Nucl. Phys. B213, 223 (1982) and E B223, 542 (1983).

40 - For a discussion see P. Bagnaia and A. Weidberg - Contribution to this meeting. - 429 -

41 - S. Dimopoulos - Nucl. Phys. B168, 69 (1980).

42 - S.D. Drell and T.-M. Yan - Phys. Rev. Lett. 25, 316 (1970).

43 - G. Altarelli and G. Parisi - Nucl. Phys. B126, 298 (1977).

44 - S. Berman, J.D. Bjorken and J. Kogut - Phys. Rev. D4, 3388 (1971).

45 - W. Furmanski and H. Kowalski - Nucl. Phys. B224, 523 (1983).

46 - CDHS Collaboration, H. Abramowicz et al. - Zeit. f. Phys. C13, 199 (1982) and F. Eisele - private communication (1984).

47 - E. Eichten et al. - ref. 13; R. Baier, J. Engels and B. Petersson - Zeit. f. Phys. Ç2, 265 (1979); M. Glück, E. Hoffman and E. Reya - Zeit. f. Phys. C13, 119 (1982).

48 - J. Ellis - SLAC preprint PUB-3127 (1983).

49 - I. Hinchliffe - Talk presented at the 4th Workshop on pp Collider Physics, Bern (1984),

quoting results of ref. 13.

50 - J. Kuti and V.F. Weisskopf - Phys. Rev. D4, 3418 (1971).

51 - H. Georgi, S.L. Glashow, M. Machacek and D.V. Nanopoulos - Phys. Rev. Lett. 40, 692, (1978).

52 -S.J. Brodsky, C. Petersson and N. Sakai - Phys. Rev. D23, 2745 (1981); V. Barger, F. Halzen and W.Y. Keung - Phys. Rev. D24, 1428 (1981); R. Horgan and M. Jacob - Phys. Lett. 107B, 395 (1981).

53 - C. Gossling - private communication (1984).

54 - EMC Collaboration, J.J. Aubert et al. - Nucl. Phys. B213, 31 (1983).

55 - B.A. Campbell - Carleton Univ., Ottawa preprint (1981).

56 - V. Barger, F. Halzen and W.Y. Keung - Phys. Rev. D28, 1838 (1982).

57 - J. Ng and P. Zakarauskas - Phys. Rev. D29, 1838 (1982).

58 - Z. Kunszt - Bern University, preprint BUTP-84/10 (1984).

59 - R.N. Cahn and S. Dawson - Phys. Lett. 136B, 196 (1984), E 138B, 464 (1984).

60 - C. Jarlskog - private communication (1984).

61 - S.L. Glashow, D.V. Nanopoulos and A. Yildiz - Phys. Rev. D18, 1724 (1978).

62 - R.W. Brown and K.O. Mikaelian - Phys. Rev. D19, 922 (1979);

R.W. Brown, D. Sahdev and K.O. Mikaelian - Phys. Rev. D20, 1164 (1979).

63 - H.E. Haber and G.L. Kane - Nucl. Phys. B232, 333 (1984).

64 - UA1 Collaboration, G. Arnison et al. - Phys. Lett. 122B, 103 (1983).

65 - B.A. Campbell, J. Ellis and S. Rudaz - Nucl. Phys. B198, 1 (1982); C. Kounnas and D.A. Ross - Nucl. Phs. B214, 317 (1983); S.K. Jones and CH. Llewellyn Smith - Nucl. Phys. B217, 145 (1983).

66 - I. Antoniadis, L. Baulieu and F. Delduc - Zeit. f. Phys. C23, 119 (1984 ) - 430 -

67 - D. DiBitonto - private communication (1984).

68 - V. Barger, A.D. Martin and R.J.N. Phillips - Phys. Lett 125B, 339 (1983);

E. Berger, D. DiBitonto, M. Jacob and W.J. Stirling - CERN preprint TH-3821 (1984).

69 - W.J. Stirling - private communication (1984).

70 - R. Barbieri and L. Maiani - Pisa Univ. preprint IFUP TH 7/84 (1984).

71 - I.-H. Lee - Phys. Lett. 138B, 121 (1984).

72 - G.G. Ross and J. Valle - private communication (1984).

73 - J. Ellis, G. Gelmini, C. Jarlskog, G.G. Ross and J. Valle - in preparation (1984).

74 - P.F. Smith and J.R.J. Bennett - Nucl. Phys. B149, 525 (1979);

P.F. Smith et al. - Nucl. Phys. B206, 333 (1982).

75 - S. Dawson, E. Eichten and C. Quigg - FNAL preprint Pub-83/82 -THY/LBL-16540 (1984).

76 - S. Dimopoulos, S. Raby and G.L. Kane - Nucf.- Phys. B182, 77 (1981).

77 - G. Girardi, P. Méry and P. Sorba - Nucl. Phys. B195, 410 (1982). - 431 -

Figure Captions 1 - Tree level scattering cross-sections (a) should fall as 1/E2 at high energies, if 14 loop diagrams (b) are not to be unrenormalizably divergent 2 - The tree-level diagrams for f? - gauge boson pairs in a non-abelian gauge theory.

3 - The necessary correction diagrams due to the exchange of something like a Higgs boson. 19 + - —

4 - The decay width of a heavy Higgs into W W , Z°Z° and tt, assuming mt = 30 GeV. Also shown are lines corresponding to = (10-2, 10"1) m^.

5 - (a) Loop corrections to the Higgs mass, due to fermions, vector bosons, and scalar 24 bosons, (b) Scalar boson propagating through space-time foam 6 - The generic model for producting a new massive state though a generalization of the 42 Drell-Yan mechanism. 7 - Effective parton-parton luminosity functions plotted in terms of /r. They do not vary much between /s = 10 and 40 TeV. Note the similarity of the luminosities in pp and pp"

collisions for A < 0,1 corresponding to mx< yrj Ss- 8 - Some of the parton-parton luminosity functions of fig.7 multiplied by a geometrical cross-section factor 1/m2 (3.5). The horizontal dashed (dotted) lines correspond to 1 cr=0 (YQ-) pb above which cross-sections should be observable with a hadron-hadron luminosity of 1032(1033)cm~2sec"1. 4Q +

9 - Rapidity distribution for pp- W + x at Ecm = 40 TeV. 10 - The angle of archaeology: today's physics emerges at wide angles, yesterday's physics emerges closer to the beam pipe, last week's physics even closer, etc. 22 11 - Double-subprocess due to two simultaneous hard collisions analogous to that in fig.6 occuring in the same event. 51 12 - Quark loop diagram for gg - H.

13 - Cross-sections for gg •* H at /s = 10 TeV, 20 TeV and 40 TeV, evaluated with mt = 35, 70 and 100 GeV. 14 - The rapidity distribution of the Higgs decay products for different values of m^. cy ro

15 - Examples of Higgs bremsstrahlung diagrams ' for gg -»• ttH and qq - ttH.

16 - Cross-sections for TtH production for /s = 10, 20, 40 TeV and mt = 35 GeV.

17 - Final state distributions for TtH production with m^ = 200 GeV at /s = 20 TeV:

(a) rapidity distribution of the Higgs,

(b) rapidity distribution of the t(t) quark,

(c) Pj distribution of the Higgs,

(d) pT distribution of the t (T) quark,

(e) invariant mass for the (Tt) system. 59 _ 18 - Diagram for WW - H production in qq, qq or qq scattering. - 432 -

19 - Cross-sections for WW -»• H production.

20 - Distribution in the subprocess centre-of-mass rapidity y for Higgses in WW collisions fin

. Note the flat distribution which builds up the logarithm in equation (3.16).

21 - Diagram for qq -* W* W+H production

22 - Cross- sections for cfq -> W* -»• W+H production.

23 - A compilation of Higgs production cross-sections in pp collisions at /s = 20 TeV.

24 - Total cross-section for Tt production, to be considered as a background to searches

for Higgses or technipions P8. CO 25 - The cross-sections for (tttt) production and (ttH) production CO 26 - Final state distributions for (tttt) production: (a) the rapidity distribution for a (Tt) pair, (b) the invariant mass of a (Tt) pair (note the peaking at m^. < Zm^, just where we would want to look for the Higgs), (c) p^ distributions for t quarks and for (Tt) pairs. Note the similarities between these distributions and those given for (TtH) production in fig.17. 27 - Total cross sections for W W" and Z°Z° production in pp and pp collisions, as functions of /s.

28 - Invariant mass distributions for W+W" and Z°Z° pairs produced by qq annihilation.

29 -Angular distributions (a) for W+W", and (b) for Z°Z° production at different values of /T. 39

30 - Cross-sections for coproduction , indicating the sensitivity to m~.

31 - The missing pT signature from gg~ production followed by g->- q + q" + y decay.

32 - Cross-sections for gTf production followed by g~ ->-q. + q~ + y decay giving final states with pmiss y 4g as defined in equation (3.25). 33 - Rapidity distribution for q and ~q jets from gg~ production followed by - q + q" + y decay.

34 - The distribution of the py of the minimum pT jet from~g~g production followed by q+q+y decay. ~~ 39 ~ 35 - Cross-sections for qq production , indicating the sensitivity to m^.

36 - The missing PT signature from qq production followed by (a) q •* q + g decay (b) q -»• q + y decay. 37 - Cross-sections for qq production followed by q ->• q + g decay, giving final states with p!J!1ss > 4o as defined in equation (3.25).

38 - The rapidity distribution for q and q jets from qq production followed by

(a) q * q + g, g + q + q + Y. (b) q - q + Y-

39 - The distribution of the PT of the minimum Pj jet from qq production followed by q * q + g, g -»-q + q +y decay. - 433 -

40 - Distribution in the scaled minimum transverse mass E E m*/m~ for diffractive gg production. The sharp peak comes from correctly paired jets, while the broad distribution comes from wrong combinations.

41 - Distribution in Pylss transverse to the nearest final state jet axis (a) for gg, g -»• q + q + y decay.

42 - Cross-sections for coloured technipion P8, coloured technivector V8 and techniquark

continuum QTQT production.

43 - Sharply peaked centre-of-mass angular distribution for gg •* tt, to be compared

with the isotropic distribution from P8 •* tt decay.

- 435 -

hadron

hadron

Fig. 6 L 'H¿ - 437 -

—i—i—i—i—i—i—i—i—i—i—i—i—•—i—i—i—i—i—i—i—i—i—i—r

di' * uüVpp a) /T=40TeV /T =20 TeV /T = 10 TeV

l/?=40TeV /s = 20 TeV V7 * t0 TeV

I ' ^2

i i i I I I I Jia I I

123456789 10 Mx/TeV Fig. 8 - 438 -

Angle of archaeology

Fig. 10

Fig. 11 439

100 f o-{pb)'

10

id*

10*

\) Js =40 TeV :} ./s =20 TeV

10" .}

?}mt = 100GeV

:Jmt =70GeV

=}mt =35 GeV

10 _l L. -I I 1_ _1 i L. 100 200 300 400 500 600 700 800 900 mH(GeV)

Fig. 13

Rapidity Distributions

/s = 20 TeV — m = 100 GeV m =200 GeV \ — m = 500 GeV

-2 6 y

Fig. 14 440

H

Fig. 15

i 1 r pb Total cross-section for the process pp—» tTrWX

=100 GeV 10

/ / / mH=300 GeV / / / / / 0.1 / / / r/ / / /

10 20 30 40 yT TeV

Fig. 16 - 441 -

"1 1

Rapidity distribution of a^ $Z tpb/unit of rapidity] the Higgs in n 1 1 1 r [ b)" pp —^ttH _ Rapidity distribution of /s = 20 TeV the t-quark in pp-»-tfH N

mH =100GeV \mH =100 GeV

Iff1 \

mH =300 GeV \ ^\ \

i i i w \ 12 3 4 5

1 r i 1 1 1 r c) dcr pb/100GeV)

dpT PT distribution of the Higgs in pp —-ÛH

=100GeV 10 N \ \ \ \ \

V vniH=300GeV \

10

—i 1 1 1 1 1 1 1

40 80 120 160 200 240 280pT[GeV] Fig. 17 - 442 -

Cpb/»GeV]

dpT i 1 1 1

PT distribution of the t-quark u)

in pp—*-ttH

\ vT = 20 TeV \ 10' \ \ \ \ \ \ \ \ \ 10 U N NmH = 100GeV

mH = 300 GeV J L J L ¿0 80 120 160 200 2¿0 280 PT [GeV]

gg[pb/20GeV] i 1 1 1 1 1 1 e) pp—*-ttH *X ^\ ,/s=20TeV

N Iff1

m H = 100 GeV 1Ö2

mH = 300 GeV

J L J I L 80 160 240 320 400 ¿80 560 6¿0 m(tt) TGeVl Fig. 17 - 443 -

H

Fig. 18

200 400 600 800 1000 1200 1400

mH{GeV)

Fig. 19

dg r i i i i i i i i dy s = 400(TeV)2

3 MH=2MW 310' f> = 1 x 10'2 nb

210

10'

i i i i i i i i i >

2 3A subprocess rapidity y •

Fig. 20 - 444 -

Fig. 23 o-(pb)

Fig. 25 - 446 -

Fig. 26 I 1 1 1 n I r-

m(W*W") (GeV)

Fig. 28 - 448 -

t .92 .70 38 0 -.38 - .70 - 92-1 cos9 1 .92 .70 . 38 0 -.38 -.70 -.92-Icos6

n 5 3Tl 7n: Tl 6 5Tl/ 7rt/ Tt 6 0 T^B Tty 3*78 /2 TV8 /4 /8 0 K/s rt4 3n'& ^ 8 ^ 8 Fig. 29

Fig. 30 - 449 -

rapidity

Fig. 33 - 450 - pp~gg m§ =TeV

c 3

rÇin(GeV)

Fig. 34

Fig. 35 Fig. 36 Fig. 39 Fig. 40

- 457 -

WHY IS THIS ENERGY RANGE SO INTERESTING?

R. Barbieri

Dipartimento di Fisica - Università di Pisa

INPN, Sezione di Pisa, Italia

1. INTRODUCTION

Almost a hundred years from the discovery of radioactivity,the first

laboratory detection of a weak interaction effect, direct experiments in

the region of the Fermi scale

4 2 Cp" ' = 246 tyur (i)

start being finally available. The purpose of this meeting is to discuss

the interest and the feasibility of a machine whose energy might exceed (1)

by two orders of magnitude.

In spite of the beautiful experimental and theoretical successes of

the standard model, there are good reasons to think that the exploration of

this energy range will give rise to surprises, which in turn might shed

light on:

i) the origin of the Fermi scale itself (or the^>r^rfalemof the origin of

mass altogether);

ii) the flavour problem (or the calculability of fermion masses and mixings);

iii) the origin of P and of CP violation.

The standard model relates the first problem to spontaneous symmetry

breaking via the Higgs phenomenon. As it is well known, consideration of

perturbative unitarity requires the mass of the physical Higgs particle^

not to exceed the value of a few Tev's. This is the first guarantee that

something must happen in the region of energies to be explored. I believe

however that the findind of the Higgs cannot be the only discovery to be

made, at least because no good reason is known for its lightness relative

to any hew higher necessarily existing physical threshold A. Are we missing

a new principle here which could explain why/*/y\^<1? I find it unlikely

because a light Higgs relative to a high scale A would anyhow require the

"low energy" physics to depend upon a fine detail of the high energy physics

at A . Barring this possibility, a satisfactory explanation of the physi•

cal origin of the Fermi scale calls for new physics.

With this problem, and the others listed above, in mind, several inte - 458 -

resting theoretical possibilities have been proposed and are at present un

der investigation. They include:

1. The incorporation of the standard model into a perturbative supersymme- 1 ) trie theory ; 2) 2. Technicolour models ; 3. Composite models of quarks and leptons as well as of the Intermediate 3) Vector Bosons ; 4) 4. Left-right symmetric theories

With the greatest respect of everybody's prejudices, I believe that

one cannot attribute at present on physical grounds a determinant preferen•

ce to one of these possibilities over the others. To me its seems more in

teresting to realise that any one of them gives rise to distinctive signatu

res which can be discussed and, more importantly, can be looked for in pre•

sent and future experiments.

In the following I will briefly review the theoretical limits on the

relevant physical scales in the various cases (Sect. 2). I will then make

some remarks on possible high precision measurements (Sect. 3). Finally

I will discuss the light fragments of the new particle spectra implied by

the various theoretical options, as well as some suggestions to detect them

(Sect. 4). It should be clear from the extension of the subject that the

following is only a collection of selected remarks rather than an exhausti•

ve review.

2. THE RELEVANT SCALES (bounds on)

1 ) 2.a: Supersymmetry

Unlike the case of the standard model, a supersymmetric extension of

it can stabilize the Fermi scale against corrections of order gA. After su•

persymmetry breaking however these corrections get replased by contributions

proportional to the mass splittings AM within each supermultiplet. One

would like these corrections not to exceed the order of magnitude of the

Fermi scale itself: for a coupling g^ of the i-th supermultiplet to the

Higgs scalar, one gets - 459 -

In a perturbative supersymmetric extension of the standard model any known particle should find its superpartner with a mass consistent with the bound (2).With a typical gauge or Yukawa coupling for g^,

AM. £i M. (superpartner) J$ 1 - 10 Tev (3) i i •

With an eye to actual supersymmetric models, I do not think however that this bound should be saturated by all superpartners: some of them are expec ted to be substancially lighter, infact lighter than the W-boson itself

(See below).

2) 2b. Technicolour

In this case we do not only know of a bound, but rather of a precise relation between the W-mass and the technipion decay constant

from which

or io

Tc XV.5 "4 (6) A ^ X40*AC - ° ¿5f«T T TeiT.

This relation holds in the conventional technicolour scenario. Also in view of the insolved difficulties that this approach faces (read: fer• mion massed and Flavour Changing Neutral Currents), one should perhaps con sider a broader class of theories where in general the longitudinal compo• nent of the IVB's is given by a composite scalar. An inverse radius A for such a particle somewhat higher than (6) would in principle make life easier.

Except that one would again be faced with a naturalness problem if A » L~f^_ *,

3) 2c. Composite models

Consideration of the problems listed in the introduction has laid to the speculation that quarks and leptons themselves, as well as the IVB's, might be composite particles. In principle the hyphothesis of composite quarks and leptons has to be kept distinct from the more radical idea of composite IVB's.

In absence of définit models or theoretical schemes, one has to resort - 460 -

to phenomenological considerations in order to get bounds on the hypotheti•

cal compositeness scale /\H . These bounds come from the non-observation of

form factor behaviours (mainly from the muon anomalous magnetic moment) or of residual contact 4-fermion interactions (mostly from Bhabha scattering 3) experiments) for the known fermions . For the electron and the muon, ba•

sed on effective Lagrangian considerations incorporating approximate chiral

symmetry, one obtains in a rather model indepent way A^C^J^) 800 Gev (7)

This value is certainly low enough to be of interest for a supercollider fa cility. In general the observable effects of a compositeness scale A^. largely discussed in the literature, die off as A . Sensitivities of the n order of A^2t10 Tev might be reached. On the other hand, unless one wants to make a connection between A . and C¡— fwe do not know of any at the mo- ment) there is no upper bound on /»^ , not even theoretical.

Altogether, untill we lack a full understanding of the physical origin of the Fermi scale, the possibility of composite IVB's, both the longitudi• nal and the transverse components, cannot be completely dismissed.

Perhaps there is such a concept as an approximate gauge invariance of the effective interactions between composite vectors light relative to their

inverse radiusAg. Althought it is difficult to make a quantitative state• ment, I believe that the agreement of the standard gauge picture with expe• riments requires

(H^/A6) * 4% M A^^ATw (8)

On the other hand, again not to make the lightness of the IVB's relative to

A^ a too serious problem,A g , if it exists at all, should appear not far above 1 Tev.

4) 2d. Left right symmetric theories

These models may have a lot to do with the breaking of parity and of

CP. With an heavy right handed neutrino, the direct lower limit on the mass of a right handed W-boson is relatively modest

M (tf/p.) > loo (¿ZAT o)

However, in the interesting class of models where the left and right quark mixing matrices are directly related to each other, consideration of the - 461 - box diagram contribution to the K^-^ system with one W and one W exchan R L — ge leads to a rather strong lower bound (barrying unexpected cancellations)

M(W) £ 1.6 Tev (10) R Notice, on the other hand, that the same box diagram can give a contri bution to the imaginary part of the K -K mass difference, the CP- violating L S é parameter, even in a two family model, unlike the case of the standard theory. In turn, supposing that this same contribution be a main source of

CP-violation in the kaon system gives this time a lower bound M(W ) & 22 Tev (11) R

HIGH PRECISION EXPERIMENTS

It may seem bizarre to speak of high precision experiments in this meeting. It is not so if one wants to know the limits of the standard mo• del tests, relevant to the construction of a new machine, or if some of the high precision experiments can actually be done at a supercollider facility.

3a. The electroweak ^ parameter

An important parameter in unified electroweak theories is the ratio of the neutral-to-charged current Fermi constants ^ . Deviations from the pre dieted value, defined as 2

8? - ~ ' <12) would be extremely important. The Glashow - Weinberg - Salam theory pre- 5)

diets 0 , including radiative corrections, to an accuracy

£o (WKCVC' kaol. ü&c. £>o6, ) = ± (2. -3) AO <13)

due to uncertainties in the hadronic vacuum polarization. The same standard model includes a contribution from top-bottom vacuum polarization diagrams (m = O for simplicity), b 2

\o^r,urJ (14)

as well as an Higgs contribution which grows only logarithmically with

the Higgs mass £ >> KA-t. )

1 ' 4** 1 *\ MÍ loo - 462 -

To appreciate the importance of possible deviations from the predicted value, one would like to know the contribution to £y from the various ex• tensions of the standard model that we are considering. They have been com puted ^ in technicolour models with a result

-3 (technicolour) = + 2 • 10 (16) dependent upon the actual model considered. 7) From supersymmetric contributions - within low energy supergravity - one has

_3 (supersymm.) = + (1 -r 3) 10 , (17) namely again a small effect with the only possible exception of a top-quark mass heavier than the supersymmetry breaking scale. In this case, other than the contribution (17), the scalar top-scalar bottom exchange would gi• ve an addition effect doubling the conventional top-bottom contribution in (14). For composite models, in absence of any definite scheme, one can guess

Sq (comp.) = + O f —T1 ) (18) at least in those models where an approximate "custodial" global symmetry is present. No significant deviation is expected in the case of left-right symme• tric gauge theories. Which are the prospects in the comparison between theory and experi- 8) ment? At present = 1.002 + 0.015 (19) exp ... • - which agrees well with theory. To become sensitive to the mentioned contri^ butions, at least two independent precision measurements are needed. + - 2 a At an e e collider such as LEP or SLC they could be the Z-mass and sen by measuring the Z—resonance position and the polarization of *K produced from the Z. The Z-width measurement offers another possibility. On the other hand the 1% precision perhaps atteinable at the present fa^>

collider via the direct determination of Mw and M^, although very signi• ficant, does not look sufficient to test the standard model at the level of its genuine weak radiative corrections. - 463 -

3b. CP violation

It is well known that a foreseen precise determination (a few %0level) of the fe'/é parameter from kaon decays will give a very significant test of the standard model. The measured B lifetime has the consequence that, if CP violation is to be explained by the KM mechanism the value of fc'/6 should be quite close to the present upper limit

¡e'/éf < 2% / (20) for YK £ 100 Gev. This is in opposition to the case of SU(2) xSU(2) •v LR theories with spontaneous P and CP violation where a value of €yffe smaller -3 then 10 can be attained. I have said already that these theories, for

M(W ) 20 Tev, may provide an alternative source of CP violation already in the é parameter, as could be required if the top is too light.

In principle, also the different new interactions and new particles in supersymmetric extensions of the standard model allow for the introduction of new sources of CP-violation other than the KM mechanism: a typical exam• ple would be a gluino mass with a sizeable imaginary part (with a proper de finition of the gluino field). Altogether however these new sources tend to give too large contributions to be unnaturally fine tuned. On the con• trary the same KM mechanism in a supersymmetric model may change the predic tion of the standard model for /\Yr\ (^L.^^.^), both the real and the imagina ry part, due to supersymmetric t-t or gluino exchanges in box-like dia• grams .

A brief comment, to conclude on B„-B0 mixing. It is expected to be

large in the standard model (unlike the case of D0-D0). In view of the large number of B mesons produced, this represents a possible observation of CP violation that could be made in a collider facility. Suitable detec tors may be needed to study specific final states in B meson decays with identified CP properties.

3c. Rare flavour changing effects

The last observation naturally brings us into the subject of rare fla• vour changing effects. Again a supercollider would be such an intense sour ce of t ,K, B, T-mesons that one could reveal unconventional decay modes even with very small branching ratios. In this connection, the discovery of new flavour changing neutral current and/or lepton number violating decays would be extremely important. It would amount to the discovery of - 464 -

a new basic interaction, which in turn might shed light on the flavour pro•

blem mentioned in the introduction. The possible connection between fer- 9) mion masses and new interactions suggests a parametrization of these hypo

thetical interactions as proceeding via exchange of a massive boson with a

mass A>M^ and a coupling -v ^^/^^where is the relevant fermion mass.

This could give rise to the following relative rates (taking A~ M14/ )

10 K+sW- "ty/HITÉ ±6 (21)

These figures have to be compared with the production rates of the decaying

particles, which, in a high luminosity { fix t » AO (sYH, J high energy col- 10 12 lider, can be as large as 10 - 10 number of particles.

4- LIGHT FRAGMENTS OF THE SPECTRA

As I said in the introduction, the various theoretical options suggest

(or even imply in some cases) a full spectrum of new particles all sitting

around the Fermi scale. The lightest fragmenta of this new spectra are

those more easily amenable to an experimental discovery. Some of them

should in fact be discovered even before the future super colliders will

become available. The following is a collection of remarks related to the•

se "light" particles, some of which have been widely discussed in the theo•

retical literature.

2) 4a. Technipions and Technimësohs

A general aspect of technicolour models is the spontaneous breakdown

of a large technicolour flavour group giving rise to a large number of

pseudo-goldstone bosons (technipions:P°, P—, ... ) Switching on the standard

strong and electroweak interactions does not give mass to the colourless

electrically neutral technipions (P°), whereas it gives a mass to the char•

ged ones (P—) rather safely estimated as - 465 -

(22)

The point is that the technicolour force dynamically breaking the electroweak group cannot be the full story. Also the fermion masses break

SU(2) x U(1) as well as independent global symmetries. Which is the source of these masses? Isn't it likely to give anyhow an additional contribution to the technipion masses, maybe substancially larger than (22). Even in rather definite schemes (read extended technicolour) the estimates of the additional contribution range from 2 up to 40 Gev. The present e+e sear• ches give negative results up to

m(P-) > 16 Gev (23)

Interesting reactions to search for them are

+ + W- -f P-P o (24) t-*P+b.

Although more massive, (m *i 100 * 300 Gev) also the color triplet lepto- guarks and the color octet technipions are interesting.

4b. Composite IVB's

As I said already in Section 2, if all the IVB's are composite, not only their longitudinal components, then they must themselves represent the light fragments of a new spectrum (/^g » fí,^ Of course in this case there could be residual interactions among the IBV's and, for example, the photon and the gluon weighted by powers of the confinement radius.

This will certainly be the case if the constituents of the IVB's have co• lour, as well as charge as they must. However, the smallness of the ra• dius would make these interactions undetectable. Except that the same me• chanism that should keep their masses small relative to the inverse radius might also enhance these residual interactions. They could be weighted by inverse powers of M or M themselves rather than A . This is the some w z £ extent suggested by the largeness of the mixing between the composite W 2 and the elementary photon, needed to explain the observed value of sen &

In such a case, particularly interesting reactions are^0'^' ^ + ^-*¿+2T (25) - 466 - for collider and e e physics respectively. Notice that the reaction

g + g Z + g (26) is not suggested in a picture where the photon is elementary and the compo

site W—, Wq are members of an isotriplet under a suitable global SU(2) sym metry .(26)could rather follow in a scheme where the all IVB's are elementa• ry but their longinal component is given by a composite Higgs whose consti tuents carry colour .

4c. Left-right symmetric models

In terms of new particles, these are the most economical schemes. Here one should essentially catch the W , which, as I said, may be not ve- R ry light. The right signals however exist, as e.g., via

with an overall branching ratio maybe as large as 3%. With a center of mass energy ranging from fs" = 10 Tev to 40 Tev one could be sensitive to right-handed W's with masses less then 3 up to 7 Tev.

4d. Light gauginos

If supersymmetry is relevant at all to particle physics, altogether I believe that the lightness of the gauginos (gluino, photino, w-ino and z-ino) is likely to be the most significant feature of the superpartner spectrum. One could almost elevate this statement to a theorem in à renor malizable globally supersymmetric theory. Unfortunately these theories do not work at least in a simple way. Therefore one should rather take it as a guess. In a class of models the masses of the various gauginos can be calcu- 12) lated in terms of the supersymmetry breaking scale (the gravitino mass)

This possibility has arisen during a conversation with L. Maiani and G. Parisi. - 467 -

Qev

" (U 1 10 Tev

^ »V /v Fig. 1 - Photino (¿r), gluino (

and of the top quark mass (which strongly influences only the gluino mass).

All of them are lighter then the W with masses ranging from 1 to 50 Gev.

A typical spectrum is shown in Fig. 1 versus the gravitino mass

100 Gev < m ^ 10 Tev and for m = 40 Gev. The gluino mass scales quadrati •v ~ t ~ cally with m^. One can also envisage the possibility of a gluino lighter

than the photino, in which case the characteristic missing PT signature simply

does not exist since it is the photino which decays into a gluino and not

viceversa. This spectrum can also be made consistent with cosmological in•

formation.

5. CONCLUSIONS

The possibility of making esperiments directly in the region of the

Fermi scale will characterize particle physics in this and the next decade.

A central problem in our field is precisely the physical origin of the Fer•

mi scale. Altogether, this is the best guarantee for discoveries to be ma•

de. Perhaps the search for a relatively light fundamental Higgs scalar

field may not be the basic tool to shed light on this issue. This even

if one does not dispute the Higgs phenomenon as the correct description of

the breaking of the electroweak group.

As we saw, the theoretical alternatives in extending the standard mo•

del to incorporate new physical phenomena in the region of the Fermi scale

are not lacking. Will some of them turn out to be true? - 468 -

REFERENCES 1) For a recent review and list of references see, e.g., H. Nilles, Univ. of Geneva preprint UGVA-DPT 1983/12-412; see also R. Barbieri, to appear in the Proceedings of the Munich Summer School, Sept 1983. 2) For a review and references see E. Farhi and L. Susskind, Phys. Rep. 74 C , 277 (1981) . 3) For a recent review and references see R. Barbieri, Proceedings of the 1983 Symposium on Photon and Lepton Interactions at High Energies (Ed. by D. Cassel and D. Kreinick, Cornell Univ., Ithaca 1983) p. 479. 4) J. Pati and A. Salam, Phys. Rev. D10, 275 (1974); R. Mohapatra and J. Pati, Phys. Rev. D11 , 566 (1975); R. Mohapatra and G. Senjano vich, Phys Rev. Lett 40, 912 (1980); Phys. Rev. D23, 165 (1981). 5) For a recent discussion see W. Marciano and A. Sirlin, Brookhaven preprint BNL - 33819 (1983). 6) R. Renken and M. Peskin, Cornell preprint CLNS82/540 (1982). 7) R. Barbieri and L. Maiani, Nucl. Phys. B224 , 32 (1983); L. Alvarez-Gaume, J. Polkinski and M. Wise, Nucl. Phys. B221, 495 (1983). 8) See M. Davier, Proceedings of the 21st Int. Conference on High Energy Physics, Paris 1982, p. C3-471. 9) G. Kane, Michigan preprint UM TH 83-25 10) F. Renard, Phys. Lett. 116B , 269 (1982); 132B, 450 (1983). 11) M. Leurer, H. Harari and R. Barbieri, Weizmann preprint 1984, to appear on Phys Lett. B. 12) R. Barbieri and L. Maiani, Pisa preprint, IFUP TH7/84 (1984). - 469 -

HARD HADRONIC COLLISIONS — EXTRAPOLATION OF STANDARD EFFECTS

A. Ali1»2, P. Aurenche3, R. Baier1*, E. Berger5'2, A. Douiri3, M. Fontannaz6, B. Humpert7'2, G. Ingelman2, R. Kinnunen8»2, E. Pietarinen8, R. Rückl2, D. Schiff6'2, D. Soper9'2, W.J. Stirling2 and B. Van Eijk10'2 (Presented by A. Ali)

ABSTRACT We study hard hadronic collisions for the proton-proton (pp) and the proton-antiproton (pp) option in the CERN LEP tunnel. Based on our current knowledge of hard collisions at the present CERN pp Collider, and with the help of quantum chromodynamics (QCD), we extrapolate to the next generation of hadron colliders with a centre-of-mass energy Eon = 10-20 TeV. We estimate various signatures, trigger rates, event topologies, and associated distributions for a variety of old and new physical processes, involving prompt photons, leptons, jets, W* and Z bosons in the final state. We also calculate the maximum fermion and boson masses accessible at the LEP Hadron Collider. The standard QCD and electroweak processes studied here, being the main body of standard hard collisions, quantify the challenge of extracting new physics with hadron colliders. We hope that our estimates will pro• vide a useful profile of the final states, and that our experimental physics colleagues will find this of use in the design of their detec• tors.

INTRODUCTION

The present CERN pp Collider has established that hard hadronic collisions involving quarks and gluons can be very cleanly separated from the seemingly formidable background of soft interactions and studied quantitatively. The discovery of the W* [l] and Z° [2] bosons, the observation of energetic jets and measurements of the inclusive prompt lepton [43 and dilepton [53 events among a host of final states have conclusively demon• strated the potential of hadron colliders as powerful machines to study basic partonic interactions. The fluffy In s physics, which dominated the era of the CERN Intersecting Storage Rings (ISR) {ß~\, has not posed a serious problem in the extraction and interpreta• tion of hard collisions at the CERN pp Collider. It is, therefore, not unreasonable to assume that the separation of the signal (QCD hard processes) from the background (minimum bias events) would be much less of a problem at the next generation of hadron colliders. The experience gained at the CERN Collider makes the extrapolation of Standard Physics to higher energies a relatively safe exercise.

1 DESY, Hamburg, Fed. Rep. Germany. 2 CERN, Geneva, Switzerland. 3 LAPP, Annecy-le-Vieux, France. 4 Univ. Bielefeld, Fed. Rep. Germany. 5 Argonne National Laboratory, Argonne, 111., USA. 6 LPTHE Univ. Paris-Sud, Orsay, France. 7 Univ. Lausanne, Switzerland. 8 Univ. Helsinki, Finland. 9 Univ. Oregon, Eugene, Oreg., USA. 10 NIKHEF, Amsterdam, Netherlands. - 470 -

The aim of this report is to undertake this extrapolation and provide reliable rates and distributions involving hard QCD processes at the LEP Hadron Collider having a centre- of-mass energy /s = 10-20 TeV. At the same time it should provide a comparative study of the pp versus pp option as well as a study of the question involving machine luminosity versus centre-of-mass energy. Since the primary goal of the machines such as the LEP Hadron Collider is to unravel the mechanism of spontaneous symmetry breaking, which presumably involves an energy scale of order 1 TeV at the partonic level, we compare the merits of pp and pp Colliders centred around 1 TeV in the parton centre of mass. Theoretical estimates presented here should also provide such mundane (but, for any experimental program, impor• tant) information as trigger rates, event topologies, and energy spectra of prompt photons, leptons, W*, Z°, and jets.

We work in the context of quantum chromodynamics (QCD). This input enters at two levels. First, in the evolution of probability densities, Fp^(x,Q2), of finding a parton i with a fractional energy x E 2E-¡//s and virtuality, Q2, within a proton (equivalently anti- proton) having an energy /s/2. Next, one has to calculate the interactions among quarks and gluons using perturbation theory giving rise to leptons, photons, jets, W* and Z° bosons in the final state. We make use of the QCD higher-order corrections to the Born diagrams involving electroweak processes whenever this information is available. In some reactions the higher-order corrections play an important role in qualitatively changing the topology of events in comparison with the lowest-order expectations. For example, including higher-order QCD contributions leads to large-p^ production of W*, Z°, y*, and y, which in turn lead to large-pp photons, monojets, lepton pairs, etc. Since some of these topologies are expected signatures in supersymmetric and composite scenario f_7], reliable estimates of standard background due to higher-order QCD processes are absolutely essential. A rela• ted aspect of the higher-order corrections is that they increase the acceptance of Drell-Yan type processes, which otherwise, not having the benefit of a large-pp component in the pro• duction, would throw final states in forward directions.

The other most important feature is the increasing role of the gluon-initiated pro• cesses with /s in hadron-hadron collisions. There is good evidence that the hadronic jets seen by the UA1/UA2 detectors are dominantly due to the quark-gluon and gluon-gluon scatter• ings [8j|. Extrapolating to /s = 10 TeV, the gluon structure function dominates up to x i. 0.3, thereby leading to the dominance of gluon-initiated processes for J% ^ 1.0 TeV. Thus, many of the low-energy distributions based on quark-antiquark annihilation at Js = 540 GeV would change at high energy. For example, the angular distribution do/d9(p-£+) meas• ured [9] in the process pp -»• WXfW* £~v¿) would undergo a substantial change with /s owing to the gluon initiated process g + q -+ W* + q'. This is a definite prediction of QCD [JLO] and constitues an interesting test of perturbative QCD.

The topics discussed in this report are as follows.

i) Parton densities (structure functions) for 0.54 TeV < /s~< 40 TeV in pp and pp colli• sions.

ii) Drell-Yan-type processes of the form [ll]

pp(p) - W±, Z, y* -* MX,

including the production of yet heavier W'± and Z'° bosons. - 471 -

iii) Prompt-y production in inclusive reactions [12]

pp(p) -»• y + X .

iv) Production £13] and energy-angle profiles of jets in the processes

PP(P) jet + X ,

including effects of multiple gluon emission [14].

v) Heavy quark production at large pp in the processes [15]

ppCp) - Q + Q + X CQ = c, b, t)

and in the diffractive processes [16] (AQ = heavy baryon, M = heavy meson)

pp(p) -*• AQ + M + X .

In this section we also calculate the yield of prompt leptons due to the heavy quark pair production and semileptonic decays L"l5J

PP(p) + Q + Q + X -»• îrX , 2(£±)X.

We discuss the consequences of weak mixings in hadron collisions [17] and estimate rates in the same-sign dilepton signal.

vi) Heavy quarkonia production [18]

n + X PP(P) {J/ty, T, JT, nc, nb, t^ • vii) Finally, the production and decays of yet heavier quarks [19].

There are two main uncertainties in the estimates of rates. The first is due to the lack of higher-order CCD corrections in inclusive jet and heavy-quark production cross-sections to the desired level of theoretical accuracy. A closely related point is the choice of scale

2 in the argument of ag(Q ) and in the evolution of the parton densities. The second uncertainty is due to the lack of precise determination of parton densities at low energies. We have fixed the parameters of our calculations from the UA1/UA2 data at ^i" = 540 GeV for the processes p + p -* jet + X, y±y±X, W±X, Z°X and yX using the Glück-Hoffmann-Reya (GHR) parametrizations [20], which we use generally. The dispersion in the structure functions and parton luminosities corresponding to other choices of structure functions are studied extensively in section 1. In particular we compare the GHR parametrization with the one due to Duke and Owens (DO) [21] extrapolated up to /s = 20 TeV. We find that they differ from each other only for extremely high and low values of /s and therefore it is reasonable to conclude that the spread in extrapolation to /s = 10-20 TeV due to parton luminosities is small (y 10-201 in the region of interest). Thus, the over-all rate presented here should hold to within a factor of 2. The extrapolations of electroweak processes should pre• sumably be more reliable since we do take into account higher-order QCD processes and have the benefit of the UA1/UA2 data to normalize.

1. STRUCTURE FUNCTION AND PARTON LUMINOSITIES

The cross-section for a hard collision process in hadron-hadron interactions can be schematically written as - 472 -

where G is the product of coupling constants (a, a^, as for electromagnetic, weak, and strong interactions, respectively); R^j (xi, X2) is the product of probabilities of find• ing partons i and j in the hadrons 1 and 2 with fractional energies x'i, x2 (= 2El^2//s~):

^ij-+x 'X z ' '"^ rePreseirts the cross-section for the hard-scattering subprocesses, some examples of which are given in Table 1; the symbol ® represents convolutions of the probability functions R-^(xi, x2) with the parton cross-sections (x., x., ...); ) • • means summation over all parton species (i.e. quarks, antiquarks, and gluons) and integra• tions over all the remaining variables involved in the phase space of the subprocess i + j X.

Note that the function R^j(xi, x2) acts as a sort of parton luminosity sampling func• tion reflecting the fact that at high energies liadrons are broad-band beams of quarks, anti- quarks, and gluons. Having Rij(Xj, x2) at a given s (centre-of-mass energy squared), the cross-section in Eq. (1.1) can be trivially calculated, given X.

In order to make the functional interpretation of Eq. (1.1) clear, we review the simplest of the hard-scattering processes in hadron-hadron collisions, namely the massive lepton-pair production in pp annihilation. From Table 1 we have

where q^(x) is the distribution probability for quarks of species i (= u, d, s) and charge e^. The dilepton mass squared is M1 = SX.XJ = S 1 with X„XT = Jïi^ + k-Z +X) , X = |X,-3C*| . (1.4) It is straightforward to write down the differential (lepton pair) invariant mass distribu• tion,

+ + 2 2 where a0 is the well-known point-like cross-section for e e" -*• u y~, a0 = 4TTOC /3M . The interpretation of the function rCdL^/di) as a differential parton luminosity is immediately apparent. Thus, the function tCdL^/dr) defined as Table la

Differential distributions (d2a/dMdy) [op(p) ->• y*, Z •+ £+î,~] and (do/dy) [pp(p) -»• (W,Z) + x]

2 2 Here = sin 9w * 0.22. Xi,2 = /T e*y and T = M /s . Sabprocess

utwO -»(T u(x,) mx2) + u(x2)ll(x,}

éiV^wO-Xw^CM*-^)** Pi m1» 3 J

dd-**!?-» iV d(xi)d(x,) + d(*a)d(*.)

CM

+ Gp^^ cosie ud^> W u(x,)d(%2) + LL(x2)d(x.) c

3 u s -» W U(x.) s (Xx) + u(x2) s (X.)

3

a It -> 2° mx,) u(x2) + ufro a(x.) 3J2

dd-»Z° d(x,)d(x2) -H d(x2)d(x,) 3JZ [i - 474 -

Table lb

Total cross-section for heavy quark pair production in the notation of Eq. (1.1).

Here x » (1 - ^/s)^; § = xix2s.

sabprocess C*" x0 Ô-.J

-(?+3 3S ,f)4|

i + jx +(l+4f9+f?)LaLi - 475 -

Table le

Differential cross-section for jet production in the lowest-order QCD:

3 2 E(do/d p) = £ /dxjdx, (xlfx2) 6(s + t + Û) 4(Q )ai:J i,i

/\ A S Lib process RcjC*«^*) S (T¿j

, c\(xl)

fc 1. q^HH +clix13Ç'(*1)

¿- VPVÍ ^ Q+ U~7 "2? IT

q(3c.)q;(*.) A » A

r _ 32 UNÍ1 8 5. qq-^qg » » "ST - » î*

1 U +1 3 A + T 8 Sx

qcx,)g(x ) 2 A. U, + ^ , U + S T" iî

A A /s ^ ,» 8. ge^qq gwqft) |(3-^-f - ^ - 478 -

occurs at /s = 1.5 TeV. The corresponding number for 20 TeV pp is /s* - 3.0 TeV. Of course the real cross-section for ^process is obtained by including the coupling constants and the colour factors. Here again (except for W* and Z0 production) the gg and gq scatterings have favourable multiplicative factors. Hence unless one is discussing production of very heavy W', Z' and heavy quarks with M//s » 0.1, the potential of the pp and pp machines are very similar.

Concentrating for the time being on the gg 'cross-section' we compare in Fig. 2c the performance of a pp machine with /s = 10 and 20 TeV. Since the gluon structure function falls very steeply for large x, the gg 'cross-section' falls rather steeply for large values

of /s. We find that 5(/s = 20 TeV)/5gg(/s = 10 TeV)!^^ TgV = 7 with the ratio increas• ing to ^ 35 for /§ = 2 TeV. Thus, the interesting event rates around /% - 1 TeV in a 20 TeV pp machine are comparable to those in a 10 TeV pp machine but with an order of magnitude bigger luminosity. Again, for heavier objects with M//s » 0.1, the higher energy pp machine will have substantially larger event rates. In Figs. 3a-c we show the cross-section ö (pp or pp), ô -(pp), and ä-(pp) for the DO parametrizations for /s = 0.54, 2, 10, 20, gg uu uu and 40 TeV.

fi (TtV) Fig. 3 The partonic cross-section do/dr at /s = 0.54, 2.0, 10.0, 20.0, and 40.0 TeV using the Duke-Owens structure functions: a) p + p(p) g + g; b) p + p ->- uü + üu; c) p + p u5 + üu. - 479 -

Probably a better measure of the event rates is the 'differential cross-section'

2 d a^j/dydT|y_0, i.e. rates for central production. It is important to recall that most of the QCD processes show marked forward (and backward) peaks. This is particularly marked for low /s (or pj) events, which, because of the Lorentz boost, go forward and would be lost in most detectors which have limited acceptance in the forward direction. In Figs. 4a-c

2 we show the differential cross-sections (d Ogg/dydT) (pp/pp) |y_0, (d^^/dvd-r) (pp) \^_0, and

2 (d auQ/dydT)(pp)|y_0. The dominance of the gg subprocess is still evident also for the 'differential (in rapidity) cross-sections' for objects with M//s Í 0.1. However, in the region of interest, namely /s - 1-2 TeV, the enhancement in the rates for central production going from /s = 10 to 20 TeV is now less pronounced than the one in the 'integrated cross- sections' . In particular we find

«r2 «r1 w0 w1 fi CTeVI

Fig. 4 The double differential partonic cross-section do7dTdy|y=0 at /s = 0.54, 2.0, 10.0, and 20.0 TeV using the Duke-Owens structure function: a) p + p"(p) •* g + g; b) p + p -»• uü + üu; c) p + p •+ uü + üu. - 480 -

This feature emphasizes the importance of machine luminosity in sampling the bench-mark region around /§ = 1 T>eV. For M/Vs » 0.1, however, there is no marked difference in the acceptance between all y and y=0 regions, since the decay products of such a heavy object are expected to go in the central region.

2. DRELL-YAN TYPE PROCESSES

In this section we shall discuss Drell-Yan type processes of the form ± pp(pp) y*. W > Z° -> II' + X (2.1) we shall also discuss the production of heavier W'* and Z'° with the couplings similar to the standard model, as well as the production of two gauge bosons from the set (W,Z,y,Y*) in pp (and pp) collisions. The simplest of the processes (2.1) is the one via an intermediate virtual-photon y*> i.e. the standard Drell-Yan process. The differential distribution in the invariant di• lepton mass for the DY process —+ , . * —>v / y + (2.2) p p(p)U +1- x can be written as 1 il da M « sjçfi y e a (M) (2.3)

where now we have introduced a factor K due to higher-order QCD effects. The phenomenological

2 K-factor needed at low energy is typically 2-2.5. With higher centre-of-mass energy, as(Q ) decreases and probably so does the K-factor. We have taken K = 2 for the numerical estimates.

The invariant mass distribution can be obtained using the partonic cross-sections öu-, 5^ calculated in Section 1. In Figs. 5a,b we show the distribution (2.3) for /s = 10 and 20 TeV pp collisions. It is clear from Fig. 5 that 1 pb limit is obtained at M^-t-^- = 60 GeV essen• tially for both /s = 10 and 20 TeV. However, dileptons with such a small value of m/Vs (typically ^ few times x 10"3) would go mostly forward, and only a very small fraction of them will be observed in a typical detector.

Perhaps it should be remarked that the formula (2.3) which lumps the effect of higher- order QCD corrections in a multiplicative K-factor is not a very useful one for estimating the acceptance of DY-type processes. The reason is that higher-order QCD diagrams such as, for example,

0 +. - (2.4)

would produce th9e leptonn pairs at large p^, (balanced by the quark jet). To have realistic estimates of the acceptance for DY lepton pairs in a typical detector, the large pj, topologies - 481 -

Mu (CSeVJ

Fig. 5 Invariant mass distribution for the massive Drell-Yan production p + p •*• (Y*>Z) -*• £+£ including the leading-order (in ag) corrections at a) /s = 10 TeV; b) /s = 20 TeV.

should be included. However, since the absolute rate for (2.2) is rather small, we refrain from doing this. We shall discuss this point later when we calculate the observable rates involving W* and Z° production.

2.1 W* and Z° production

In proton-antiproton (and proton-proton) collisions, events with large missing trans• verse energy or with a large transverse momentum lepton are expected to signal the occurrence of 'new physics'. Thus the SU(2) ® U(l) charged weak bosons W* were discovered at the CERN Super Proton Synchrotron (SPS) Collider in events where an electron or positron with Pp > 15 GeV was associated with a large missing transverse energy f_l]. Recently, events with a large transverse missing energy in association with a hadronic jet or with a neutral electromagnetic cluster have been reported [_22]. Whether these events are to be entirely explained by the higher-order QCD processes leading to processes of the type p + p-+Z + jet + X and p + p •*• jet +X is at this point not entirely clear. The observation of the so-called monojet events is expected in the Standard Model via p + p -+ Z° + jet + X (Z° -*• vv) and

v Tne p+p •+ W* + XJfW* •+ T*VT •+ (TT,P,A, ...)* x3- monojet events are also expected in many supersymmetric theories [23] and it is therefore extremely important to calculate as care• fully as possible the rate and the Py, spectrum of mono jets in the Standard Model.

The higher-order QCD corrections in the processes p + p(p) •+ W±X;Z X are important from an additional point of view: namely, the actual cross-section for W* and Z° production observable in a detector with limited forward detection. The point heie is that in the DY process (Fig. 6a) the W* and Z° are produced with longitudinal momentum only, apart from the small transverse fluctuations associated with the primordial-ky of the partons in the colliding hadrons. Higher-order QCD diagrams such as those of Figs. 6b,c will communicate transverse momentum to the weak bosons leading to more central production. As we are going to show in this section, the fraction of events observable in a detector with a typical pseudorapidity range |n| - 2.5 is decreased by only 25% at /s = 10 TeV, if the large-py, mechanisms are included. In contrast, in the estimates based on pure Drell-Yan W*, Z° pro• duction, about 80% of the cross-section falls in the range |n| > 2.5. Thus higher-order QCD corrections play a more important part than supplying a mere K-factor in the rates. - 482 -

«.GLQJ) < G(QJ) b)

• Q v ""Sw ,'' Fig. 6 Feynman diagrams for the process / V p + p + W±X(W± -»• e^g): a) Born level; b) 0(a,

:n _ c) 0(a„) Compton diagrams g + q _ -»• W~ + g(W _ e-v < / annihilation diagrams q + q ->• W + g(W~ -»• e VE) :

We have made use of the calculations for the processes

(2.5) P + P 2° • X , 2° . jet « X

done completely to 0(ag). The diagrams for the W~ production are shown in Fig. 6 and those for the Z° are similar and are not shown explicitly. There axe several calculations in the literature [10,11] which differ from each other essentially in the treatment of the small- Pp ' ' region, where the contribution of the diagrams in Fig. 6 diverges and some resumma- tion technique has to be employed. We use here the method of Ref. [24], where the details of the calculations can be seen. We have used the Glück-Hoffmann-Reya parametrization with 2 Î,2 the scaling violation set by the scale Q = pp /4. The contribution of the hard corrections (Figs. 6b,c) is obtained by multiplying the corresponding matrix element by a regularizing 2 2 W < W > < W >2 factor 1 - exp(-p-. ' T>Y sof^ where Pp S0£t is calculated by the resummation of the order

< > = -as leading double logarithm terms. This yields Pp soft 6»6 GeV at /s = 540 GeV, giving about 180 pb for the W* production cross-section in the soft processes and ^ 170 pb for the contribution from the hard processes, leading to a(p + p -»• W* + XfW* -* ^v^)' - 350 pb at /s = 540 GeV. This cross-section (multiplied by 2) is to be contrasted with the recent measurements [25] cxBtW-^ev) - 530*100tioo pb (UA2)

The theory and data are in reasonable agreement, and one should bear in mind the (±25)% uncertainty in the theoretical predictions related to the structure functions. In - 483 -

Fig. 7 we show the pj. spectrum of the W* normalized to the 43 events of the UA1 data. Again the agreement is reasonable. A recent theoretical update by Altarelli et al. [l] gives a similar distribution.

In Figs. 8a,b we show the distributions d2a/dp^W'Z-'dy for the processes p+p •*• W* + X and p + p •+ Z° + X for /s = 2, 10, and 20 TeV. The most striking feature of Figs. 8 is the rapid growth of the large -pT' tail with /s. Perhaps it should be remarked that the 0(as) pT-

2 distributions shown here could increase substantially when 0(as) effects are included. The K-factor for the pj-distribution of the DY pair calculated by Ellis et al. [il] is ^1.6;

2 W Z Fig. 8 The differential pT-distributions for the W* and Z° bosons, d CT ' /dp^dy| , for /s - 2, 10, and 20 TeV: a) p + p •+• W* + X; b) p + p •* Z° + X. y_ - 484 -

W Z

2 2 it is not unreasonable to assume that the distribution d a/dpp' dy in 0(as) also receives a similar enhancement. If the present UA1/UA2 data have to be reconciled with the Standard Model, at least such an enhancement is certainly needed. In Table 2 we show the integrated cross-sections for both y = 0 (central production) and all-y values (total cross-section). As remarked earlier, QCD corrections tend to make the W* and Z° production more central. The values of and are also listed in Table 2 for various /s. Again these values may very well turn out to be underestimates owing to the absence of 0(ct ) and higher effects.

Table 2

Production cross-sections for W1 and Z° bosons in pp collisions in leading-order QCD.

/s (TeV)

0.54 10 20

o f" pp -»• W" + X n'b 0.7 8.2 11.9 I - A * all y

a f pp W* + X "I nb

y 0.68 6.5 7.9 I •* A J iv i < 2.5

o" fPP * Z;X "1 nb 0.06 1.2 1.7 all y

a f pp -+ Z° + X Ï 0.055 0.82 1.1 I - uVj |yU| < 2S

GeV 7.6 16.6 19.3

GeV 9.1 23.3 24.5

There are two additional features of the W* and Z° production in pp and pp collisions at large /s, related to QCD effects which we would like to note. The first feature is the distortion of the Jacobian peak in the process p + p -»• W~ + X(W~ •* &-v¿), and the other is the change in the angular distribution of the Sir measured with respect to the beam direction.

In Fig. 9a we show the 0(as) corrected pp distributions at /s = 0.54 and 10 TeV for Iy^-I S 2.5. In Figs. 9b,c we show the distributions da/d6(p-A+) for p^ < 30 GeV and Pj, > 30 GeV for /s = 0.54 and 10 TeV. Note the change in the shape of the angular distri• bution with /s. This is due to the increasing role of the gluon-initiated processes with /s, and constitutes as such a test of perturbative QCD [10], - 485 -

T 1 1 r

IGeV)

1 II

c) pp - W* . X

p** > 30 GeV h = 10 TeV /S = 540 GeV

1 KT2

Fiq. 9 a) The lepton-pj distribution da/dpji, integrated over a pseudorapidity interval I yA ¡ < 2.5 at /s = 0.54 and 10 TeV for theprocess p + p -»• W* +X (W* ->• ÄrVß) . b) The angular distribution do7d9p-j¡+ with the cut-<¡jff < 30 GeV but otherwise the same parameters as in Fig. 9a. c) Same as Fig. 9b with p£ > 30 GeV.

The predictions for the process pp •+ Z° + X(Z° -> SL+!L~) follow qualitatively the same pattern as for the process pp_ -» • +W + XfW+" •+ +l v¿) , namely: i) large increase of thije tail with /s as shown in Fig. 8; ii) fattening of the p^ distribution distorting the Jacobian peak shown in Fig. 10a where again we compare /s = 540 GeV with /s = 10 TeV; and iii) the change in the angular distribution of the lepton dc/d6(p-Jl+) with /s shown in Figs. lOb-c.

In Table 2 we have presented the cross-section for p + p Z° + X, the fraction of 70 observed cross-section in the interval |n| - 2.5, and the average values for various values of /s. We again remark that the fraction of observable Z° events in a typical detec• tor with an angular acceptance 10° < 6 < 170° is not small owing to higher-order QCD effects. In conclusion, we find that in the multi-TeV energy region the weak bosons W* and Z° are produced with large-p^, owing to higher-order QCD processes. The Compton-like process will play a dominant role at these energies. A consequence of this is that the rates of W1 and Z° production are expected to be very similar in proton-proton and proton-antiproton collisions. The topology of the observed events (i.e. non-forward) would be such that the W* and Z° would be dominantly accompanied by a jet (or jets). The present CERN pp Collider experiments have clearly seen such events, and their rates are expected to grow rapidly at large /s. - 486 -

O 30 60 90 120 150 O lp-l*| Ideg!

Fig. 10 a) The lepton pT distribution da/dp£ integrated over a pseudorapidity interval

ly^l < 2.5 at /s = 0.54 and 10 TeV for the+urocess p+p •*• Z° +X(Z° •*• I*ST), b) The angular distribution da/d9p_j¡,+ with the cut-off p£ < 30 GeV but otherwise the same parameters as in Fig. 10a. c) Same as Fig. 10b with p|+ > 30 GeV.

2.2 Production of heavier W' and Z' bosons

The LEP Hadron Collider has the potential of producing weak bosons, W' and Z', much heavier than the Standard SU(2)^ x U(l) bosons, should these heavier objects exist. There are a variety of models in which W' and Z' exist, either as fundamental bosons, such as W*

and Z° in the SU(2)L x U(l) model, or as composites having non-standard decays. Among these

models there exists a particularly attractive one with the weak group G = 50(2)^ x SU(2)R x U^B-L an^ ^L= % E2(>]. This model generates parity violation spontaneously. The usual phenomenology of the Ki/Kg mass difference translates (albeit with some assumptions) in a lower limit on the right-handed boson mass [27] m^ > 1.5 TeV. In yet other classes of R models, generating charge conjugation, parity violation, and CP violation spontaneously, one could put an upper bound on the mass of the right-handed boson assuming that the

SU(2)R intereactions are the sole source of CP violation. The present data on the CP- violating parameter e in the kaons gives then an upper bound m^ S 21 TeV [28]. Thus it seems possible that the region around 1-2 TeV is also the habitat of the right-handed W and Z bosons. We have calculated the production cross-sections for the processes involving W' and Z' in pp and pp collisions, namely p + p(p) -»<^+^-»W,Z +X . (2.6) - 487 -

Assuming universality one could calculate the cross-sections for the processes (2.6) in terms of the standard W and Z boson cross-sections. Using the relation

(2.7)

or(WfZ) mi- ¿(Zw,i-5%£) the results are shown in Figs. 11a and lib for the W and Z' production, respectively. The cross-section is higher for the pp case as compared with the pp case for identical values of m^/ and m^I, with the difference becoming larger for larger m^t and m^/. The observable rate depends on the trigger. If the W and Z' have decays (and branching ratios) similar to the standard W and Z, then they could be found in the standard decays W,' —> i\ (I - Z —» I* IT (2-8) U',2' '—*.<[<( -> 2 Jets

In other models the decays of the W'* may involve massive neutrinos, which in turn decay leptonically or semileptonically:

EM ITEVJ

Fig. 11 The production cross-sections for heavier Wf± and z'° bosons with assumed mass my/ 2' = ^» 3» and 5 TeV as a function of the centre-of-mass energy: a) p + p •+ w' +X (solid lines), p +p W' + X (dashed lines) ; b) p + p -+ Z'° + X (solid lines), p+p •* z'° +X (dashed lines). - 488 -

giving rise to rather spectacular signatures although at the cost of event rates. However, we are confident that by the time the LEP Hadron Collider starts operating, the jet-jet invariant mass technique would have become a standard tool in the repertoire of our experi• mental colleagues in their search for new bosons. Recent attempts by the UA2 Collaboration in the jet-jet invariant mass reconstruction are certainly very encouraging f¿29]. Figures 11 could be used directly to estimate event rates. Assuming that a cross-section

a(w'x, z'x) = 0.1 pb is observable in pp or pp collisions, the maximum values of m^, and mz# are listed in Table 3. A 20 TeV pp machine is certainly capable of probing W'1 bosonic masses up to ^ 4 TeV, and Z' masses up to ^ 3 TeV. Forward-backward asymmetries in W decays have played a crucial role in establishing that the spin of the W~ is 1 £l}. They are also expected to be useful in identifying the characteristic couplings of W,± and Z'°. This point has been discussed in detail by Rosner et al. in Ref. [10].

Table 3 Maximum mass of W and Z' bosons observable in pp and pp collisions

assuming aCW'X, Z'X)observable = 0.1 pb.

PP PP

/s (TeV) 10.0 20.0 10.0 20.0

(ny)"13* (TeV) 3.2 4.8 2.7 4.1

max (mz,) (TeV) 2.1 3.0 1.7 2.6

2.3 Associated production of W+ and Z° bosons

The simultaneous production of two gauge bosons from the set (W, Z, y> Y*) is con• sidered in this subsection. The processes

p + p(p) -> ofi -> VsAV , W 1° c2.io)

and £

(2.11)

have been studied in Ref. (30), where the importance of non-Abelian couplings in Wy, W+W~ and W Z° was emphasized. Furthermore, the W~y channel involves the (anomalous) magnetic dipole and electric quadrupole moments of the w± boson, causing a zero in the angular dis• tribution of the parton cross-sections if their standard values are chosen [31]. The pro• cesses (2.10) and (2.11) have recently been reanalysed in Ref. [32] for pp collisions using the GHR structure functions, where the background to (2.10) and (2.11) from the four- parton processes was also calculated. We extrapolate the calculation of Ref. (32) to high cm. energies. - 489 -

The cross-sections for the seven processes listed in (2.10) and (2.11) are shown in Fig. 12a, where a pp-cut of 5-10 GeV has been put on the photon momentum, and the mass of the virtual photon has been chosen to be 10 GeV for illustrations. (All W* cross-sections are equal to the W" cross-sections.) The cross-sections for WW. WZ, and ZZ are also shown separately in Fig. 12b. The cross-section for the three processes sensitive to the non- Abelian couplings show a definite hierarchy, namely: a(W~Y) > o-(W+W~) > afT^Z0). The pro• cesses W+W" and W~Z°, calculated without the non-Abe lian diagram, would in fact be signifi• cantly larger since the (Abelian) ® (non-Abelian) interference term is negative. All three

Fig. 12 a) The production cross-section for the processes p+p •+ VjV2X, where Vj, V2 are any members from the set y, y , Z°, and W~. For processes involving a Y> a momentum threshold

+ x of pY = 5-10 GeV is assumed. The curve p + p •+ Y Y corresponds to my* = 10 GeV. + + b) The projection of (a) involving only weak boson pair-production processes p+p •+ W~W~, wV, zV. - 490 -

cross-sections are in excess of 1 pb at /s = 20 TeV. The existence of non-Abelian coupling in the weak boson sector is certainly testable at the LEP Hadron Collider.

The striking aspect that the Standard Model predicts a zero in the Wy centre-of-mass angular distribution is also testable. This behaviour can be used to distinguish the funda• mental nature of the W~ from the composite scenario, where, in general, both the magnetic dipole and electric quadrupole moments could deviate from their SU(2) x U(l) values [32]. Thus, for example, if the magnetic dipole moment K = +1 (instead of the standard value K = -1) then the dip in the angular distribution (do/d cos 9) disappears.

The production of multiple weak bosons W* and Z° is interesting from yet another point of view: namely, they test the mechanism of spontaneous symmetry breaking. If the usual Higgs mechanism is replaced by a strongly interacting sector so that the physical Higgs boson and the longitudinal W~ and Z° bosons are then strongly coupled to one another (though still weakly coupled to ordinary matter and to the transverse W, Z, and y), then this system will deviate grossly from perturbation theory, for example, showing resonance formation [33] or high W£ and z£ multiplicity. It has recently been argued in Ref. [34] that the multiplicity of these gauge bosons can he estimated based on analogues of the low- energy pion theorems (as in QCD) or statistical models (used in the infancy of e+e physics). Thus cross-sections for the following processes,

p+ p(P) -> % +i

(2.12) -» vi would all be measurably large at the LEP Hadron Collider in this scenario. The perturbative estimates for the processes (2.12) are small in the standard theory (by which we mean that rH

3. PROMPT-y production

Prompt photons by definition here are energetic photons produced by the hard scattering of partons in colliding hadrons. In leading order QCD, photons are produced by the qq annihilation process qq gy and the 'Compton1 scattering gq •+ yq. Compared with the jet production, the prompt-y processes are down in rate not only by a power of the electro• magnetic coupling constant. a , but, quite importantly, the y I jet-yield is also suppressed owing to the absence of the gg -*• gy scattering in this order, the strong interacting analogue of which, namely gg •*• gg, dominates the jet-jet cross-sections at collider energies. On the other hand, the y/ir yield is an increasing function of the pp, since the production of single hadrons at large Xj, = 2pj,//s falls very rapidly because of the fragmentation of a final-state parton in a jet. It has been estimated, for example, that at a cm. energy of \/s = 53 GeV and 9^ = 90°, the inclusive-y rate becomes equal to the inclusive TT° rate at x^, = 0.45 [12]. Since the hadron yield at large Xj, is falling very steeply with /s owing - 491 - to the double scaling violation (i.e. the QCD scale-breaking in both the structure functions and the fragmentation functions), the y/ir" crossover is expected to occur at smaller values of Xj as the cm. energy increases. Preliminary data from the CERN pp Collider at /s = 540 GeV indicate that the ratio y/it" may exceed 1 at Xp = 0.1 [35]. Thus we expect that at /s = 10-20 TeV, the Y/T0 crossover in pp or pp collisions could take place around x^, - 0.02-0.03.

Prompt photons are interesting in their own right. They provide a detailed test of QCD and, in particular, offer a good method for determining the structure functions of the gluon. This is made possible because of the increasing importance of the quark-gluon scattering processes at large /s, particularly in proton-proton collisions. Perhaps it should be remarked that conceptually the reaction pp ->- Y + X is superior for the determina• tion of G(x,Q2) as compared with the deep-inelastic reactions where the gluon density G(x,Q2) appears only in higher-order corrections.

The hard QCD processes give rise to event topologies in hadron-hadron collisions lead• ing to events with single isolated -Y, Y + jet, Y + multijet with photons having large pp. Since large-pp Y'S are expected signatures in a large variety of new physics phenomena (for

+ J + + + example, in the decays xT -* Jp Y, j * nT Y» T>p -*• Y Y, JT •+ Y H°, Q -+ Qy, ...)» it is extremely important to have reliable rates for prompt-y production via standard (QCD) hard collisions.

The complete list of the standard hard-collision processes giving rise to pp(p) •+ Y + X and pp(p) -»• Y + Y + X is given in Table 4. Note that the order of the processes listed

Table 4

The leading order in the strong (as) and electromagnetic (dem) coupling constants of various subprocesses contributing to the production of single and double photons in hadron-hadron collisions.

Description Order Subprocess

Annihilation aemas qq Yg Compton aemas qg Yq Single bremsstrahlung aemaI qq qqy gq gqY gg qqY qq qqY

QCD induced gluon photon coupling aemas gg Yg 2 Pure QED annihilation auem qq YY Single bremsstrahlung contribution to two-photon ->• em s qg Y(q Y) Double bremsstrahlung «em«! qq -y (q- Y)(q + y) gq -»• (g - Y) (q + Y) gg -y (g - Y) (g ^ Y) QCD induced gluon photon coupling a|mas gg YY - 492 - refers only to the lowest-order Born diagrams. Here we shall discuss only processes up to order a a2, which have recently been computed [36]. The relative contributions of the higher-order processes (a2 a2, a2 a ) listed in Table 4 are not expected to rise above a few percent even at /s = 10-20 TeV, and so we shall neglect them here.

The inclusive cross-section for the production of a point-like photon at large pT can be written as

xi{ig^v)5(H

TC J

s

The sum i,j runs over all quarks, antiquarks, and gluons in the initial hadrons. The quantities da^/dv are related to the Born cross-sections and contain the finite next-

to-leading-order corrections. The mass Qs (Q¿) sets the scale-breaking effects in the structure (fragmentation) functions and Qç is the argument of the running coupling constant,

2 as(Q = C¿). The complete cross-section is obtained by adding to Eq. (3.1) the contribution of the pieces coming from the fragmentations g •*• y and q -»• y. This piece, which is known in the literature as the anomalous photon component, is obtained from the collinear emission of a photon by a final-state parton, and in 0(0^^) is given by the fragmentation of any final-state quark or gluon into a photon by the eight 2 •+ 2 parton scattering processes listed in Table lc. The anomalous y cross-section has the form

tJ du dp* . .4- J x3

421LJ"k($,V) 5(1-W) . (3.2) X TTv s^ dv

111 2 where DJ^ " (x3 »Q^ ) is the fragmentation function of a parton k into a photon with the scaling violation set by the mass Q¿, and can be written as

_ anom rx 1 Q r - 493 -

The simple photon bremsstrahlung 'Born approximation' gives

C3.4) f,.*W - ° where e^ is the electric charge of the quark. Leading-order corrections in QCD modify the shape of the functions f(z) and induce an indirect coupling of the gluon to the photon.

We make use of the calculations reported in Ref. [36] to calculate large-pp photon

cross-sections at 6Y = 90° in the proton-proton (antiproton) cm. system. For the q •+ y

fragmentation function D^ Y(Z, Cy), we use the leading-log parametrization of Duke and Owens [37] but we have set f (Z) = 0. Unless otherwise stated, we use the GHR structure

z functions with as(Q ) given by

A with A(= Aj^g) = 200 MeV. All other scales in Eqs. (3.1) and (3.2) are set equal to pp, i.e. Q¿ = Q| = Q| = pf.

In Fig. 13 we show the differential cross-section E(d30/dp3) for prompt-y production in the process p + p -»• y + X at /s = 540 GeV, 10 TeV, and 20 TeV. The prediction at /s = 540 GeV is compared with the UA2 data on 'unaccompanied neutral energy' [35]. The agreement is reasonable although the experimental accuracy is limited owing to statistics. However, the large increase in the y yield at fixed pp with increasing /s to the multi-TeV

2 range is evident. Figure 14 shows the differential cross-section d o/dy dp^ly_0 for pp -»• y + X. Note that the cross-section is substantial also in proton-proton collisions.

For example, at /s = 20 TeV, a counting rate of 1 photon per 10 GeV pT per day is obtained around pj = 500 GeV with a machine luminosity S£ = 1032 cm-2 s"1. In fact, in the range of energies obtainable at the LEP Hadron Collider, /s = 10-20 TeV, very similar yields are obtained for both the proton-proton and proton-antiproton machines up to very large values

of pj,. For example, (da(pp)dydpT)/(do(pp)/dydpT) at /s = 20 TeV and y = 0 increases from 1.0 to 1.1 between pp = 20 GeV and 500 GeV. Beyond that, the pp yield dominates the pp but the absolute cross-section itself becomes very small.

In Fig. 15 we show the relative contributions of the subprocesses qg •+ yX, qq -*• yX, and gg yX in pp collisions at /s = 10 TeV for 6y = 90°. Note the dominance of gq y + X up to very large values of pj and the negligible contribution due to the fusion process gg •+ y + X. This behaviour is at variance with the low-energy ISR [12] and the CERN pp collider data [35], where the process pp •*• y + X is dominated by qq annihilation. However, this changing of roles is a consequence of the fact that at low energies very large values of Xp are needed in order to overcome the background from the single-hadron production, for which the gluon-quark luminosity functions are very small. On the other hand, at /s = 20 TeV, for a typical photon trigger pj = 100-500 GeV corresponding to Xp = 0.01-0.05, one is probing very small x^-distributions where the gluon flux is concentrated. Thus the prompt-y experi- - 494 -

Fig. 13 The prompt-y distributions Ey(d3a/d3pY) Fig. 14 The p| spectrum in the process p+p-+y + X for central production (9^ = 90°) in the process (9Y = 90°) at /s - 2, 10, and 20 TeV. p + p -+ Y+X at /s = 0.54, 10, and 20 TeV. The theoretical curve at /s = 0.54 TeV is compared with the UA2 data on large-pT 'neutral energy' distributions.

Fig. 15 Relative contributions of the three parton-parton processes, » qg •* qy p + p qq qqy * gg + Yg to the differential distribution d2o/dydpY at 6 = 90° and /s = 10 TeV. - 495 - ments in the multi-TeV energy range will probe x values much smaller than those available at present.

Before closing this section we would like to discuss two technical aspects, first the importance of the OC0^01^) contribution [over the one due to Ofag^g)]» i.e. the K-factor, and secondly the dependence of the cross-section o[pp(p) y + X] on the structure functions. In Fig. 16 we show the quantity C defined as

C(PT,e/N/s) = -ÊXÉ£

(CRAW cxemÄs)

for the process pp •+ y + X. The contribution from the anomalous component alone [i.e. pro•

a a are portional to fçp^Cz) and the complete 0( em s) shown separately. We remark that the C-factors in both cases are substantial and decrease with p^. Typically C = 0.4 around

pip = 400 GeV. Thus, terms proportional to <^en^s are by no means negligible even at the multi-TeV pp and pp collisions.

The inclusive-y cross-sections do not depend sensitively on the structure functions available on the market. This is particularly true for the two sets of structure functions presented in the section on parton luminosity. In addition, in Fig. 17 we present the ratio

2 + of the cross-section d o/dydpT (y = 0) in pp -+ y X at /s = 10 TeV for the GHR parametriza- tion, and yet another distribution with Baier-Engels-Peterson quark distributions [38] plus the CDHS gluon distributions [39]. The two sets give cross-sections in the observable pi range (20 GeV < J_ < 500 GeV) which differ by ±201. i Py.

—1 1 1—1—1 1 1 c 1 1 1 1 1 1 1 11 1 \ \ pp-tX 1.4 \ . \ A = M TeV 1.2 8=90»

1.0

0.S - 0.6

0.4

0.2 Fig. 16 The 0(ag) correction factor C(py) in 1 1 1 1 1 1 1 1 1 1 • I i i I i I the process p + p + Y + X at 6 = 90° and Á = 10 TeV. 0 40 60 80 100 200 400 600 1000 Pt IGeV)

1 —r— i i i R-RRJ -R i—i—V i i i pp-ïX - /s = 10 TeV 8=90° -

Fig. 17 A comparison of the differential dis• tributions d2a/dydp^ in the process p + p+y + X at 6 = 90° and /s = 10 TeV for the two sets of structure functions (called GHR and BEP in the

i i i i i 'il text). 40 60 80 WO 200 400 600 1000 PT IGeV/cl - 496 -

In concluding this section we remark that an appreciable production of prompt photons from standard QCD processes is expected in the 10-20 TeV energy range. The proton-proton and proton-antiproton have almost equal cross-sections up to observable p£ = 500 GeV. Both pp ->- Y + X and pp •+ y + X at these energies are dominated by the Compton-like process g + q -> Y + q» therefore the gluon distribution in the proton can be studied up to very small values of x. Finally, the observed photon will be found in the debris of a fragment• ing parton in a substantial fraction of the prompt-Y events.

4. JET PRODUCTION

The emergence of a clear two-jet structure in the process p + p+ jet + jet + Xat the CERN pp Collider [3] confirms the underlying parton-parton hard scattering mechanism in QCD [40]. The analyses of the UA1/UA2 groups have demonstrated that it is a relatively simple matter to extract jets from the minimum-bias events which have typically small pp, "v< 500 MeV, but are otherwise abundant in pp collisions. The jets/minimum-bias events separation is expected to become even simpler at higher energies since both theory and extrapolated data predict a shrinking of the jet-size (localized energy deposition in the sense of a Lego plot), a linear increase in the pp of a jet, and a mild increase in the multiplicity (and ) of minimum-bias events In s - (In s)2]with the cm. energy /s. Extrapolating from a typical UA1/UA2 jet-trigger, say Ep > 15 GeV, one expects that at

/s = 10-20 TeV a typical trigger, ET > 50 GeV, should result in well-defined jet structures of approximately the same quality. The qualitative difference with the present (i.e. /s = 540 GeV) topology is expected to lie in the emergence of multi-jet structures. The jet-multiplicity at the CERN pp Collider is certainly low with two- and three-jet events

almost saturating the large-pT physics.

Jet-Jet physics is an interesting subject on its own, but, as in most cases in high- energy physics, the discovery of to-day becomes a background of tomorrow! The standard jet-jet physics is bound to be a very important background for new processes expected to occur around /s = 1 TeV, involving non-leptonic or semi-leptonic final states. For example, the production and decays of a Higgs via

p + P(P) —» H° + X |L-ybb,tb

I J~z? LvL , tb,...

or of a high-mass QQ pair production t\>, . . -

p + pep) —» QQ + X 3 W' .

or of a bound flavour + x p + p ( p) —» At - 497 - all involve the detection of a structure in the jet-jet invariant mass. It is expected that the jet-profile reconstruction techniques would make big advances. These techniques, com• bined with information on the flavour content of a jet, for example via vertex detectors and lepton energy measurements inside or nearby a jet, would enable one to tag a heavy- flavour jet in particular. In addition, the ability of reconstructing jet-jet invariant mass with a good mass resolution is going to be a particular asset. The obvious places where the jet-profile reconstruction techniques can be refined are in the processes involv• ing W* and Z° production, since their masses and widths (approximately) are known. A begin• ning has already been made in this direction by the UA2 Collaboration [35], who have re• ported a ^ 3a signal for W production in the process pp •+ W1 + X (W* -»• qq'). In the fol- iet lowing we present rates for the process pp(p) -+ jet + jet + X and calculate the pp - and jet-jet invariant mass-distributions. We also estimate the quark/gluon jet-angular radii, and energy-flow in hard scattering QCD processes taking into account semi-hard effects (multiple gluon emission) and soft effects (hadronization of jets). The leading-order inclusive jet yield is computed by the eight 2 2 QCD subprocesses involving quarks and gluons, shown in Table lc, by convoluting the QCD cross-sections with the corresponding parton-parton luminosity functions RV.j(Xr> xz> PfO* F°r example, we have

dydp;

f J

where &\j •+ f are the differential parton-parton cross-sections, which are also shown in Table lc. The relative importance of the various subprocesses is a function of pp (or equivalently of x). Sinceifgg(pp) is very large for small x (dominance of the gluon flux at low x) and the colour factors in gg scattering are favourable (gg:gq:qq are in the ratio 1:4/9:16/81 in the leading log approximation), the parton-parton scattering is dominated by the process gg •*• gg at small pp. For the UA1/UA2 trigger, however, the present p£rigger is not small, and so in the process p + p->-jet + jet + X, final states are dominated by gq and gg scattering. At very large Pp the qq -»• jet + jet + X takes over.

The situation at the LEP Hadron Collider at /s = 10-20 TeV is expected to be an all- glue affair, since the dominance of the gluon-gluon luminosity if (x = pp/s") at those energies would extend to fairly large values of pp. These pp values are much larger than a typical pp trigger (say, p^rigger = 50 GeV at /s = 10 TeV). Therefore, the jet physics in the multi-TeV range is going to be dominated by the gluon-gluon scattering — a corollary of which is that the jet yields in pp and pp collisions are expected to be very similar. We have calculated the inclusive jet cross-section d2o/dy dpp at y = 0 for the processes

(4.2) - 498 - for /s = 0.62, 2, 10, and 20 TeV. The integrated cross-sections

(4.3)

pT>prW99- are shown in Fig. 18. The cross-sections shown correspond to the GHR parametrization with Q2 = p| and A = 0.4 GeV. Note the large increase in the yield of the high-pj, events with •s.

In Table 5 we present the integrated cross-section

Ar, cl cr

.mui = o

for the exclusive two-jet processes

p + P(P) —* jet + jet +• X (4.4) 499

Table 5

2 Integrated cross-section / dp™(d a/dydpT) for the processes p + p(p) •*• jet + jet + X 'mm withp~in = (Zf.Jpj)mi n

/s = 10 TeV 20 TeV 40 TeV pfn (TeV) PP PP PP PP PP PP

0.1 1.36 yb 1.36 yb 4.25 yb 4.25 yb 4.5 yb 4.5 yb 0.5 3.0 nb 3.0 nb 8.6 nb 8.6 nb 31 nb 31 nb 1.0 0.13 nb 0.13 nb 0.62 nb 0.62 nb 2.0 nb 2.0 nb 2.0 1.85 pb 2 pb 24 pb 25 pb 120 pb 120 pb 3.0 7 xio-2 pb 8xio"2 pb 2.35 pb 2.5 pb 20 pb 20 pb 4.0 3xl0"3 pb 4.5 xio"3 pb 3.4 xlO-1 pb 3.8 xlO-1 pb 4.8 pb 5.0 pb _1 6.0 1.0 xio"2 pb 1.4 xlO-2 pb 4.2 xlO"2 pb 4.5 x io pb

with a global trigger p~in = E^lp^l £or 6 = 90° ^ = 10» 20» 311(1 40 TeV- We remark that the highest possible E|ppJ range which could be explored does not scale linearly with the cm. energy /s. For example the cross-section limit a(pp •* jet + jet + X) = 1 pb is reached for p~in = 2.2, 3.4, and 5.2 TeV for /s = 10, 20, and 40 TeV, respectively. Thus the maximum l|p£| that can be explored in a pp or pp collision is increasing approximately as (/s)0-6. The jet yields for the pp and pp collisions are nearly identical except for very large p^. values (x^ £ 0.4), where the pp cross-section becomes more effective. However, the absolute cross-sections themselves at such large-Xj, values become very small owing to the approximately 1/xp behaviour of da/dxp.

Next we discuss the dispersion in the theoretical extrapolation of jet yields in multi- TeV pp and pp collisions. Since the p^, values used for jet triggers are so large, the variation in the cross-section due to a change in the value of A within a factor of 2 does

not effect the value of as(p|) by more.than 15%. For a given value of A, the same is true

2 2 2 2 2 2 if one changes the scale from Q = p| to Q = V2 Pp or Q = 2 § t û/(§ + t + û ). The dependence of the two-jet cross-sections on the scale Q or the QCD parameter A at the CERN pp Collider are more pronounced, and the smoothing of this behaviour at /s > 10 TeV is a

2 2 reflection of the insensitivity of ag(Q ) on A for very large Q . However, there are two more uncertainties in the extrapolation of absolute cross-sections and they are concerned with the initial parametrization of the gluon/quark structure functions and the present

3 lack of 0(as) and higher-order QCD corrections. The latter should, however, become some•

z 2 what smaller as Q increases owing to the decrease in the value of as(Q ).

To have a reasonable idea of theoretical uncertainties, we reproduce here, from Ref. [41], the results of a numerical analysis using five different sets of parametrizations: the BGOR [42], GROR [43], BETAL [44], GHR [20], and the CDHS [39]. In Fig. 19 we present the energy dependence of the inclusive jet cross-section with a pp cut-off in p+p jet + jet + X. - 500 -

pp-»jet«jet>X

(Integrated cross section]

102 103 10* 10s 0 100 200 300 400 /s [GeV] qt, p, [GeV]

Fig. 19 The integrated jet cross-section p+p •*• jet + jet+X, with p£rlgger = 15, 50, and 150 GeV. The hatched area signifies dispersion in jet rates corresponding to the various structure functions discussed in the text. Also shown are the individual contributions from the various subprocesses listed in Table lc. The curve labelled E. = 1 TeV is the departure from QCD for a possible quark substructure (for details see ref. 41).

The shaded areas show the theoretical uncertainties associated with the various parametriza- tions just listed. At large energies, almost all parametrizations lead to predictions which do not differ by more than a factor of 2. The predictions of the DO parametrizations [21] are rather close to the one for the GHR parametrization, as can be seen from the parton luminosity functions. Figure 19 also shows the dominance of the processes gg •+ gg and gq -+gq over all the rest. Since these processes are common to both pp and pp, the cross- section estimates of Fig. 19 also apply for the process p + p •+ jet+X.

In Fig. 20 we plot the jet-jet invariant mass for two values of the pp"rigger, ptrigger = 50 and 150 GeV at /s = 2 and 20 TeV, and for p^rigger = 15 and 50 GeV at /s = 540 GeV. The effect of putting a rapidity cut-off |n| - 1 is also shown. As in the case of pp distribution, the jet-jet invariant mass distribution is also dominated by the gg and gq subprocesses at multi-TeV range. Again this is not the case for m^ > 100 GeV at /s = 540 GeV. Note that owing to the relation

m* - q/J 2 * eft'~^ e a cut in the rapidity variable, at fixed M2, pushes the transverse momentum q^, to large values and therefore reduces the rates. This may be of some help in reducing the background for some new processes, for example those due to quark compositeness [4l]. - 501 -

pp-» jeNjet.X

[Mass distribution) Full y-range Iyl*1

1QÏ 15 2 3 t~5 i 2 • »103 " * M [CeV]

Fig. 20 The jet-jet invariant mass distributions do/dM for the process p+p -* jet + jet+X

ri er with pT 8ê = 15 and 50 GeV (for /s = 540 GeV) and ptngger = 50 and 150 GeV (for /s = 2 and 20 TeV). Also shown are distributions with the rapidity |y| ^ 1, together with the contributions from the subprocess qg •+ gq and gg •+ gg. The curves labelled with £ values represent departures from QCD due to possible quark substructure (for details see ref. 41)

4.1 Jet-fragmentation and angular radii

The inclusive jet cross-sections presented above in this section are relatively insensitive to the details of the quark and gluon fragmentation functions owing to the inclusive-jet triggers which, as the UA1/UA2 analyses have shown, are less prone to the details of inclusive particle (hadron) distributions. This is a redeeming feature as com• pared to the jets seen in e+e~ annihilation at relatively low cm. energies where the frag• mentation effects are large. Thus a much more direct test of the underlying parton scatter• ing is possible even at the present-energy for pp collisions. Of course the onset of SLAC Linear Collider (SLC) and LEP will provide a jet environment involving large cm. energies extending up to 170 GeV without any initial-state complications. However, as already pointed out, at the LEP Hadron Collider, one expects a visible jet cross-section involving pp61 in excess of 1 TeV for /s = 10 TeV. The production of jets having Q2 = 1-2 TeV2 is a distant goal for e+e~ machines and so hadron-hadron collisions will provide testing grounds for the space-time evolution of final states at typically Q2 = 1 TeV2. In particular the parton showering ideas [45] will be put to a crucial test.

The energy-angle profile of a jet is an extremely important attribute for designing detectors at super-collider energies. Clearly, fixed-order perturbation theory is not suf• ficient to provide such a profile. Ideas based on semi-hard processes and non-perturbative fragmentation mechanisms have to be invoked. Much effort in this direction has recently been made [46]. Many aspects of jet physics which are important for detector design and trigger have been examined extensively by a separate study group [47], We shall here con• fine ourselves to a discussion of the hadronic process and a study of the energy-angle pro• file of a jet. - 502 -

Two partons emerging from a large-Q2 process can be very much off-mass shell up to Q/2 — where Q = /s in e+e~ and = /s in hadron-hadron collisions — and are therefore expected to radiate gluons and quarks and thus produce a shower of partons. Such a cascade process has been discussed by several authors [46]. The common features of such approaches are that first-order QCD matrix elements in the leading logarithmic approximation are used for each separate branching. Provided that the off-shellness of the partons is strongly ordered, i.e. m2 » m2 » m\ etc., in Fig. 21, the cross-section factorizes into a product of the probabilities for each separate branching. This results in an iterative process, suitable for Monte Carlo simulation techniques, which is stopped when the off-shellness of all partons

is below a certain cut-off value Together with AQQD, this cut-off regulates the amount of radiation.

The parton-showering picture has been developed for time-like processes such as y* QQ. Its extension to space-like processes involves a certain analytic continuation, the details of which are not yet worked out. In this study we have used the parton-shower scheme of Marchesini and Webber [46], which has the additional feature that soft gluon interference

is taken into account by imposing an angular ordering in the emission, i.e. 6i > 92 > 83 etc. in Fig. 21. This has the effect that the treatment of parton showering becomes more sophis• ticated than a classical treatment of radiation. The practical result is that for a given tcut value and /s, the parton multiplicity is considerably reduced as compared to the classical evolution picture [46], since fewer soft partons are emitted, as a result of interference.

In the non-perturbative region, below the tcut value, one has to invoke some model for the final fragmentation into hadrons, the details of which can presumably be taken from our current knowledge of the jet-fragmentation properties at available energies.

In Fig. 22 we show the fragmentation function of a gluon jet at Q2 = 1 TeV2 for three alternative models. The solid line shows the result when the partons from the perturbative

a. Im2)

Parton offshellness

Fig. 21 A schematic representation of a parton Fig. 22 The fragmentation function of a gluon shower resulting from an initial qq pair pro- jet with virtuality Q2 = 1 TeV2 corresponding duced at high Q . to the three models discussed in the text. - 503 - cascade (and whose colour ordering is perfectly known) are connected by a colour triplet force field and the Lund string model [48] is applied for the final hadronization. This scheme has modest dependence on the t^ value since, in the string fragmentation model, if the shower is driven further the extra gluons emitted will only produce small distur• bances on the string structure obtained if they had been omitted. An alternative approach would be to just let the partons from the cascade fragment independently of each other using, for example, the Field-Feynman type parametrization [49]. This gives a softer spec• trum, as shown by the dashed-dotted curve (a gluon is here split into a qq pair using Altarelli-Parisi functions).

The independent fragmentation picture in its present form is more sensitive to the value. The reason for this behaviour is that the energy of two partons can never add cut up again by going into the same hadron. This leads to a softer particle spectrum for low tcut values- To illustrate the effect of the parton shower we show (dashed curve in Fig. 22) the result of a naive extrapolation of a gluon jet (in the string fragmentation model) without the perturbative cascade. It is clear that the effect of multiple gluon emission is quite substantial and the LEP Hadron Collider would provide quantitative tests of these models.

Finally, we calculate the jet-radii for quark and gluon jets. Let 9 be the angle be- between the jet axis and an infinitesimal calorimeter that measures the hadronic energy dE flowing into an infinitesimal solid angle diî. A QCD prediction for the energy distribution dE/d cos 6 = 2ir(dE/dfi) can be obtained from the summed leading log QCD distributions [50] and certain non-perturbative functions which can be fitted from data on the energy-energy correlation function measured at PETRA and PEP [51]. Defining a parameter Gy^ (which is a measure of the angular width of a jet) to be that value of 9 at which dE/d cos 9 has dropped to half of its peak value, i.e.

2 [&cx>se/ (4.5) I—) e = o in Fig. 23 we show 0!, as a function of the quark- and gluon- (jet-) energy. Note the con- /2 siderably larger value of 6^ for the gluon-jet compared with an equivalent energy quark-jet. At a jet energy >\» 1 TeV, we get (9/2)gluon « 20 mrad. A similar number is obtained if we use the parton shower model just described.

TTT] 1 I I A¡6=150MeV

KT' Cluon jet

«r1 Fig. 23 The half-angle of a quark-jet and gluon-jet as a function of the jet energy. Note that 6i£ is defined as the jet openin angle, where the jet energy distribution function reaches half the maximum value. 100 1000 10000 Jet energy (GeV) - 504 -

5. HEAVY-FLAVOUR PRODUCTION

In the past, hadron-hadron colliders have been the most copious sources of heavy quarks, both bound and open. The charm production cross-section measured at the ISR is of order 100 pb. Estimates of charm and bottom pair-production at the CERN pp Collider based only on the fusion mechanism (i.e. q + q •+ QQ and g + g •+ QQ) give typical cross-sections [57.]:

Although only a fraction of these cross-sections survive the experimental conditions (such as trigger, acceptance, etc.), the observation of the inclusive-u and uu events with large Pj by the UAl Collaboration confirms the above estimates. The total heavy-flavour produc• tion cross-sections in pp and pp collisions are of course much larger, since both diftrac• tive processes and non-perturbative large p^, production of cc and bb pairs, coming for example from the fragmentation of a gluon, contribute quite substantially. Extrapolating to multi-TeV pp and pp collisions, it is not difficult to predict that heavy-flavour physics, involving both old and new quarks, would be a very flourishing enterprise!

The calculations reported in this section are mostly based on the so-called fusion mechanism model, namely qq -*• QQ and gg -*• QQ. We briefly discuss diftractive production of heavy flavours at the end. It should be remarked that the fusion mechanism neither des• cribes the rate of charm production at the ISR nor the shape of the longitudinal momentum distribution [53]. On the other hand, at the present CERN pp Collider, the fraction of dif- fractively produced cross-sections visible in the UA1/UA2 detectors should be small for the charm and bottom mesons owing to the limited rapidity available and to the trigger conditions. This, however, is not the case for quarks of larger mass. Thus at the present collider a good fraction of the tt diffractive production cross-section should still be visible [54]. In Fig. 24 we show a typical model calculation for the acceptance of the diffractively pro• duced tt cross-section (with m^. = 40 GeV) as a function of /s for three values of the pseudo-

rapidity cut, with an additional pT cut ôf 5 GeV. The fraction of tt events observable in

Fig. 24 Fraction of events from the diffrac•

tive process p+p •+ AT +Mrj +X which are detec• ln ted,, f (/s, pS = 5 GeV, nc) with 114. = 40 GeV. - 505 -

a detector with a rapidity range |n] - 3 is expected to be less than 1% at /s = 10 TeV. Thus the diffractive mechanism would be significant only for the production of very heavy quarks in the multi-TeV range, /s = 10-20 TeV.

The differential cross-section for large-pip heavy quark pair-production can be expressed as

= Y íd-ld-JR¿¡(x,,xIiQ)5(S*t.Ct-2r»4) , cs.u x d.eSicsA"-t ) where dô^j/dt represents the differential cross-section for the subprocesses q + q -»• Q + Q

2 and g + g •+ Q + Q ~55]. The Born cross-sect ions in 0(as) are finite since IIIQ f 0 regulates the infrared singularity. So, in an strict mathematical sense the heavy quark pair-produc•

2 tion cross-section in 0(as) is integrable down to pp = 0. This is to be contrasted with the jet yield in hadron-hadron collisions, which needs a large-pp trigger in order for it to be well defined in perturbative QCD. Integrable as it is, the cross-section for g + g -> Q + Q has the asymptotic (s •*• °°) behaviour (see Table lb)

5.2)

indicating that the expansion parameter diverges in this limit and that a straightforward perturbation theory estimate is somewhat unreliable down to pp = 0. Thus the cross-section (5.2) should only be calculated with either a p^ri^^er or with a rapidity cut-off. These observable cross-sections turn out to be smaller for realistic detectors and experimental conditions than mathematical cross-sections obtained by integrating Eq. (5.1) completely.

In Table 6 we present the inclusive cross-sections for p + p(p) -»• Q + X obtained by integrating Eq. (5.1) over the interval |VQ| < 2.5 and píj? > p"1"1 with rx^m = 0, 20, and 50 GeV. The noteworthy feature is that the inclusive charm and bottom cross-sections for pmin = 0, decrease yd-th /s. The net effect of the Lorentz boost is such that keeping the rapidity interval fixed but increasing /s amounts to increasing the effective (Pj),,^ which reduces the cross-sections. Using a realistic jet-trigger, for example p^rig^er = 20-50 GeV, and a fixed rapidity interval |HQ| - 2.5, one expects only a modest increase in the inclusive heavy quark cross-section (a factor of 2-3) as /s increases from 10 to 20 TeV. Nevertheless, it is worth pointing out that even under these realistic experimental conditions, the cross- section p + p ->• t + X (or p + p -»- t + X) increases by approximately 3 orders of magnitude between /s = 0.54 and 20 TeV. In Figs. 25a,b we show the differential cross-sections da/dpj; (y = 0) for pp •+ Q + X = c, b, t, at /s = 0.54, 10, and 20 TeV.

It should be remarked that there could still be an important non-perturbative source of heavy quark hadronic production, coming for example from the process g + g -»• gg ->• ccX, bbX.

Since the cross-section g + g g• + g is expected to be huge, even a ratio (gg -»• cc, bb)/ (gg •+ all) 'VJ 5% would result in a substantial cross-section for pp(p) ->• QQX. This is certainly going to complicate heavy quark-jet identification. On the other hand, the longi• tudinal and transverse momentum spectra of such hadrons would resemble those of inclusive - 506 -

Table 6

Integrated cross-section o[p + p(p) -+ Q + X] obtained with (Pptrigger > ^^min |y^| < 2.5. Note that only fusion processes q + q •*• Q + Q and g + g •+• Q + Q are included in the cross-section calculations.

/s (TeV) 10 20 10 20

C$min C«V)

a(pp ->- c + X) a(pp -+ c + X)

0 76 ub 34 pb 75.5 yb 33.5 yb 20.0 2.3 y 4.2 yb 2.25 y 4.1 yb 50.0 120 nb 315 nb 115 ñb 310 nb

a(pp -+ b + X) a(pp) -+ b + X)

0 44.6 yb 19.1 yb 44.2 yb 19.0 yb 20.0 2.7 yb 4.1 yb 2.6 yb 4.05 yb 50.0 125 nb 290 nb 120 nb 280 nb

a(pp •+ t + X) a(pp -+ t + X)

0 210.0 nb 510.0 nb 200.0 nb 500.0 nb 20.0 200.0 nb 450.0 nb 190.0 nb 445.0 nb 50.0 57.0 nb 130.0 nb 55.0 nb 128.0 nb

I I I I I 1 1 1 I I 1 1

pp-»tNX b) nif = 40 GeV

13

«r1 -

olí ^ V ^N^Vî: 20 TeV

^VjOOTeV = \ >. 2.0TeV \o.54TeV i i i \ i i i i\i i i i 50 100 150 200 250 300 3 25 50 75 100 125 15017 5 200 225 250 275 300

P? (GeV) Pt(GeV)

Fig. 25 The distribution (d2o7dydp§) „ for the process p+p-»-Q + Q + X (Q = c, b, t) at 0.54, 2.0, 10.0, and 20.0 TeV: a) p + p -+ ccX, bbX; b) p+p -+ ttX, m^. = 40 GeV. - 507 -

pions and should be negligible at large xp and pp. The fusion mechanism, however, has the interesting feature that it leads to rather high heavy-meson/heavy quark-jet yield at large Xp and Xp. This is a consequence of the rather hard fragmentation functions Q •* M for heavy quarks, more so for the bottom and top quarks. In Figs. 26a,b we show the pp distri• butions (dc/dpp) (pp + M + X) I 0 for M = D, B, and T mesons at /s = 10.0 and 20.0 TeV. These p^. distributions are in striking contrast to the D* distribution measured by the UAl Collaboration [56], which is distinctly soft, owing to the g •+ QQ •* D*x mechanism, as opposed to the corresponding distribution c •+ D*x measured in e e~ experiments at more or less com• parable . Thus heavy-flavour tagging in hadronic collisions should still be possible, although at the cost of some efficiency.

Next, we turn to the discussion of prompt-lepton production at the LEP Hadron Collider. We will content ourselves by calculating some representative rates and distributions to get an idea of the lepton-associated signals at /s = 10-20 TeV. With this view we shall discuss processes expected to give 'isolated leptons', e.g. from the Drell-Yan type processes dis• cussed earlier: p <• p(p) —* W + X + X L •» IT (5.3) and processes giving 'leptons inside or near a jet', for example from

p + p(p) —> QÖ + X (5.4) U L* + X

The distributions do/dpp for the processes (5.3) are shown in Figs. 9a and 10a, taking into account the 0(as) QCD corrections to the lepton spectra.

1 1 i i i i PP—oax a) pp—QSX b) t*M.X' - LM.X' £ = K> TeV D \/s = 20 TeV -

- 10°

O -o -

D

i i i > i i 50 100 150 200 250 300 50 100 150 200 250 300

PÏ (GeV) PÏ(GeV)

2 Fig. 26 Transverse momentum distribution d o/dydpT for the heavy mesons (D, B, T) from the process p+p •+ Q + Q + X(Q •+ M + x') using the GHR structure functions and the Peterson et al. fragmentation functions: a) /s = 10 TeV; b) /s = 20 TeV. - 508 -

The lepton yields from the processes (5.4) have been calculated assuming the standard V-A interaction and parametrizing the heavy quark •+ heavy meson fragmentation à la Peterson et al. [57]:

f M = - es, s) fco-*) -0-3O-ebej• with

_ ( E + PH)M and

ec = 0-3 , eb= oo2 , et = oooos

+ 2 2 The numbers for ec and are fits to the e e" data at Q = 1300 GeV . We have neglec• ted scaling violations in the heavy quark fragmentation function fq^C*) but included them in the structure functions [20]. We have set BR(b-+Jlx) - 0.12 and BR(c->-î,x) = 0.085, which are the present world averages [58], and the branching ratio BR(t-*-£x) has been calculated based on the free quark decays t •+• bí.v¿, bqq'.

There is still a residual uncertainty of roughly a factor of 2 in predicting the large- Pj, inclusive lepton yield because of uncertainties in the structure functions, the evolution scale Q, and the non-availability of the K-factor calculation in p + p(p) -+ Q + Q + x. We have fitted the parameters of our model [59] by fitting the UA1 large-pT (p^, £ 5 GeV) dimuon data at /s = 540 GeV [5].

In Fig. 27a we present the pp distribution from the process

P + P I

a) pp(iy'i<2.5)

10

S w \ Sri 10

10 ^V/^s^Ä = ZOTeV

^N^OTeV

i i 100 150 P} (GeV) Fig. 27 Inclusive lepton cross-sections from the fusion processes p + p •+ Q + QX(Q tr +X') at /s = 10 and 20 TeV: a) da/dp^ with the lepton-rapidity |y | < 2.5. b) integrated cross-

2 A tri er sections /(d a/dydp^)dpTdy (jy [ < 2.5). Also shown are the integrated p£ > (p|) 8S cross-sections for dileptons (= uu or ee) from p+p •+ Q + QX •* írírx'. - 509 -

integrated over |y | < 2.5 at /s = 10, 20 TeV. The heavy quark pair-production cross-

= section was evaluated with a pj cut-off, (Pp)mjJ1 20 GeV, in view of the discussion in the early part of this section. An appropriate procedure is to sum the leading logs in the region (P^m^n > Pj > ^» but tn^s resummation is not yet available for heavy quark produc• tion in hadronic collisions. The (Pjbjujjj would certainly lead to an underestimate of the lepton yield at low p^, (p^ £ 5 GeV), but presumably a positive lepton detection requirement at /s = 10-20 TeV would push the threshold p£ in excess of 5 GeV. In any case the large-p^ yield is insensitive to the (p^)m¿n cut and hence is reliably calculable. We note that the large-p¿ cross-section rises by several orders of magnitude between /s = 0.54 and 20.0 TeV. ± ± We plot the inclusive lepton (i.e. y or e ) cross-section

at /s = 10 and 20 TeV as a function of the p^ trigger. Note that the cross-section o(pp ->• u* + x) with (p¥)trigger = 5 GeV is of order 400 nb at /s = 20 TeV. The cross- section with (p^i)trigger = 250 GeV is 0.5 pb and 3 pb at /s = 10 and 20 TeV, respectively. Thus, we expect measurable cross-sections for prompt leptons with pj, in excess of several hundred GeV at the LEP Hadron Collider.

Since the inclusive-lepton cross-section at the LEP Hadron Collider is so large, the corresponding dilepton and trilepton cross-sections are also expected to be substantial. The multilepton cross-sections are of considerable theoretical interest since definite charge combinations could signify weak interaction mixings (analogous to K°-K° mixings). Theoretical calculations predict significant mixings in the B°-B° mesons [59, 60j and, with some luck, possibly also CP violation in the neutral bottom-meson mixings and decays. In Fig. 27b we plot the dilepton cross-sections as a function of (p^)trigger. For example, one expects (S, = e,y): = 50 nb + . + . at YJS = 10 TeV o-[pp(p)-*l~l~X] p L>5GeV/c = 85'nb T at Js = 2o TeV . (5.6) Thus, the prospects of analysing leptons with definite charge combinations are quite bright. In this respect of particular interest is the quantity [59-62]

a[p+.p(p)-» i+r + X] which is related to weak mixings in the neutral mesons (D° ' -*• 5°, B° -»• B°, B° .-»• B°, T° T°, etc.). The chances of observing weak mixings through a non-zero measurement of 0 0 R with definite event topologies are not bad at the present CERN Collider. - 510 -

At higher /s the contributions to the same-sign dileptons from the cascades b c •*• s and t + b->c+sas well as from the process W+ -»• tb become enormous. We could combine various vetos, for example the pp cut-off measured with respect to the jet axis to remove b •+ c -*• I leptons [63], and select jets with low invariant masses to remove the tt and W~ tb backgrounds. We will not go into these details here, except to recall that theoreti• cal estimates give [59]

RLL(bb) - 0-2 -0-3 , (5.8)

ML - oo where R (bb) is the contribution to R from bb pair production.

An amusing effect of mixing in the B-B sector is that it leads to the same-sign ener• getic dileptons in the decays of a single t-quark (T-meson). Thus, for example, we could have the decay chain as a result of BS~BS mixing (-TS) -» (BS) LV

L-^ (Ï>S) (5.9) ^ i\ x leading to same-sign energetic dileptons in a single (t-quark)-jet. The background to pro• cess (5.9) comes from the normal t-cascade itself, namely from the chain + t -> b L vL

I—» C Cfy (5.10)

U S RVL

+ However, the lepton from the cascade c •* si v0 is very soft and can be removed by a cut on the pp measured with respect to the jet axis. Techniques for separating the b and c quarks, similar to the one just described, have been successfully used in e+e experiments [64] and they can be taken over as such to hadron-hadron collisions. Perhaps an interesting feature of the events (due to the induced B mixings),

( P + P(P) -* L*C + X) same-jet is that the hadronic junk X in the jet should contain dominantly either an F+ or J/ip. De• fining the ratio [59]

(5.11) "^some-jet ~ a( p+p(p) Vü + X ) same-jet - 511 -

R trigger we expect same_jet(tt) to be ^ 0.1 [where we have assumed that the (p!p) is such that the soft c -> í,v¡¡x component has been removed]. Assuming a dimuon efficiency for t -+ uux of about II, we still have a signal of ^ (300-500) pb for observing energetic same- sign dimuons in the same-jet at /s = 20 TeV. Of tremendous theoretical interest is the

R charge asymmetry in both R and same_jet> which we define as

U + S - R (+ )-FW-> es.«) A(«)-f'ftll (~u )

A = same-jet ^* ^ ^ sarne-iefc ( "")

saw-jet ^same-jeb

These charge asymmetries are related to CP-violation. Theoretical estimates [59,61] for 6 or 8 . based on the standard Kobayashi-Maskawa matrix are of order (10~3), and so S9ïïlc—J measuring a non-zero 5 or 6 . . in hadron collisions is going to be a formidable propo- SclÏÏlC- J CL sition. However, the KM model has not yet been crucially tested in the CP violation sector but the tantalizing measurement of e'/e in the kaons [65] is something to watch for. The consequences for the LEP Hadron Collider could be that could indeed turn out to be much larger. Thus the charge asymmetry (5.12) and (5.13) is something to keep in mind. We are led to the conclusion that a good lepton detector which also measures the charge of the lepton is an essential component of all future experiments in e+e~ and hadron-hadron colli• sions. Next we turn to the problem of tagging heavy flavours. The charm and bottom hadrons have the possibility of being observed as tracks in a vertex detector since their lifetimes lie in a region where a detector having typically ^ 20 ym resolution should work rather efficiently [66]. The present known lifetimes of the D°, D*, Ac, F*, and are shown in Table 7. Noting that at these energies the impact parameter 6 = ycr = CT and assuming a resolution of 20 pm, the efficiency of a positive detection for a 4o signal are also given Table 7. We see that the detection efficiencies in all these cases are expected to be rather high. However, if the fragmentation process g •*• ce •*• D*x [and g -»- bb •*• (B,B*)x] indeed turns out to be as significant as seen by the UAl Collaboration, then we have to use the addi• tional cuts on the longitudinal and/or transverse momentum of the tracks so as to remove the soft D , B , and other hadrons. This, of course, means also a corresponding loss in the detection efficiency for the heavy hadrons originating from the fragmentation Q •*• Mx. To estimate this efficiency we need the pj, and x^ (= 2E^/Vs) distribution of the heavy hadrons at /s = 10 and 20 TeV. We have already presented the distribution (do/dpp) [pp(p) •* QQx •*" Mx) i-n Figs. 26; the corresponding (scaled-) energy distributions for the top, bottom, and charm hadrons are given in Figs. 28a,b. We remark that the fraction of events surviving an x^ cut of 0.05 (corresponding to E¡^ = 250 GeV at /s = 10 TeV) is not small. Scaling the g •+ D x distributions from /s = 540 GeV and taking into account QCD D* B* corrections will lead to only a small contamination for E ' > 250 GeV at /s = 10 TeV. - 512 -

Table 7

Measured lifetimes for the charm and bottom hadrons, the impact parameter 6 = ex at /s Z 10.0 TeV, and detection efficiency at 4cr with a resolution a = 20 um.

X 6 e ^13 (x 10 s) (urn) (»)

3.9 ± 0.4 117 ± 12 50

+ 33 72 -0 . 9 +3 6

F* 75 34 -0 • 7 -21 +0.7 A 66^ 30 c 2 2 -12

14 ± 3 420 ± 90 83

0 .1 .2 .3 A .5 .6 0 .1 .2 .3 .4 .5 .6

X=2E7ß x = 2E«/fs

2 Fig. 28 The distribution (d a/dydxn)y=o for heavy mesons (M = D, B, T) from the process p + p Q + Q + X(Q + M + X) : a) /s = 10 TeV; b) /s = 20 TeV.

Such a cut will of course also reduce the background from the minimum bias events. While still on the subject of vertex detection, the average size of a jet at the LEP Hadron Col• lider is a quantity of considerable practical importance. We have already shown the.half-

< > angle, Qy2 > in Fig. 23. We could also extrapolate from the measured half-angle of the

jet, 6i£, at /s = 540 GeV. Using 6yz (Vs = 540.GeV) = 15° and using the OCD-based guess

0 6 <5> ^ 1/f/s) - , we get <ôy2> (/s = 10 TeV) = 7° [67].

Before leaving the subject of heavy-flavour detection, we would like to recall that the top-quark jet at /s = 10-20 TeV could be identified through its semileptonic decay mode t -»• Mv¿ and by measuring (pp) with respect to the jet axis. Since the (PJ-DJ,^ has the end- - 513 -

2 point (m - m|3/2111! in the decay mx •*• rt^iv^, the contamination o£ the lepton signal from b •*• ix, c •*• ix and g ->• D* -»• £x, etc., can all be removed rather efficiently.

Finally, in this section we would like to discuss briefly the mechanism of diffractive heavy-flavour production in high-energy pp and pp collisions [16]. The diffractive process consists of the following two steps:

p + p -» X .+ p -»A, • (Q.0 • X' , (S14) where ÄQ = Qqq. This is the case when the proton is quasi^elastically scattered. The G- mirror case, when instead the p is quasi-elastically scattered, is understood. It is diffi• cult to predict the cross-section for process (5-14) from first principles, but the observa• tion of a large diffractive charm signal at the ISR suggests that, for example, the top quark diffractive production rate at /s = 540 GeV may be sizeable [54]. Assuming that such cross-sections decrease with the quark mass as m^2 for IÏ1Q/S small, and noting that the associated ACD production at the ISR is reported to exceed 100 ub, one expects a cross- section of order 10 nb for the production of a 40 GeV top meson at the CERN pp Collider. This is roughly an order of magnitude bigger than the cross-section from the fusion mechanism, which typically gives cr(tt) = 1 nb for m^. = 40 GeV and /s = 540 GeV. On the other hand, the confirmation of an approximately m^2 behaviour from the pp Collider experiments is still eagerly awaited.

Since the heavy-flavour baryon in the diffractive process (5.14) has two valence quarks as opposed to the heavy meson which has only one, the baryon is expected to keep some lead• ing role, but the meson is produced predominantly at lower to medium xp (the Feynman scaling variable) and with a rather small pp. The meson should therefore be more often detected since fragments of the ÄQ baryon are likely to be lost at not very forward angles [54].

On the other hand, the diffractive mechanism rapidly becomes unimportant much above the threshold since, being a small-pj. process, both the heavy baryon and the mesons are produced at very forward angles as /s increases. So, unless detectors are built to catch events at angles of a few milliradians, the efficiency of producing and detecting the dif• fractive events for the charm, bottom, and top quarks very quickly plummets to zero. For example, assuming that above the threshold 0Q(S) ^ In S or S01, with a S 0.5, the diffrac• tive cross-section ot (/s = 10 TeV, |n| S 3) is only a fraction of a nanobarn and is com• pletely negligible compared with the perturbative QCD processes which, for example, predict oti (/s = 10 TeV, |TI] 1 2.5) = 100 nb.

There is considerable uncertainty in scaling the mass of the heavy quark and the energy dependence in the diffractive cross-section. However, using an IIIQ/S behaviour, and an increase in the diffractive cross-section like In s above the threshold, the diffractive mechanisms are much more efficient in producing very heavy quarks. Thus at /s = 20 TeV, the process p + p + Aq + ^ + X has a cross-section of about ^ 1 nb for II)Q = 4 TeV. As we shall discuss in a later section, the perturbative QCD cross-section for pp ->- QQX, with mg = 4 TeV, is ^ 10"2 pb and hence, in comparison, is completely negligible. - 514 -

The semileptonic decays of the diffractively produced heavy meson have received special attention in the search for the top quark at the CERN pp Collider [54,68]. From the decays

(5.15) M, -> jet +1 + vL one could introduce a variable (called 'minimum invariant mass' in Ref. 54 and 'cluster transverse mass1 in Ref. 68) defined as

i -[f

(5.16)

where the four-momenta are labelled (E¿, pp., pL.)> with i = 1, 2, 3 for the jet, muon, and neutrino, respectively, and Mj^ is the transverse mass of the system composed of 1 and 2. It is obvious that M* is invariant under longitudinal boosts of the parent meson. The dis• tribution da/dM* is strongly peaked at the true invariant mass ~ the mass of the meson M. The distribution in the scaled minimum invariant mass should follow the distribution given by the free quark decay model Q •* qSLv^ (£ = M*/M) [54],

2Ç r d? /F^Ll+2*- J

with limiting behaviour

1 älT ^ —J= / Tt + 2,\ (5.18)

r r d? N/T^ç I 4 3^ showing narrow peaks at E, = 1. The minimum invariant mass method can be used to determine the mass of the heavy meson M.

6. HEAVY QUARKONIUM PRODUCTION

Two of the landmarks of the hadron-hadron collisions have been the discovery of J/TJJ and T. Both of these resonances were found as bumps in the dilepton invariant mass via the process p + p -*• J/<|>, T They have provided a test of the underlying QCD mechanisms of heavy quarkonia hadronic production [53,69]. Thus there is good reason to believe that the theoretical framework evolved for the hadronic production at FNAL/ISR energies can be - 515 - extended with some confidence to the multi-TeV range. Of course, the paramount interest in the top-quark and the tt bound states makes it mandatory to explore the toponia production at the LEP Hadron Collider energies and elsewhere. In the following we present a few typical cross-sections and distributions for the processes p + p(p) •*• M + x, where M = J/I¡J,

T, JT, nc, nD, nt in the cm. energy range 10 TeV < /s Í 40 TeV. We rely on a model which gives a reasonable description of the J/ty and T production at the FNAL/ISR energies [70]. The relevant Feynman diagrams are shown in Figs. 29a and 29b, which give rise to low-pp and large-pj productions, respectively. Several comments are in order: 2 5+1 i) The effective couplings of the various resonances ( Lj) are evaluated using the non- relativistic quarkonium-model wave functions with the parameters given in Ref. [70] and [71], except that for the toponium wave functions we adopt the result of Ref. [72]

obtained from the Richardson potential. In particular, we use rEE[JT(80) ->- e e~] =

3 13.0 keV, where JT(80) denotes the Sj-toponium ground state with a mass of 80 GeV.

If we rather believe that the value Fee/eq ^ 10 keV observed for the a>, J/i|>, and T resonances also applies to the toponium systems, then we have to reduce the toponium cross-sections (shown later) by a factor of 3. ii) The quark distributions used in the calculation are those given in Ref. [7l]. For the gluon distribution, however, we use the CDHS parametrization [39]. The large momentum scale is taken to be M2 + pp. iii) As can be seen from Fig. 29, in the lowest-order perturbation theory there is only one high-p^, process, to wit gg 3Sjg, which directly produces a 3Sj state. In all other cases, 3Sj resonances are produced via P-wave production and radiative decay, 3Pj •+3 Si + y. The latter mechanism dominates the J/ty production even at large-pp and

3 is still important for T production. Large-pp St-toponium production, on the other hand, proceeds dominantly via gg -»•3 Sjg.

a) o(a|)

b) o(a|)

Fig. 29 Lowest-order and next-to-leading-order QCD pro-

9 9 3 l 3 *l*if Vfo eJ^^' cesses for quarkonia production ( Si, S0, Pj) in had- - 516 -

iv) At high energies, qq annihilation processes contribute only at the level of < It. As a consequence, there is virtually no difference between quarkonium production rates in pp and pp collisions.

3 Figure 30a shows the expected pp distribution of the St toponium ground-state with Mj = 80 GeV at three values of the cm. energy, /s = 0.54, 10, and 40 TeV. In Fig. 30b the JT(80) pp spectrum is compared with the corresponding J/IJJ and T yields arising from

3 gg •+ S,g at /s = 10 TeV. The differential cross-sections are rather small. For JT(80) and 9 = 90° we expect about 1 pb/GeV at pp = 20 GeV, dropping to 0.1 pb/GeV at Pp = 60 GeV. Here, the leptonic branching ratio, which is expected to be of the order of 10t, is not yet included. Somewhat surprising is the prediction that at large pp the rates should increase with increasing quark mass. This is a direct reflection of the mass dependence of the wave functions. More specifically, at pp » M2, we find [70]

r\, — r\s ' (6.1)

d ¿y Pr PT PT

where R(0) is the radial wave function at the origin. Thus, assuming ree/eq

01(80) Ä 1 : 30 : 20,000

Unfortunately, owing to the small absolute yields, this feature is mainly of academic interest.

Fig. 30 The distribution (d2o7dydpj)y»o for the ground state 3Si quarkonium production in

3 pp collisions: a) Large-pT production of the toponium Si state, JT, with roj_ = 80 GeV, at

/s = 540 GeV, 10 TeV, and 20 TeV. ta) Large-pT production of J/i|i, T, and JT(80) at /s = 10 TeV. - 517 -

1 Figures 31a,b exhibit the corresponding distributions for the S0 resonances n , nb, and nt- As discussed in Ref. [70], the different spin orientation of the quarks together with the helicity-conserving quark-gluon coupling results in a relative factor dcrC'Sj)/

3 2 da( Sj) ^ §/M and thus leads to considerably larger cross-sections for nc» n^, and nt pro• duction than the ones expected for J/4J, T, and JT production, respectively. In the energy range considered, there is a gain of about two orders of magnitude. Unfortunately, the 'S,, two-body decays which give a good signature, such as rig -»• YY> have tiny branching ratios ¿ lt. This leaves a marginal chance for the nt detection. In contrast to the pat•

3 2 Ï tern of Si states at p| » M , the relative abundance of the S0 states is expected to be proportional to the masses, i.e. nc:n^:nt(80) = 1:3:30.

The integrated large-p^, yields, ( and T should be considered as lower limits due to the neglect of P-wave contributions. Also listed are the 0(a2) cross-sections, (do"/dy) 0, evaluated from the diagram in Fig. 30a. This mechanism yields small-p^, bound states, as already pointed out, but give rise to sizable cross-sections ranging from 1 nb [for nt (80 GeV)] to ^ 5 yb (for n ) at 9 = 90°. The total production cross-section for the 3Sj toponium state (80 GeV) is about 25 pb at 9 = 90°, which is sufficient to detect the J^, (80 GeV) in the dilepton channel. The e+e~ machines certainly fare much better in this respect and deserve a careful study.

Our conclusions about the heavy quarkonia production in hadron-hadron collisions in the multi-TeV range are then as follows:

3 i) The prospects of discovering the Sl toponium states through the classical bump in the dilepton invariant mass are marginal. One should build dedicated e+e" machines to study toponia spectroscopy.

2 l Fig. 31 The distribution (d o7dydprj.)v=0 for the ground state S<) quarkonium production in

pp collisions: a) Large-p-p production of riT with = 80 GeV, at /s = 540 GeV, 10 TeV,

and 20 TeV. b) Large-pT production of ric, n^,, and T>J. at /s = 10 TeV. - 518 -

Table 8

Low pp-(a) and large pp (b) resonances cross-sections at /s = 10 TeV calculated from the lowest-order diagrams of Figs. 29a and 29b, respectively.

(a) 00

da OO da ay1 y=o dpj, (pb) £nif n ^ % y=0 States min Pp (GeV) (nb) 20 50 100

\ 4700 830 7 0.1 % 320 2470 25 0.5

nt(80) 0.9 500 75 6

11 -6 J/* 500 0.4 8 x 10" 4 x 10

T 5 10 3 x 10-2 2 x lO""

J(80) 1.4 x 10-2 10 2 8 x 10"2

ii) The most favourable rate in pp and pp collisions, among the toponium bound states, is

for the state nt with a production cross-section of 0(1 nb). However, in order to

+ avoid a drastic loss in rate by searching in the mode nt Y Y> one would need a

+ very good resolution in the jet-jet invariant mass to tag the process nt •* g g"*"2 jets.

7. HEAVIER (THAN TOP) QUARK PRODUCTION

Although the standard SU(2)2 ® U(l) model, with three families of quarks and leptons, seems to describe the weak interaction phenomena remarkably well, yet clouds could be seen gathering over it. A recent measurement of the CP-violating ratio |E'/E| in the kaon decays, for example, points to a possible area of crisis for the Standard Model [65]. It is con• ceivable that the phase structure of the weak mixing matrix is more complex than just the Kobayashi-Maskawa phase [73]. One way of having a more complex phase structure is to admit a fourth family of leptons and quarks. We would then have six (Cabibbo-type) mixing angles and three (Kobayashi-Maskawa-type) phases, which could be so arranged as to avoid any immediate conflict with the data on CP violation.

From a theoretical point of view, the most stringent constraints on the masses of heavy fermions come from their contribution to the weak interaction parameter p, defined as

G (neutral current) (0 = G ( C h arged. carreo b) - 519 -

The value of p found from deep-inelastic vy and scattering data is [74]

p = 1 02 + 0 02 . (7e2) At la, the contribution of the fourth-generation fermions is bounded by Ap S 0.04. This translates into the following bounds on the fermion [75] masses + m m M -R ( Qu" Q¿ I ( * M* < (3IOGeVf (73, where the notation is obvious. As long as = (m^ - mQ^/mQ^ « 1, the absolute masses are unbound. With the assumption that perturbation theory is not to violate partial-wave unitarity [76], we obtain the following bounds [77]: < 50O GeV

™Qct < 700 GeV » (7.4) mL < qooGeV < 1000 GeV ( ™,

An improvement in the value of p would considerably reduce the limits (7.3). Thus it seems that with the CERN pp Collider on the verge of discovering the top quark [78], there still exists the possibility of observing heavier fermions between m^ and ^ 0.5 TeV. In this section we calculate the QQ production and some of their possible decay mechanisms.

We use the fusion processes 3+5>—> Q + Q to estimate heavy quark pair-production in pp and pp collisions at /s = 0.62, 2.0, 10.0, and 20.0 TeV. The results are shown in Fig. 32. Assuming a production cross-section °[PP(P) QQ] = 1 pb, 0.1 pb as a limit for observing heavy quarks, the maximum quark masses observable in a pp or pp machine are listed in Table 9. We remark that the maximum quark mass accessible in hadron colliders is^not increasing linearly with /s. A better approxima• tion for this dependence is m™^* ^ (s) ^. The fusion mechanism underestimates the heavy quark production cross-section, and so Fig. 32 and Table 9 should provide a lower limit.

Having convinced ourselves of the possibility of heavy quark production at hadron col• liders with mg » m^, we now consider their decays and related signatures in hadron-hadron collisions. To this end we write down a representation of the KM matrix due to Wolfenstein [78],

V - - 520 -

Table 9

Maximum quark mass (in GeV) observable in pp and pp collisions, corresponding to heavy quark pair-production cross-sections of 1 and 0.1 pb. The limits are based on the fusion mechanism.

PP PP

/s (TeV) 0.64 2.0 10.0 20.0 10.0 20.0

0(QQ) = 1 pb 110 240 600 850 520 780

a(QQ) = 0.1 pb 130 330 900 1300 720 1150

where the present knowledge of the bottom-meson lifetime [79] and the bound on

R = T(b + u£vA)/r(b •* (AvA) [58] gives

A L A = SINEC« 0-23 , A = 10 + 02 , P +^

Thus the entries Vht, V. , and V, are in the ratio

* I :: 7? : 4 i A3 (7.7) |VJ • |Vbe| : |Vblt| - 521 -

A generalization of the 3x3 matrix V to the 4x4 case could then he written numerically as (ignoring phases) d s b Qd.

(7.8)

where 1- means an entry slightly less than 1 in order to ensure the unitary character of the matrix V.

Assuming that the heavy quark-mass spectrum repeats itself, i.e. Q¿ < 0^, and concen• trating on the decay of the lighter quark Q^, a possible decay pattern emerges from formula (7.7):

(7.9)

Thus the decay u is expected to be negligible. There are three possibilities, depend• ing on the mass of Q¿:

1) mq^ > iity + n^: This will give rise to final states:

p + p(p)-» QdQd + x (7.10) UwV'tt -> WVjet jeb ,

with niw+jet = ny-jet = niq. The t-quark can presumably be tagged through the decays

+ t l vt (bjefc) t —» 3 jets

The Q-decay width [ignoring Ofm^/mg) terms] is

(7.11) - 522 - where io = m^/niQ. The ratio T/mg « 1; hence it should be possible to construct the heavy quark invariant mass without much distortion. The ratio r(Q -+ W^/TCQ •*• ^t) is (apart from a small phase space difference) just the ratio of the angles squared (_= I ^QdC^Q^t 12 ^ •

2 + > ) "fy ~t mQ > ~W: This is a particularly interesting range. The two decay modes

wrea l +• C (7.12) and

(7.13) Q -> V/'vir. + t

could compete with each other. The relative rates (ignoring the W-pole enhancement) [80] are given by

(7.14)

Cb " ríQ^W^t) GmF *[3a firnißJ + ^imî/m;)] where f(x) - l - £?xz + 8x¿ - x-28 ^ x*1 Lax and qXm^/mq) is the phase-space factor in the decay Q ttb. The ratio in Eq. (7.14) is plotted in Fig. 33 as a function of the heavy quark mass for three representative values of the quantity IV^/VQ | = X, X/2, and X2. Below m¡y < MQ, both Q -»- W"c and W~t transitions are virtual. It is amusing that if the ratio I^Qc/^Qt^ ~ ^en tne virtual transition (7.13) dominates over the decay of Q into a real W* boson and a (c,u) quark (7.12) Q8l].

t

Fig. 33_ The relative rate T(Q -»• W~ + c)/ T(Q -»• W + t) for the decay of a heavy quark as a function of mg for three values of the

angle ratio v v = X x and x l Qc/ Qtl c» c/2> c- mW 100 IV m, 150 200

m0 (GeV] - 523 -

Since the mixing matrix (7.8) predicts such an angle ratio, it is quite plausible that the decay mode (7.13) is indeed the dominant Q-decay mechanism. We would then have the follow• ing final states: b + p ( p) —*Q+Q+X t~E * Jets tt f l*X + jets C7.15) bl + tT X The final states (7.15) are not as clean a signature as the ones provided by the decay Q -•• W + jet. The multiplicity of jets in (7.15) would depend on the ability to separate overlapping clusters but in principle could be up to four (both non-leptonic decays of Q) and two (one non-leptonic, one semileptonic decay).

The virtual transiton (7.13) also involves the decay mode [80]

Q —> b t + t C7.16) if allowed by phase space. Since the top quark mass now very probably seems to be less than 50 GeV [82], the threshold required for (7.16) is around m^ = 80-100 GeV. The transi• tion (7.16) affords the possibility of associated toponium production in e+e~ and hadronic collision which could be detected via leptonic modes of J^,:

(7.17) eel i L-*x

I > Tr + (B,B",...) The branching ratio for (7.16) is given by

VIOLAI +bb) BR(Q-»t + bb) =

(7.18)

l This ratio could be as large as ^ /5. The branching ratio for Q •* (JT, J^,, ...) + b is a fraction of (7.18) which can be estimated by evaluating the overlap integral,

I = , and could be as large as 'v Vi0. Thus it is not unreasonable that a branching ratio such as the one in the b quark decay, b -»• J/ty + s, may be seen, i.e.

BR[Q JT,J^, ... + b] = 0(11), giving

a(p + P(P)-*Q+Q+X) * 0-02 a(p + p(p)-*Q*Q + X)

J^. + b . (7.19) - 524 -

For /s = 20 TeV pp (or pp) and mg =¡ 120 GeV, the cross-section (7.19) could be as large as (50-100) pb, which, compared to the standard QCD processes, is bigger by a factor of (20-50). Again for the mass range of interest, namely m^ + mt > IIIQ > m^, the diffractive production process

p + P(P) Aq + RQ + X

U JT +(BJET) (7-20)

could easily beat the fusion estimate (7.19). How much of the diffractive cross-section can actually be seen depends on the ability of forward detection.

3) We will briefly mention the possibility of the existence of a heavy quark in the range m^ > mg > mt. The decay of such an object would probably be dominated by the mode

Q —* t + W^>.

^ L"vL , Ha-, cs (7.21)

(see, however, Fig. 32, for the ratio V t in this range) with the width given by

T - =1 C F (M /M ) I T E VQtr (7.22) GF r„ -

The lifetime would be too small to measure unless \Vq¡\ < X". For example, for nig = 70 GeV,

3 Vqt ^ X , one expects

6 r(™Q* 70GeV) * 5eV T0 & 1-2 * lO~' s. (7.23)

The experimental signatures would be

p + p (p) Q + Q. + X

U T + T + k- jets (7.24) C- X + 1*1" X - 525 -

Again, the diffractive mechanism would probably give a bigger observable cross-section at the CERN SPS (/s = 630 GeV) and the Fermilab Tevatron (/s = 2 TeV) with the characteris• tic signature

p + p —» A,, + Ma + X (7.25) U L"vt+ t and the charge correlation (£~ with p) opposite [54] to the one expected for the tt case.

The existence of a fourth generation of leptons and quarks has rather interesting con• sequences for the search for the Higgs boson or technipion. Since the decay of the lighter

l of the quark doublets (which we have taken to be Q = - /3 quark, Q^) is expected to be greatly suppressed owing to weak angles, the vector heavy-onia VfQ^Q^) would decay by the usual strong and electromagnetic interactions without any significant weak decay contribution. In that case the radiative decays [83]

V(QDQD) H° * V and/or

V (QdQd) -* TU'° + Y C7.26) would become a significant mode. Thus the relative branching ratio for the Higgs + y mode compared to the e+e mode would be

QQ (7.27)

> I for m0>/40GeV, mH4m2

The branching ratio for the mode involving a technipion, IT'0, and a photon is also similar [84]

p ( (<35)-v > e*e") 4.02TC0C

where np, is the number of techniquark doublets. The processes (7.26) allow us to search for a H°(Tf/0) nearly up to the vector boson mass m^, which makes it probably the only viable mechanism for looking for an H° (IT'0) in the mass range m^ < m^o, m^/o < 2 [80]. The existence of a seventh quark is therefore very welcom in the search for a Higgs/techni- pion. - 526 -

Finally, in this section we briefly discuss the decay of the heavier of the fourth

quark doublet, which we have assumed to be 0^. The production and decays of QUQU could involve up to four W~ bosons via the chain pip) p + -»~L* u Q, * * Qu, + * _

leading to p + p (p) -> wVwV + x (7.30) t X - jets, ivl

This mechanism could provide a significant background for multiple W* production, often advocated as tests of the underlying mechanism of spontaneous symmetry breaking.

8. SUMMARY

In this report we have discussed the extrapolation of hard collisions in pp and pp col• lisions at /s = 10-20 TeV relevant to the LEP Hadron Collider. We have used the UA1/UA2 data and information available from e+e~ annihilation and deep-inelastic scattering experi• ments to test the theoretical framework and fix the various parameters. The standard SU(3) ® SU(2) ® U(l) theory describes a very vast amount of experimental phenomena rather successfully, and so as far as the standard hard collisions are concerned, extrapolations to the LEP Hadron Collider energies should not be too much off the mark.

Starting from a study of parton-parton luminosities at the present pp and future pp/ pp colliders, we have found that, unless very massive objects with masses m//s » 0.1 are being sought for, the hard-hadronic collisions would be dominated by gluon-gluon and gluon- quark initiated processes. Thus, if hard collisions at the parton centre-of-mass energies /s = 1-2 TeV are the main focus of the LEP Hadron Collider, then there is no compelling case for the pp option. Using the luminosity functions, we have calculated production rates and distributions for a variety of hard hadronic collisions which would test the standard model at Q2 ¿ 102 TeV2. At the same time, calculations presented in this report should pro• vide useful background rates for new physics, for example, as expected in supersymmetric and composite theories. The standard processes that we have dealt with here in some depth, in• clude production of prompt leptons, prompt photons, jets, W~, Z°, pair production of gauge

1 bosons W±Z°, W ^, W^, Z°Y, Y*Y> heavy quarkonia, heavy quarks, and some consequences of weak interaction mixings.

Mostly we have studied the standard hard collisions, but occasionally we have also discussed such issues as the production of even heavier bosons (W'*, Z'°) which may be identified with the right-handed bosons W^, Z* existing in left-right symmetric models. In the same vein we have also presented possible phenomenology of the next generation of quarks - 527 -

(i.e. extension of the standard three-family model). Depending on the weak mixing matrix, a very interesting pattern of decays (and hence final states) involving the next heavy quark may emerge. The existence of such a quark opens a window on the search for the Higgs boson (or technipion) which may not be accessible otherwise. Depending on the heavy quark mass, the decay of the next quark may admit the mode Q •+ ttb leading to a rather substantial source of toponium production in high-energy hadron-hadron and e e" collisions.

Finally, we hope that the information contained in this report will be useful to our experimental colleagues when they are designing their detectors for pp and pp collisions at high energies.

REFERENCES

[l] G. Arnison et al. (UAl Collaboration), Phys. Lett. 122B, 103 (1983); G. Banner et al., (UA2 Collaboration), Phys. Lett. T2lB~, 476 (1983). [2] G. Arnison et al. (UAl Collaboration), Phys. Lett. 126B, 398 (1983); P. Bagnaia et al. (UA2 Collaboration), Phys. Lett. T2§B, 130 (1983). [3] M. Banner et al. (UA2 Collaboration), Phys. Lett. 118B, 203 (1983); G. Arnison et al. (UAl Collaboration), Phys. Lett.~~T2"3B, 115 (1983). [4] C. Rubbia (UAl Collaboration), talk given at the Neutrino '84 Conf., Dortmund (1984). D. DiBitonto, talk given at the VIII European Symposium on Antiproton Interactions, Durham (1984). r5~J C. Rubbia, Proc. 4th Topical Workshop on Proton-Antiproton Collider Physics, Berne, 1984 (CERN 84-09, Geneva, 1984), p. 218. [6] See, for example, M. Jacob, CERN preprint TH-3807 (1984). [7] Sally Dawson, E. Eichten and C. Quigg, Fermilab Report 83/82-THY/LBL-16540 (1983); J. Ellis et al., these proceedings; R.D. Peccei et al., these proceedings. [8] G. Arnison et al. (UAl Collaboration), Phys. Lett. 136B, 294 (1984). [9] G. Arnison et al. (UAl Collaboration), Phys. Lett. 129B, 273 (1983). [10] P. Aurenche and R. Kinnunen, Phys. Lett. 135B, 493 (1984); J.L. Rosner, P. Langacker and R.W. Robinett, Enrico Fermi Institute Report EFI 84/8 (1984). Til] B. Humpert and W.L. Van Neerven, Phys. Lett. 95B, 456 (1980); P. Aurenche and J. Lindfors, Nucl. Phys. B185, 274 (1981); G. Altarelli, R.K. Ellis, M. Greco and G. Martineiii, CERN preprint TH-3851 (1984). For QCD corrections to the Drell-Yan processes, see G. Altarelli, R.K. Ellis and G. Martinelli, Nucl. Phys. B157, 461 (1979); C.T.H. Davies, B.R. Webber andlO. Stirling, CERN Preprint TH-3987 (1984); R.K. Ellis, G. Martinelli and R. Petronzio, Nucl. Phys. B211, 106 (1983); See also Proc. Drell-Yan Workshop, Batavia, 1982 (Fermilab, Batavia, IL, 1983). [l2] C.W. Fabjan, Proc. Int. Conf. on Physics in Collisions, ^> Como, 1983 (Ed. Frontières, Gif-sur-Yvette, 1984), p. Ill; E.L. Berger, E. Braaten and R.D. Field, Nucl. Phys. B259, 52 (1984). [13] B.L. Cambridge, J. Kripfganz and J. Ranft, Phys. Lett. 70B, 234 (1977); R. Cutler and D. Sivers, Phys. Rev. D 17, 196 (1978); Z. Kunszt and E. Pietarinen, Nucl. Phys. B164, 45 (1980) and Phys. Lett. 132B, 453 (1983); B. Humpert, Phys. Lett. 140B, 105 (1984) añcTCERN preprint TH-3934 (1984); A. Ali, E. Pietarinen ancTTO. Stirling, Phys. Lett. 141B, 447 (1984). [14] G. Ingelman, CERN preprint TH-3969 (1984); G. Ingelman and D.E. Soper, CERN preprint TH-3970 (1984); See also T. Akesson et al., preprint CERN-EP/84-77 (1984), Report of the Jet Study Group at this Workshop. - 528 -

[15] .V. Barger and R.J.N. Phillips, Univ. Wisconsin, Madison, Report PH/155 (1984); E.W.N. Glover, F. Halzen and A.D. Martin, Durham Report DTP 84/2 (1984); R. Kinnunen, preprint CERN-EP/84-19 (1984); E.L. Berger and D. Soper, CERN preprint TH-3850 (1984), to be published in Nucl. Phys. A. Ali, B. van Eijk and E. Pietarinen, CERN preprint in preparation. [16] D. DiBitonto, Proc. Int. Conf. on Proton-Antiproton Collider Physics, Madison, 1981 (AIP Conf. Proc. No. 85, New York, 1982), p. 26, and references quoted therein; E.L. Berger, D. DiBitonto, M. Jacob and W.J. Stirling, Phys. Lett. 140B, 259 (1984); S.J. Brodsky, H.E. Haber and J.F. Gunion, Stanford preprint SLAC-PUB-3300 (1984). [17] A. Ali and C. Jarlskog, Phys. Lett. 144B, 266 (1984). [18] F. Halzen, Proc. 21st Int. Conf. on High Energy Physics, Paris, 1982 [j. Phys. (France) 43, Suppl. C12, Paris, 1982], p. C3-381; R. Baier and R. Rückl, Phys. Lett. 102B, 364 (1981), Z. Phys. C 19, 251 (1983), and Nucl. Phys. B208, 38 (1982). ~~ [19] V. Barger, H. Baer, K. Hagiwara and R.J.N. Phillips, Univ. Wisconsin, Madison, Report MAD/PH/150 (1984); A. Ali, report in preparation; J.L. Rosner, CERN preprint TH-3910 (1984). [20] M. Glück, E. Hoffmann and E. Reya, Z. Phys. C 13, 119 (1982) (called GHR parametriza- tion). [21] D. Duke and J. Owens, Phys. Rev. D 30, 49 (1984) and Erratum; See also E. Eichten, I. Hinchliffe, K. Lane and C. Quigg, Fermilab Report 84-17-T (1984). [22] G. Arnison et al. (UA1 Collaboration), Phys. Lett. 139B, 115 (1984). [23] J. Ellis and H. Kowalski, CERN preprint TH-3843 (1984); S. Dawson et al. and J. Ellis et al. in Ref. 7; See E.L. Berger and M. Jacob, CERN preprint TH-3919 (1984) for a possible explanation of exotic events in terms of coloured meson production. [24] P. Aurenche et al. in Refs. 10 and 11. [25] J.R. Hansen, same Proc. as Ref. 5, p. 20. [26] J.C. Pati and A. Salam, Phys. Rev. Lett. 31, 661 (1973) and Phys. Rev. D 10, 275 (1974); R.N. Mohapatra and J.C. Pati, Phys. Rev. D 11, 566 and 2558 (1975). [27] G. Beall, M. Banden and A. Soni, Phys. Rev. Lett. 48, 848 (1982); R.N. Mohapatra, G. Senjanovic and M. Tran, Phys. Rev. D 28, 546 (1983); G. Ecker, W. Grimus and H. Neufeld, Phys. Lett. 127B, 365 and 152B, 467 (1983), and Nucl. Phys. B229, 421 (1983). [28] H. Harari, Proc. 10th SLAC Summer Institute (SLAC Report No. 259, Stanford, 1982), p. 121. [29] P. Bagnaia et al. (UA2 Collaboration), preprint CERN-EP/84-40 (1984). [30] K.O Mikaelian, Proc. 1975 Isabelle Summer Study (BNL-20550, Brookhaven, 1975), p. 340; R.W. Brown and K.O. Mikaelian, Phys. Rev. D 19, 922 (1975); R.W. Brown, D. Sahdev and K.O. Mikaelian, Phys. Rev. D 20, 1164 (1979). [31] K.O. Mikaelian, M.S. Samuel and D. Sahdev, Phys. Rev. Lett. 43, 746 (1979); R.W. Robinett, Univ. Wisconsin, Madison, Report MAD/TH/83 (lM3). [32] B. Humpert, Phys. Lett. 135B, 179 (1984). [33] H.J. Schnitzer, Nucl. Phys. B193, 195 (1981); J.M. Gipson and H.C. Tze, Nucl. Phys. B183, 524 (1981); J.M. Gipson, Virginia Polytechnic InstTl-port VPI-HEP-83/1 (1983); R.N. Cahn and M. Suzuki, Phys. Lett. 134B, 115 (1984). [34] M.S. Chanowitz and M.K. Gaillard, Lawrence-Berkeley Laboratory Report LBL-17496/UCB- PTH-84/5 (1984). [35] P.B. Bagnaia et al. (UA2 Collaboration), Z. Phys. C 20, 117 (1983); A.T. Clark, private communication. [36] P. Aurenche, A. Douiri, R. Baier, M. Fontannaz and D. Schiff, Phys. Lett. 140B, 87 (1984). [37] D.W. Duke and J.F. Owens, Phys. Rev. D 26, 1600 (1982); Erratum in D 28, 357 (1983). [38] R. Baier, J. Engels and B. Peterson, Z. Phys. C 2, 265 (1979). [39] M. Abramowicz et al., Z. Phys. C^12, 289 (1982). - 529 -

[40] B.L. Cambridge, J. Kripfganz and J. Ranft in Ref. 13; R. Horgan and M. Jacob, Nucl. Phys. B179, 441 (1981). [41] B. Humpert, Phys. Lett. 140B, 105 (1984) and CERN preprint TH-3934 (1984). [42] A. Buras and K. Gaemers, Nucl. Phys. B152, 269 (1978); J.F. Owens and E. Reya, Phys. Rev. D T77~3003 (1978); (called BGOR parametrization). [43] M. Glück and E. Reya, Nucl. Phys. B150, 76 (1971); J.F. Owens and E. Reya in Ref. 42; (called GROR parametrization). [44] R. Baier, J. Engels and B. Petersson, Z. Phys. C 2, 265 (1979) (called BETAL parametri• zation) . [45] A.H. Mueller, Phys. Lett. 104B, 161 (1981); B.I. Ermolaev and V.S. Fadin, JETP Lett. 33, 269 (1981); A. Basetto, M. Ciafaloni and G. MarchesiriTT Phys. Reports 100, 201 (1983); B.R. Webber, preprint CERN TH-3569 (1983). [46] R.D. Field and S. Wolfram, Nucl. Phys. B213, 65 (1983); G. Marchesini and B.R. Webber, Nucl. Phys. B238, 1 (1984); B.R. Webber, Nucl. Phys. B238, 492 (1984); R. Odorico, Nucl. Phys. B~2~~ 381 (1983); T.D. Gottschalk, Nucl. PhyiT B214, 201 (1983). [47] See T. Âkesson et al. in Ref. 14. [48] B. Andersson et al., Phys. Rep. 97, 31 (1983); T. Sjöstrand, DESY Report DESY-T-84-01 (1984). [49] R.D. Field and R.P. Feynman, Nucl. Phys. B136, 1 (1978); A. Ali, E. Pietarinen, G. Kramer and J. Wïïlrodt, Phys. Lett. 93B, 155 (1980). [50] J.C. Collins and D.E. Soper, Nucl. Phys. B193, 381 (1981) and B197, 446 (1982). [51] Ch. Berger et al. (PLUTO Collaboration), Phys. Lett. 99B, 292 (1981); D. Schlatter et al. (Mark-II Collaboration), Phys. Rev. Lett. 49, 251 (1982); B. Adeva et al. (Mark-J Collaboration), Phys. Rev. Lett. 50, 2051 (1983); H.J. Behrend et al. (CELLO Collaboration), DESY Report 82-022 (1982). [52] V. Barger and R.J.N. Phillips and E.W.N. Glover et al. in Ref. 15. V. Barger and R.J.N. Phillips; E.W.N. Glover et al.; and R. Kinnunen, in Ref. 15; R.J.N. Phillips, Rutherford Report RAL-84-033 (1984); A. Ali and C. Jarlskog in Ref. 17; F. Halzen and A.D. Martin, Univ. Durham preprint DTP 84/14 (1984), and references quoted therein. [53] See, for example, F. Halzen in Ref. 18. [54] E.L. Berger et al. in Ref. 16. [55] B.L. Cambridge, Nucl. Phys. B151, 429 (1979). [56] R. Frey, same Proc. as Ref. 5, p. 232. [57] C. Peterson et al., Phys. Rev. D 27, 105 (1983). [58] See, for example, S. Stone, Proc. Int. Symposium on Lepton and Photon Interactions at High Energies, Ithaca, 1983 (Cornell Univ., Ithaca, NY, 198 ), p. 203. [59] A. Ali and C. Jarlskog in Ref. 17; A. Ali, E. Pietarinen and B. van Eijk, in preparation. [60] A. Ali and Z.Z. Aydin, Nucl. Phys. B148, 165 (1978). [61] For a recent theoretical update see A.J. Buras, W. Slominski and H. Steger, Max- Planck Institute Preprint MPI-PAE-PTH-7/84 (1984) and references quoted therein. [62] A. Pais and S.B. Treiman, Phys. Rev. D 12, 244 (1975); L.B. Okun, V.l. Zakharov and B.M. Pontecorvo, Nuovo Cimento Lett. 13, 218 (1975); J. Ellis, M.K. Gaillard, D.V. Nanopoulos and S. Rudaz, Nucl. Phys.~B"131, 285 (1977). [63] A. Ali, Z. Phys. 1, 25 (1979). [64] See, for example, J.G. Branson, MIT Technical Report 133 (1983). - 530 -

[65] Recent measurements on |e'/e| in K decays show a (1-2) a deviation from the Kobayashi- Maskawa predictions. B. Winstein, talk given at CERN, Geneva (1984). [66] See C. Baltay and H. Gordon, Proc. 1982 DPF Summer Study on Elementary Particle Physics and Future Facilities, Snowmass, 1982 (AIP, New York, 1983), p. 500. [67] The relation between Su and Qy is approximately 6/2 = /Qy (in radians). The number <^1/>/s-540 GeV ~ based'on private communication from the UAl and UA2 Collabora• tions. [68] V. Barger, A.D. Martin and R.J.N. Phillips, Phys. Lett. 125B, 339 (1983). [69] R. Baier and R. Rückl, Proc. Second Moriond Workshop on New Flavours, Les Arcs, 1982 (Ed. Frontières, Gif-sur-Yvette, 1982), p. 79; Proc. Rencontre de Moriond on Gluons and Heavy Flavours, La Plagne, 1983 (Ed. Frontières, Gif-sur-Yvette, 1983), p. 375. [70] R. Baier and R. Rückl, Phys. Lett. 102B, 364 (1981) and Z. Phys. C 19, 251 (1983). [71] R. Baier and R. Rückl, Nucl. Phys. B208, 38 (1982). [72] J. Kühn and S. Ono, Z. Phys. C 21, 395 (1984). [73] M. Kobayashi and K. Maskawa, Progr. Theor. Phys. 49, 652 (1973). [74] J. Kim, P. Langacker, M. Levine and H. Williams, Rev. Mod. Phys. 53, 211 (1980). For an updated analysis see W.J. Marciano and A. Sirlin, Brookhaven Report BNL-33819 (1983). [75] M. Veltman, Nucl. Phys. B125, 89 (1977); M.B. Einhorn, D.R.T. Jones and M. Veltman, Nucl. Phys. B191, 146 (1981). [76] M.S. Chanowitz, M.A. Furman and I. Hinchliffe, Phys. Lett. 78B, 285 (1978) and Nucl. Phys. B155, 402 (1979). [77] V. Barger et al. in Ref. 19. [78] L. Wolfenstein, Phys. Rev. Lett. 51, 1945 (1983). [79] N.S. Lockyer et al. (Mark II Collaboration), Phys. Rev. Lett. 51, 1316 (1983); E. Fernandez et al. (MAC Collaboration) Phys. Rev. Lett. 51, 1022 (1983). [80] A. Ali, report in preparation. [81] The decay Q W + q has also been considered by J.L. Rosner, CERN preprint TH-3910 (1984). [82] M. Delia Negra, CERN EP Seminar (1984); See also Ref. 4. [83] F. Wilczek, Phys. Rev. Lett. 39, 1304 (1977). [84] A. Ali and M.A.B. Bêg, Phys. Lett. 103B, 376 (1981). - 531 -

SOFT PHYSICS WITH A SUPERCOLLIDER

B. Andersson Department of Theoretical Physics, University of Lund, Sweden

Abstract

I discuss a set of possible, more or less adventurous, physics scenarios for the soft physics of a supercollider of 10-20 TeV cms energy. I also present extrapolations of the sizes of different quantities to these immense energies. One should always note that whether we like it or not, some 95-99 % of the cross-section is soft physics at all energies.

0. Introduction and some motivation

It is rather evident that nobody in the present physics establishment would advocate the building of a supercollider in order to study what goes on in "soft physics". Nevertheless, whether we define soft physics as "what goes on at small transverse momenta with respect to the beams" or dub it slightingly as "ln(s)-physics" we cannot get away from the fact that the overwhelming amount of the cross-section stems from these events.

Generally theorists tend to believe that we have found the theory of hadronic interactions in QCD. Therefore it is at present more a question of obtaining the means to compute inside the theory than to worry about the analysis of soft physics data. Fortunately experimentalists (and some phenomenologically inclined theorists) tend to be more humble and more inquisitive so the analysis goes on, and some of the stuff presented in here stems from such work.

Inside different perturbative schemes of QCD we are as a matter of fact at present only able to calculate 1-5 % of the cross-sections (high p± and Drell-Yan processes) and the remaining parts of general medium and low p± physics is not accessible for analysis from basic theory. There is a set of phenomenological schemes which have been proposed, arid I will discuss some of them. I will in particular use them to determine - 532 - some of the main parameters like cross-sections, mean multiplicity with its dispersion,mean p± with fluctuations. I should already now warn you that there are considerable risks for horrible "pile-up scenarios" which may drown signal of the order of 10-100 pb (where some of the suggested theoretically interesting physics for a super• collider is supposed to be).

Except for "conventional" scenarios I will also bring up some possible but more adventurous ones. After all we should remember that the results of a new accelerator has hardly ever been those we expected before the building of it.

I feel that I would like to apologize at this point to those whose work I have not included but also to those I may have included but due to time-limitations and my own lack of knowledge have included in at distorted way.

The contents of this talk is as follows.

I Cross-sections II Some theoretical scenarios A Supersoft B Soft arid no-dynamics C Soft and adventurous (These scenarios II A and £ are built around a "conventional" energy density for hadronic interactions of around 1 GeV/fm which is known from e.g. "the string-tension" ., "the bag- pressure" and "the Regge-slopes" while II B in general has no such setting.) D Hardly soft D1 Quark-gluon plasmas D2 Diffraction (These two scenarios are basically soft but in these cases the energy-densities are probably much larger.) III So what do we expect for pileups at 10 TeV? IV The cosmic bravados. - 533 -

I. Cross-sections

I have for this subsection had the great benefit of expert advice from André Martin. As he is also a participant and a speaker, you will learn all the interesting physics in his talk and I will be satis• fied with just a few remarks.

It is an unfortunate fact that the span in the expected values for

°tot at t'ie suPercoll1cler is from our present knowledge from =* 93 to 120 mb (20 TeV). We should note, however, that if anyone of my very clever experimental colleagues could device a detector setting able to measure p = Re(f)/Im(f) (with f the forward amplitude) to an accuracy of 0.01 at the SPS collider, then the possibilities would be sincerely limited. The reason for such a large span is that none of the available models is in very good agreement with data. Pre• sumably only the critical Pomeron-Model is ruled out by the observed energy dependence between ISR ana d the SPS-collider. In geometrical

as scaling a basic result is that e-\/°t0t well as ato+/B(t=0) (with B(t=0) the forward slope) should be constants and each of them is now

a known to increase. The ratio e-\/\0^ increases about 10 % from ISR to the SPS-collider but it is still a far cry from the Chou-Yang and Bourrely-Soffer-Wu kind of eikonal models in which the nuclear

opacity increases ("the nucleón becomes black") and therefore ae-|/atot approaches ¿.

An interesting and very complete recent investigation by Henzi-Vallin tells us, however, that the nucleón is evidently becoming blacker but also edgier, i.e. the overlap function increases in the middle (break of geometrical scaling) and it also has a peak in the increase between 0.7 and 1.5 fm, i.e. at its edge. It is not known what causes these increases, but the results I quoted above stem from a quadratic logarithmic fit to the forward amplitude performed by Bourrely and Martin. A corresponding result for the diffraction peak is a forward slope B(t=0) between 16 and 30 (GeV~2). If this latter results is true, then you will have to measure down to about 1/20 of a mr to deduce the optical point] - 534 -

II A. The supersoft theory scenario

I have learned about these possibilities from my friends Tran Than Van and Capella in Orsay and from a collaboration between LAPP (Aurenche) Siegen (Bopp) and Leipzig (Ranft). There is also a russian group (Kaidalov; Ter Martirosyan). In this case the energy concen• tration and the particle production ability is everywhere the same but in a catchy way we could say that there is more of this same stuff, i.e. there are more independent strings when the energy increases. In general there is a need for input parameters i.e.

for °&-\/\Qt as well as atQt (although there is a very weak dependence on these quantities) in order to compute the mean number of strings (use is made of perturbative Reggeon calculus). The mean multi• plicity estimates from these calculations lead to 55-60 charged particles (Orsay), and 65 (LAPP-Siegen-Leipzig) at 10 TeV. For the

^¡~(n=0), i.e. the central multiplicity per unit pseudorapidity, the corresponding numbers are 4.2 and 5.0 while the cross-sections for three and more times the mean multiplicity in all models increase a few per mille to now 10-12o/oo at 10 TeV.

I would like to draw your attention to- the fact that UA(5) has most definitely shown a break of KNO-scaling for their data at the SPS- collider and the question of the size of the large multiplicity tails is of large interest for everybody trying to design detectors for the supercollider. It is perfectly feasible to rephrase the problem into a problem of "cluster-multiplicity variations" as UA(5) has done, but nevertheless the question is still around. Hopefully the new run at around 1 TeV of the SPS-collider as well as the energy- doubler setups of Fermilab will tell us if the large multiplicities stem from a supersoft scenario or whether there is something else coming up.

Some problems, i.e. the long range multiplicity correlations (forward- backward correlations) as well as the quick fall off of the pseudo- rapidity (note that the available phasespace at the SPS-collider is about 6 units both in forward and backward directions) is under• standable inside this supersoft scenario. The explanation is that it is "sea-sea-strings" that populate the center of rapidity region and that the energies involved in such strings are very moderate compared to the total energies. - 535 -

Another way of thinking (which admittedly does not at present include much predictions on the population of different parts of phasespace) is

II B. A soft and no-dynamics scenario

This has been advocated by P. Carruthers and coworkers (Los Alamos) and in principle tells us that hadronic multiplicity distributions are interesting but have nothing to do with any particular dynamics.

Taken to its extreme (which according to UA(5)-parametrizations for all energies is wrong) Carruthers and coworkers have proposed that there is a connection between hadronie multiplicity distri• butions and the chaotic onset of turbulence in flows as well as the multiplicity distributions of galaxies. In all cases there is a number k which describes "the number of sources"-emitters each with a chaotic, i.e. gaussian random variable intensity. Carruthers and coworkers have related the number k to a number D which is supposed to be the same in all the above contexts (thaotic selfsimilar dissipative systems")

Generally the multiplicity distributions are then related to k as negative binominal distributions of order k (or if you like Bose- Einstein distributions).

It is easy to show (and this has been known for a long time) that such a multiplicity distribution is close to a KNO-scaling function - 536 -

We note the experimental result that for |n|<1.5 the UA(5) results are very well described by ij^ for k=2 while there are claims that k=4 also fits the "all n"-data. The increase in k with ñ as suggested by Carruthers (eq. (1)) is, however, according to UA(5) parametrizations rather opposite to the experiments at lower energies. Similar parametrizations with negative binomials have been proposed by Liu andMengwith the idea that more and more of the multiplicity distributions should stem from central "fireball production" with k=2 which then would lead to immensely wide KNO distributions (again around 10 o/oo of the cross-sections is for n>3-ñ).

A picture describing presently known data from FNAL, ISR and UÂ(5) together with fits and predictions of Liu and Meng is included as Fig. 1.

My next scenario is

II C. A soft but adventurous scenario

This has been discussed by the Lund group. The main idea is that even if a confined force-field of e.g. string character in its own (local) rest system may have ordinary energy-density (i.e. 1 GeV/fm) and therefore each part of the string produces "the ordinary amount" of particles (essentially in a Poissonian way) the different parts may have relative motion of a partially coherent kind. Then the results will be larger multiplicities (more, particles are produced per unit rapidity as measured in an outside rest system when the string moves in that direction) and more transverse momentum from the string motion. Actually, there is an interesting competition between the use of the string energy momentum for particle production and for accelerating the particles. For "small" energies, i.e. up to cms energies of order 25-30 GeV most part of the available phase-space is composed of fragmentation regions which are dominated by the (mostly forward moving) breaking of the initial beam hadrons. Then there is another scale of say 30-150 GeV where a few units in rapidity in the center may be available for the emission of either one central "swinging" string or as in the supersoft scenario.described above,a set of independent small strings. - 537 -

The idea of a swinging string is closely related to the gluon model of Lund - a gluon drags along the string field and in case many gluons move together, even if each is rather soft, the whole string will be dragged out in a bent manner. We feel in the Lund group that the symmetric model proposed a year ago defines the only possible consistent classical stochastic process for breaking up a string-like force field. What we have found lately is a non- perturbative approach to define "the string state" which "breaks up". It is a formula which (although it is at present only appli• cable to e+e~ annihilation events) interpolates between all known QCD perturbative results (in particular exhibits the reason for the strong ordering in som angular variables according to Mueller et al) and therefore predicts the probabilities for e.g. a force field composed out of many local gluonic excitations. It is interesting to note that for the range 30-150 GeV it seems favorable to pro• duce a transverse eigenmotion of around 1 GeV (per rapidity unit) jn the string and produce more particles but not very much more transverse momentum for each particle. Further up in energy the transverse eigenmotion becomes larger and not only the multiplicity grows but also the transverse momentum of each particle. It is difficult to extrapolate the results to a supercollider. If we should judge from the change between the ISR (.increased multiplicity but the increase stems from

small p±-particles) and the SPS-collider (where the main bulk of the

newly produced particles seems to have essentially larger p±), then at a supercollider with a factor 20-40 times larger energies again there should be just some swinging! Whether the string will produce music is, however, an open question.

I will now go to scenario

II D. Hardly soft

where the idea is to use soft interactions to beat the ordinary energy density. Several authors (V. Hove and Hagedorn) have advoca• ted the possibility that weare already witnessing the onset of the phase transition to a quark-gluon plasma in the center of phase- space of the SPS-collider. In particular the rise of mean transverse

momentum p± as a function of ^ for |ri|<2 has been used as an indi• cator. The idea is that multiplicity should behave as entropy and in a hydrodynamical treatment should exhibit a singularity ~ ' - 538 -

when the temperature T approaches TQ. On the other hand p± is expected to increase with temperature but not to behave singular at the transition temperature. Therefore in a plot of p. against dN

^ we expect a rise of p± until we approach TQ when the curve flattens out and this is also seen in particular in the collider data.

One sjiould, however, on the other hand remember that the number of partons with a value of may be around 10-15 for a proton. Then in each of the incoming particles at the collider such partons will have energies above 2.7 GeV and evidently a set of such partonic collisions will produce a lot of activity (presumably incoherent) in the center. Generally such a scenario is of "peasoup" character as compared to the above mentioned phase transition ideas.

My next comment is on

II D2. Diffraction

My generation of theorists have spent 15 years of their lives parametrizing "the Pomeron" but we actually do not know very much about what the Pomeron really does to a hadronic state. If we take the Good-Walker picture of diffractive scattering then a hadronic state is a superposition of eigenstates of "interaction". When some of these states are "absorbed" by ordinary low-p^ interaction then the remaining state is no longer the original hadron.

So what is it? One way of looking upon it is to consider diffraction as a measuring process. Suppose the wavefunction of one of the original hadrons is ifi (describing a hadron on the mass-shell):

and we use X and t for the position and time coordinates. Then if an "absorber" passes by moving very quickly with YM. (the light velocity c=1) then the absorber will measure the quantity

Xrt"O (O

We note the elementary commutation relations - 539 -

rEJ= 0 which means that a determination of x-t forces the wavefunction no longer to be an eigenstate of p+f and we end up with a mass distri- 2 bution in M for the final state. If we assume that there is no given scale in this distribution then we expect

JL é£ ~ —

At a supercollider the presently known diffractive masses (at the ISR up to 4-5 GeV and at the SPS-collider maybe 30-40 GeV) will be immense, maybe 400 GeV. It is not inconceivable that if the inter• action states in the Good-Walker picture correspond to more or less exposed or space-extended color states, then the absorbed states are those with the most extended color. Therefore the remainder state may be a closely space-connected, very high mass state i.e. a "moving e+e" annihilation explosion". And 400 GeV is more than SUPER-LEPl Theorists have already proposed different possible outcomes (Peterson, Gustafson and Brodsky and coworkers) - we should note that neither "intrinsic charm" nor "produced charm" is out according to data and the ISR charm signal is surprisingly large and outside the present "hard process calculations". On the other hand, can diffractive states actually be seen at a super-collider by any possible detector?

III. So what do we expect for pileups at 10 TeV?

dnch In Fig. 2 I have presented a possible scaled up version of ^— from the SPS-collider to a super-collider at 10 TeV- We note that the peak height of "the shoulder" is a measure of ^-(rpiO) while the n-value of the peak is a measure of p±. I have only made a In s-scale-up in and takenthe values of the supersoft scenario for the central multiplicity. From this figure we conclude that on the average there will be more than 20 charged particles (and consequently more than 30 particles generally) between 90°-1° - 540 -

(n:0-5) and for smaller values of the angle (nma =»0.3) somewhat more than 10 charged particles, with a mean transverse energy of 0.7 GeV we obtain a mean transverse energy of 20-25 GeV for 90°-1° and 10-15 GeV for smaller angles.

Remembering the estimates for the probability of a multiplicity fluctuation (and even not taking into account its possible corre• lation to increasedp.) it is not difficult to obtain that with a -9 probability 10 (i.e. at the 100 pb level) we may find fluctuations with 0.3-0.5 TeV in transverse energies. I have not touched upon the "spike-events" of UA(5) which occur on the \% level (the largest is 18 tracks in \ unit of pseudo- rapidity). These events have an in azimuthal angle even distribu• tion of particles and the fluctuations are compatible with the cluster Monte Carlo of the group. Whatever they are, however, such fluctuations should also be noted as possible "disturbances" from (presumably) soft physics.

I would like to end with a few words about

IV The cosmic bravados

We should notice that we are at a supercollider probing the largest cosmic ray event energies we know of and only the evidence from some of the large airshowers are above these energies. We all know that the very peculiar events known by colorful greek names like Centaurs, Chiron, Geminion and Andromeda, corresponding to 1-2 TeV cms energies, for the first three and from 2-40 TeV for the last ones, are not easily understood inside present day physics. The largest multiplicities from the largest Andromeda (expected to correspond to 13 TeV cms energy) is 200-300 but we should note that a number of more than 300 primary particles were seen already at less than 1 TeV (Texas Lone Star).

Before a supercollider starts, however, the Fly's Eye detectors will be able to gather material for further speculations and I feel that the evidence from the rather few cosmic ray events we know of at the moment should be taken more as a warning and an indication that we may be meeting some really fantastic things at a super-collider. - 541 -

Acknowledgements: Except for the people already mentioned in the text I would like to thank G. Gustafson, Lund, for extensive discussions, J. Rushbrooke, Cambridge, for providing me with his immensely interesting review from the Chicago workshop, and G. Ekspong and P. Carlson, Stockholm, for providing me with knowledge of the interesting work of the UA(5) collaboration. - 542 - - 543 -

HEAVY VECTOR BOSONS AND SUPER COLLIDERS

C.H. Llewellyn Smith and J.F. Wheater

Department of Theoretical Physics, 1 Keble Road, Oxford 0X1 3NP, England.

R.J.N. Phillips Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire 0X11 OQX, England.

THEORETICAL CONSIDERATIONS

It is obviously possible that additional heavy W's and Z's exist. We shall concen•

trate on the extra bosons predicted by left-right symmetric models, in which parity -

and also charge conjugation, in some versions - is spontaneously broken (for reviews see

refs. 1 and 2).

First we consider phenomenological constraints on the masses of "right-handed" W's.

In SU(2)L x SU(2)R x U(l)ß_L, bosons W° couple to the usual SU(2)L doublets

vu,. , etc.

e L L while couple to right-handed doublets

v u , ,„ etc.

e R R

The mass eigenstates are

WL = cosÇ - WR sin? W = cosÇ + W? sing.

If vR is light compared to the muon, u-decay experiments require |ç| S 0.05, > 380

GeV, assuming that the couplings are left-right symmetric i.e. gL = g^. If parity is

E OR E >> spontaneously broken then necessarily 8R( ) S^ÍE) ^ **WR' there will be differ•

ences at low energy due to radiative corrections but these will not be more than a few

percent if Mj^R is within reach of a super collider. We therefore assume g^ = gR hence•

forth.

Theoretically it seems most likely that v is a heavy Majorana particle. In this . 4)

case there are no limits from u-decay but non-leptonic decays still give the bound

Ç < 0.004, subject to dynamical uncertainties, while weak universality and unitarity of

the KM matrix (assuming three generations) give^ Ç < 0.0045: we shall assume £ = 0. It

turns out that the WL + exchange contribution to the - Kg mass difference contains a

large numerical factor relative to the + contribution, which puts stringent bounds

on MyR. Without any assumptions on the right-handed KM matrix or the Higgs structure,

the bound is^ 300 GeV. If the left- and right-handed KM matrices are equal ("manifest"

L-R symmetry), or are related by complex conjugation ("pseudo-manifest" symmetry) as is the

case if C is spontaneously broken, the bound increases dramatically^ to 1-2 TeV (using the

new information on the b lifetime it is found that this bound is independent of m and the 2) .4) Higgs masses ). An independent but much weaker bound of 250 GeV is obtained from K ->• 2ir and K -*• 3ir assuming the left- and right-handed KM angles are comparable. - 544 -

An attractive possibility^ is that C and P are spontaneously broken and that the relative phase y of the left and right KM matrices is the only source of CP violation.

The observed magnitude of e then requires Mu„ < 21 TeV. Furthermore the lower bound from the - Kg mass difference can only be approached for y-»-0: for sin y > 0.1 it becomes

4-8 TeV.

To summarise: The right-handed W could be as light as 300 GeV but is more likely to be heavier than 1 TeV. It is lighter than 21 TeV if the phase in the KM matrices is the sole source of CP violation, in models with spontaneous C violation. Note that if is a heavy Majorana particle, as is favoured theoretically, it will decay equally to leptons and antileptons:

e.g. r(v£ -»• u"x) = r(v£ u+X) + + + - X = ev,uv,tv,ud etc.

Thus W_ decay will produce same and opposite sign dilepton events such as: + e + WR * \ 6

-»• e X, y X +- +- •* e X, p X

In the case that X = q'q, the WD mass can be reconstructed completely. K Turning to the second Z, we note that with the minimal Higgs system:

_ ¿.cor 2cos 6W - 1.7 M " cos26„ V, *' V 2 w R R

This formula is not necessarily correct, and we should examine experimental constraints in an unprejudiced way. In a comprehensive model independent analysis, Barger, Ma and

Whisnant have shown that low energy data allow to be identical to the standard Z with

Z2 as light as 200 GeV. For simplicity we shall assume that Z^ is exactly standard

(which corresponds to putting iji = 0 in the notation of ref. 8). In this case the coup•

lings of the Z2 are given by

I I -X Q) 8 = ß( X Q) + (

gA„ = alI3» where

*L*R

« + 3 - <1-L>-5;

/(1-XL_XR)XR 2 = sin 9 w

and

0

(in a notation1 iin which gv^ = | 1^ - Xj^ Q, gA^ = - | I^). A natural first assumption is

to put x^ = x^ - 0.22 but we must ask whether radically different production cross-sections - 545 - could bè given by taking different values of x^. We can always get much bigger cross- sections by letting Xj^-^Oorx^-^l-x^ but the couplings become infinite in this limit and the model makes no sense. For the case x^ = x^, in which parity is spontaneously broken:

gR = ^ = 0.65 * xR + xc = 1]

2

c xc

where gc is the U(l)g_L coupling. For •*• 0, g^ -»• » while g£ °° for •+ 1 - x^.

This is shown in fig. 1 where we see that the couplings are a minimum for x^ = 0.53 (for which value = 0.42, g^ = 0.61).

To summarize for Z„: simple models suggest **1.7 MyR but phenomenologically 2.^ could be as light as 200 GeV. Assuming that is exactly standard (which must be nearly the case), there are two parameters: and x^. Since the primary motivation of left-

right models is to allow spontaneous parity violation, it is natural to take g^ = gR,

xL = x^. Without this assumption there is a minimum in the couplings for x^ = 0.53.

Fig. 1 - 546 -

An attractive feature of the left-right symmetric models is that they can be embedded in S0(10) and we now consider constraints from such grand unification. Predictions from such models depend strongly upon the Higgs sector and have no simple general properties.

However, if all the Higgs particles except the W-S doublet are assumed to be heavy (i.e. 9) 3 to have the natural behaviour for scalar fields) must be a 10 TeV to get near its measured value. However, by invoking an unknown mechanism to keep more Higgs fields light

(e.g. supersymmetry) it is found^"^ that M can be as low as 200 GeV.

K

A different class of models^^ is based on S0(10), breaking SU(2) to U(l) at a scale in the region of the GUT mass: at low energies there is an extra neutral gauge boson but no corresponding charged particles. Again the could be as light as 200 GeV; its coupling to fermions are similar to those of the Z^ we have considered. RATES We have calculated cross-sections using the latest Duke-Owens parametrizations of 12) structure functions . They present two models which represent normal and hard glue options respectively. We show results in fig. 2 and table I and II for model I with the recommended value of A = 200 MeV. We have considered both models with A = 100 - 500 MeV.

In the mass and energy range considered the results lie within a factor 0.5 - 2.1 of those

a [cm2)

Fig. 2 - 547 -

Table I

Production Cross-Sections (cm ) for WR and Z„ for pp Collisions.

»~ - 18 TeV

M (TeV) aZ2(xR=.22) ( 53 o_ (.22) o_ (.53) % v- > Z 2 Z2

a + - o7 (.22) W +W

-35 .52 6.3xlO-34 2.1xl0~34 6.9x10 J .33 .33

-35 -3J 5 36 1 8.3x10 2.5x10 8.0xl0~ .29 .32 -37 2 8.3xl0'36 2.5xl0~36 6.9x10 J/ .29 .29

-37 -37 38 4 4.8x10 1.5x10 J/ 3.5xl0~ .31 .23

38 38 -39 6 4.4xlO~ 1.5xl0~ 3.1x10 Jy .34 .21

/s = 10 TeV

34 -3J 4 -35 .52 3.3xlO~ 1.0x10 3.2x10 JJ .30 .32

-35 -35 36 1 4.0x10 1.2x10 3.4xl0" .30 .28

37 -37 38 J/ .22 3 3.Ixl0~ 1.0x10 2.2xl0~ .32

Table II

Production Cross-Sections (cm ) for and for pp Collisions,

i/s = 18 TeV

M(TeV) a + - ( 22) (x 53) o» (.22) a7 (.53) W +W °z2 V °Z2 R=- ^2^

a + - cr7 (.22)

W +W Z 2

-34 34 -35 .5 6.2xl0 2.5xl0~ 7.1x10 .42 .28

-35 -3J 5 -36 1 5.8x10 1.8x10 6.1X10 .31 .34

-36 36 -37 .7X10 J/ 2 3 l.lxio" 3.4x10 .3 .31

38 38 -39 4 9xl0" 2.4xl0~ 6.8x10 .27 .28 -39 6 3.5x10 J 9.0xlO~40 2.3X10"40 .26 .26

*~ = 10 TeV

-34 -35 35 .5 2.7xl0 8.5x10 2.9x10* .31 .34

-35 -36 36 1 1.9x10 5.6xlO 1.8xl0~ .29 .32

38 -39 -39 3 3.2xl0" 8.2x10 2.2x10 .26 .27

shown for pp and 0.8 - 4.2 for pp. We therefore conclude that our results are most unlikely to be grossly in error and, in particular, that they do not substantially over• estimate the cross sections.

It is not clear what rates would make discovery of new W's and Z's possible. If

there are no new decay channels beyond known quarks and leptons, W_ will decay like WT with K Li 0(8%) branching ratio into v e, v u. If, notwithstanding limits from helium synthesis, K K there are more generations, these modes are decreased while new modes W -*• vT L, L u v v - 548 - etc. are somewhat harder to detect. Likewise supersymmetric decay modes are not as easy to detect as v and v . eu

We have not investigated the background for detecting new decay modes. However, we guess that it is likely that there is a branching ratio B of at least 1% into modes which could be found at a rate of 1 event/100 days and B could be 10% or more. Below we give the mass range which is accessible at this rate for B = .1 and B = .01 for various machines :

Machine v'S(TeV) Luminosity WR mass range accessible at a rate of: cm-2s_l 1 event/100 days for 1 event/100 days for B = 0.1 B = 0.01

31 PP 10 10 3.5 TeV 2.5 TeV 18 1032 7.25 TeV 5.25 TeV

33 pp 10 10 4.25 TeV 3.5 TeV 18 1033 7 TeV 5.25 TeV

CONCLUSIONS

Supercolliders can explore a mass range for new W's and Z's which is well beyond the existing phenomenological limits and covers part of the range which is interesting from the point of view of models in which C as well as P is spontaneously broken.

REFERENCES

1. R.N. Mohapatra, lectures at the 1983 Munich Summer School (Maryland preprint).

2. G. Senjanovic, Brookhaven preprint BNL-33648.

3. J. Carr et al., Phys. Rev. Lett. 51, 627 (1983).

4. J. Donoghue and B. Holstein, Phys. Lett. 113B, 382 (1982).

5. L. Wolfenstein, Santa Barbara preprint NSF-1TP-83-178.

6. F.I. Olness and M.E. Ebel, Madison preprint MAD/TH/156.

7. H. Harari and M. Leurer, Nucl. Phys. B233, 161 (1984).

8. V. Barger, E. Ma and K. Whisnant, Phys. Rev. D28, 1618 (1983).

9. W.E. Caswell, J. Milutinovic and G. Senjanovic, Phys. Rev. D26, 161 (1982).

10. A. Sokarac, Phys. Rev. I) (in press) - quoted in ref. 2.

11. C.N. Leung and J.L. Rosner, Fermilab Pub. 88/90 Thy.

12. D.W. Duke and J.F. Owens, Tallahassee preprint FSU-HEP-831115. - 549 -

CHAPTER XIV

PHYSICS OF ep COLLISIONS IN THE TeV ENERGY RANGE

G. Altarelli, B. Meie and R. Rüokl - 551 -

PHYSICS OF ep COLLISIONS IN THE TeV ENERGY RANGE

•1*1 J G. Altarelli ' , B. Meie and R. Rückl, CERN, Geneva, Switzerland (Presented by G. Altarelli)

ABSTRACT We study the physics of electron-proton collisions in the range of centre-of-mass energies between vs - 0.3 TeV (HERA) and /i =¡ (1-2) TeV. The latter energies would be achieved if the electron or positron beam

of LEP [Ee - (50-100) GeV] is made to collide with the proton beam of LHC [E = (5-10) TeVJ.

1. INTRODUCTION

In the present study we consider e*p reactions such as can be obtained by colliding an electron beam of LEP with a proton beam of the hadron collider in the LEP tunnel (LHC). We may assume, for the electron and proton energies, the values

E ai {so- loo) GeV

Ef- (s-\o) TcV,

so that the centre-of-mass energy of the ep system amounts to

•ff * 2.V£e£f - (l-O TeV. (2)

For comparison we recall that for HERA

-Vs * 0.3 TeV (3)

corresponding to E =30 GeV, E = 800 GeV. In preparing this report we have greatly profited from the extensive work that has been done on the physics at HERA1'2-'. The interested reader can also refer to related articles3).

The pp* e+e~ and ep facilities have complementary virtues. Although an ep collider may not be comparable in potentiality and flexibility with LEP or LHC, there are still three broad domains of physics where ep processes are competitive with or even superior to e+e and pp°.

The first important area is that of the study of proton structure and of CCD*). In

a particular, one can measure the strong coupling constant as(Q ) and the quark and gluon densities following their Q2 evolution up to a scale of order Q ^ (102-103) GeV. This is interesting in itself and is an important input for predictions on (super-) collider exper^ iments. The exciting possibility of unveiling a substructure for electrons and quarks also exists.

*) Permanent address: Department of Physics, University of Rome, Italy, and INFN, Sezione di Roma, Italy. - 552 -

The second main subject (although partly related to the first one) is the search for new gauge bosons or any new effective four-fermion interaction involving quarks and electrons. For example, we can think of excited W's coupled to left-handed currents; of vector bosons connecting light fermions to heavy, still undiscovered fermions; of gauge mediators of left- right symmetric models and of their neutral analogues, and of others as well. Or we can imagine discovering new effective non-renormalizable interactions induced by forces whose explicit dynamics will only manifest itself at much larger energy scales. An example is provided by residual forces between electrons and quarks which are present in composite models for fermions.

Finally, the spectroscopy of the electron tower can be studied; that is, the sector of particles with electronic lepton number. Here the list of possible candidates includes ex• cited electrons typical of composite models, scalar electrons or neutrinos, as predicted to exist by supersymmetric theories, heavy neutral leptons, and in particular Majorana neutrinos. Of course in many cases also the corresponding quark counterparts are expected to exist. Therefore one can, in principle, think of a similar analysis at the hadronic vertex. However, the detection of signals and the interpretation of results is much simpler for the lepton sector, and this is why we focus attention on this case.

In the following sections we shall develop a fairly detailed quantitative analysis of the three main chapters of ep physics which have been briefly introduced here. As our pur• poses are purely indicative, we do not aim to give a review of all possibilities that have been contemplated in the literature in connection with HERA. Rather, we restrict our atten• tion to a few typical or particularly interesting examples.

2. QCD AND PROTON STRUCTURE

Leptoproduction structure functions remain unchallenged as the most appropriate ob• servables for a systematic test of QCD through the pattern of scaling violations, for the

2 accurate determination of ots(Q ) at large values of the scale Q, and finally for the precise measurement of the quark densities and, though less directly, of the gluon density as well. An objection against going to very high energies which is often brought up in this connection

2 is that since scaling violations are determined by ots(Q ), their relative importance decreases with Q2. Thus the detection of scaling violations becomes more difficult as the energy in• creases. First of all, this argument only holds if QCD and the whole picture is true down to very small distances, which is something one would like to test. In fact, in the following we shall exemplify what could happen because of new interactions, substructure in the quarks

2 and so on. Secondly, it must be recalled that c»s(Q ) is expected to decrease by only a factor of 2 between Q2

At sufficiently large values of Q2 the running coupling becomes essentially independent

2 of Açpy We see from Fig. 1 that even a very rough determination of as at small Q almost

2 6 2 completely fixes ag at Q = 10 GeV . To be specific, we find that for ^ 40 GeV and AQCD between 50 31x1 500 MeV» as^Z = 106 Gev2^ = °-087 ± 0.011. On the one hand, this means that we cannot hope to directly improve the precision on by simply going to high energy. The only advantage in this respect is the check, provided by high-energy data, on the rel• evance of those at lower energies in the sense just explained. On the other hand, it would

2 be of great importance to prove experimentally that the value of as at large Q indeed coin• cides with the theoretical prediction. This would provide us with direct evidence in favour

2 of (or against) the correct running of as(Q ).

Fig. 1 The running coupling constant of QCD in two-loop precision for various values of the 2 2 2 2 2 2 2 2 scale A: ag(Q ) = a0(Q )[l - b'a0(Q ) In In Q /A ] with a0(Q ) = 1/b In Q /A ; b and b' depend on the number nf of excited flavours. The charm, bottom, and top thresholds

(mt ^ 40 GeV) are approximately taken into account by defining A at 210^ < Q < 2mt, where we

2 5 5 set as(Q ) = as( )(Q ) Ca( ) meaning that b and b' are evaluated with n£= 5J" and continuing 2 5 2 2 -1 to 2mc < Q < 2mb'by setting ag(Q ) = [l/a( ) (4m ) + l/a^tQ )- l/a^ (4mg)] , and so forth, that the continuity of a and the correct large Q2 behaviour is ensured at each step.

Another conventional task of considerable importance is the precise measurement of quark and gluon densities in the proton. The knowledge of these quantities is essential for all theoretical calculations on processes such as Drell-Yan and W~/Z° production, large-angle jet production in hadron-hadron collisions, other large pT phenomena, heavy-flavour creation, and many more. In particular, it is highly desirable to measure parton densities in lepto- production at the energy scale which is directly relevant to experiments at colliders and super-colliders.

Although standard physics at future ep accelerators will be interesting it is certainly the possibility of discovering deviations from the now established framework for present energies that makes these new projects so exciting. As implied by their name, the proton structure functions are sensitive to all manifestations of compositeness for quarks. Here we shall discuss two main aspects of this important issue: residual interactions and the transition to the subconstituent regime. - 554 -

Compositeness of quarks and leptons requires a new strong force responsible for the binding. The compositeness scale A (vaguely analogous to AQQJ) must in fact be rather large because quarks and leptons appear as point-like down to very short distances. An important limit or A 5) arises from the muon (g - 2). A composite structure of the muon would contri• bute to the correction to the muon (g - 2) with terms of order <5a^ = 0(m2/A2), the extra power of m^ being due to chiral suppression. From the experimental bound

f 6ar < 1.2 -|o" (4) one thus obtains

A > CT(lTeV) . (5)

A further model-independent bound6) arises from the absence of deviations from the standard prediction for Bhabha scattering at the highest available energies, which again suggests A •>» 0(1 TeV). Even more restrictive are the bounds on A if one assumes that, for example, e and u have comnon subconstituents. In this case one would have a u e transition ampli• tude with the same dependence on A as 0(100 TeV) in order to be compatible with the absence of u -»• ey and u 3e. Considering only the former more conser• vative cases and the ambiguities in the definition of the scale A which refers to an unknown dynamics, one cannot exclude a relatively small effective value of A. Nevertheless, it seems that the really interesting region where one should look starts in the few TeV domain.

In leptoproduction, compositeness becomes directly evident when Q > A because of the drastic change of the structure functions. This change is mainly due to two effects. First, the momentum fraction of the proton carried by a single quark is divided among several preons and this produces a shrinking of F2 towards small x. This is illustrated by an indicative example in Fig. 2. Assume that the quark density in a proton (at some given scale) is

Q(x) = Z llZlî, (6) X

so that the total fraction of momentum carried by the quarks is \. Further assume that exactly the same distribution holds for preons inside Q. Then the preon density in the nucleón (also plotted in Fig. 2) is the convolution of the two:

PU) - £ J'dyil=^ ('-*)*. (7)

In addition, it usually happens that, in going from the compound to its components, the average value of the electric charge squared decreases (for example, for a proton Qp = 1,

but for p ^ uud one obtains = V3). The consequence in electroproduction is a decrease .

of F2.

Figure 3 presents a model study of the transition from the present regime to the onset of the preon description which takes place at Q

Fig. 3 Transition of the proton structure function F2(x,Q2) from the quark to the subquark scaling region for a compositness scale A = 0.7 TeV and various values of x. The arrows indicate the maximum Q2 allowed kinematically at HERA (^ t~ = 0.3 TeV) and at LEP/LHC (• : /s « 2 TeV). The numbers in the circles indicate the number of events per day, under the conditions specified in the text [Eq. (10)]. - 556 - have chosen A ^ 0.7 TeV, and initial and final parton distributions described by Q(x) and P(x) as given by Eqs. (6) and (7), respectively. The transition between the two regimes is tentatively assumed to be mediated by a dipole form factor,

f(#/Al) =(!+- filVA')"1. es)

Then F2 is approximately given by

fc a Fz(x,GL) « -f if (a*/A*) xQGO + <Ç>[l-f(*/A )]*P(xV (9)

with = 1 or Actually there is no solid argument against a more rapid transition than that given by Eqs. (8) and (9), so that our choice is rather conservative. From Fig. 3 we see that at all x the departure from the low-energy regime takes place at about the same value of Q2, i.e. Q2 ^ A2. Since for a given Q2 we get more events at low x (the number of events per day at fixed luminosity is independent of the energy of the accelerator in the scaling limit and within the allowed kinematical limits), the main advantage of increasing }/s is the possibility of reaching smaller values of x for a given Q2 (recall that Q2 < xs). Throughout this paper we assume a luminosity of

oL = 10 (ym s . (io)

Whilst direct resolution of quarks into preons might be inaccessible, one may still be able to detect new forces between ordinary quarks and leptons. These forces are due to resi• dual interactions induced by the confining force at the scale A. In the previous example we have considered the effect of the standard electroweak interactions on a target which, at a given large scale, reveals a new structure. Now we discuss the impact of the presence of new forces implied by compositeness. Of course in the real situation both the effects of the target structure and of new forces may be important at the same time.

We assume an effective low-energy Lagrangian, given by the standard model Lagrangian with the addition of a number of non-standard four-fermion interactions ' 1 , to wit a

Here the indices a, b label the left and right components of fermions, and f refers to quark flavours. Since the preon binding force is strong we further assume that

i ; (12)

which amounts to a particular definition of A. The scale A so defined is in general only very loosely related to that used in deriving the bound in Eq. (5) from the muon (g - 2). As already mentioned, one cannot do better without a dynamical theory of the binding forces. - 557 -

The sensitivity to A that one may expect at HERA and LEP-LHC (/s = 2 TeV) can be estimated from Figs. 4, 5, and 6. The calculations which go into these figures as well as into all others in the present study are based on the set of parton densities in the proton specified in Ref. 9 (set 1 with A^^ -V 200 MeV). The standard model predictions are indicated by a dashed line, and the number of events per day refers to this case. The solid lines are the resulting cross-sections

J - dxty I a* 2. C13)

Fig. 4 The cross-section dcr/dxdy normalized as in Eq. (13) for x = 0.25 versus Q2. The dashed curves indicate the standard model (Y,Z°) predictions, the full curves include residual contact interactions. The numbers labelling the curves refer to the composi• teness scale A in TeV. Also given are the event rates per day corresponding to the standard model cross-sections and Eq. (10).

10p

/s=0.314 TeV (HERA)

(LL) CONTACT INTERACTION

/s = 2TeV

10 Event-s/day.

10" w a2 IGCV2) a2 [GeV2)

Fig. 5 The cross-section do/dxdy normalized Fig. 6 The cross-section do/dxdy normalized as in Eq. (13) for x = 0.1 versus Q2 (see as in Eq. (13) for x = 0.05 versus Q2 (see explanations in Fig. 4). explanations in Fig. 4). - 558 - when a left-left operator is added to the standard model Lagrangian as in Eq. (11) with the indicated values of A and the relative sign chosen in such a way as to maximize the effect. Already at HERA, deviations corresponding to A

NEW GAUGE BOSONS

Before discussing in detail the possible interesting examples of new currents and vector bosons, we evaluate the range of Q2 values that can be explored at a centre-of-mass energy of /s = (1-2) TeV. As a first indication , we consider in Fig. 7 the average Q2 value as a func• tion of /s for a standard charged current process e~p •+ vX. In the scaling limit, one would have a linear relation between and s:

« s (14)

However, scaling violations in the structure functions and, more importantly, W-propagator effects decrease . Some indicative values of are

0.082

* j 0.033 at TeV (15) Ö. 003

Fig. 7 Average momentum transfer squared of charged-current processes as a function of the ep centre-of-mass energy. In the scaling limit this log-log plot would show a straight J line. 10* /s (GeV) - 559 -

Thus only increases by a factor of 2-3 between HERA and LEP-LHC, as can be seen from Fig. 7 which clearly shows the departure from linearity owing to scaling violations. For• tunately, although « s, one can capitalize on the tail of the distribution. One still obtains a reasonable number of events up to much higher Q2 values. This is illustrated in Fig. 8, where the differential cross-section for charged- and neutral-current deep-inelastic scattering is plotted as a function of Q2 at different values of Note that the differ• ence between charged and neutral currents is only .important at small Q2 because of photon exchange. Also shown is the number of events per day for neutral currents for the refer• ence luminosity [Eq. (10)J and for Q2 larger than a given value. A practicable rate of events is obtained at LEP-LHC up to values of Q ^ 0 (1 TeV).

New gauge bosons could be detected in ep collisions at LEP-LHC up to masses of the same order, Myyi ^-0(1 TeV). This is already evident from the study of four-fermion operators in Eq. (11). We have seen that, for strong couplings as assumed in Eq. (12), we can get to A ^ 5 TeV. If the coupling g2/4ir is reduced to the size of a normal weak coupling, the previous mass scale is correspondingly decreased to

This estimate is fully confirmed by the more detailed analyses presented below for a number of particular cases of interest. For simplicity the discussion will be restricted to charged currents, but most of the arguments and estimates also hold, with minor modifications, for neutral currents.

Fig. 8 Momentum transfer distributions for charged- and neutral-current processes at /s = 0.3 TeV (HERA) and at /s = 1.41 and 2 TeV (LEP-LHC). Also given are the neutral-current event rates per day corresponding to the integrated cross-section o(Q2 > Q2,), where Q2, can be read off from the dashed curves. - 560 -

We first consider the possibility that the single W~ of the standard model is replaced by a sequence of weak bosons W, W', W", ... . This would naturally be the case if the W is a composite1l)(similarly to the p, p', ... sequence in CCD). All W's are supposed to be coupled to the same V-A current. For indicative purposes it is sufficient to restrict our attention to two W's, Wi,2, with masses m1>2 and couplings gi,2- An amplitude in the stan• dard model, arising from single W exchange,

A(al) (17) «(a.N-i>£)

2 2 (where the relation Gp//2 % g /8m r was used) is then modified to

A, , (a1) - —* (18)

Correspondingly the definition of Gp changes into

Z — (19)

Furthermore we now know from experiment that mi ^ m^. Thus it can be concluded, that for rates :

rate QM) R = A,.fc(tf) rate. C'W) A (a1)

z mj, r t a2/ (20) + r

where

a/wc¿ s - Hi H mz . (2i)

In Figure 9 we plot R as a function of Q2 for different values of M when r is set to the representative value r ^ 1. It can be seen that effects of excited W's with masses up to 1-2 TeV can be detected and studied. - 561 -

M(TeV) ,0.« 0.6

/ 2e/c

2.5 r=1 //

20e/d / 70 e/d 3 =• 2.0 A

'1.0

Fig. 9 Ratio of the charged-current cross- 1.5 /\f> section in a model with two W bosons to the charged-current cross-section of the standard model (as described in the text) for various masses of the second W. Also given are the event rates per day expected in the standard model at /s = 2 TeV and for Q2 > Q2, where Q2 1 is indicated by the vertical lines. 1.0 1 10s a2 (GeV2)

We next consider vector bosons connecting light and heavy fermions. Clearly, if the new leptons L° and quarks Q are sufficiently heavy, only mild experimental constraints on

+ the W£ mass can be derived (such as Mw{ £ 20 GeV from their non-observation in e e colli• sions at PETRA and PEP). Models of this sort are perhaps not very attractive but they are worth mentioning here because such a light/heavy W' would not be produced in pp collisions or even in e+e~ annihilation at LEP for masses above the ordinary W mass. We studied, as an example, the case of approximately degenerate quarks and leptons:

ftt^o ~ KUß (22)

assuming the existence of heavy partners (all with the same mass) for all quark flavours. Our results are shown in Fig. 10. For 5 1 TeV at /s ^ 2 TeV one can observe heavy fer-

m mions of masses up to m^0 ^ q ^ 0.5 TeV.

Perhaps the most interesting possibility of new gauge bosons is related to left-right symmetry12). The motivation for left-right symmetric models is the attempt to understand P and C violations in weak interactions. In these theories the electroweak Lagrangian is P and C conserving before spontaneous symmetry breaking, and the observed violations of P and C are attributed to the non-invariance of the vacuum.

The electroweak group SU2 L '® Ui is replaced by SU"2 ^ ® SU2 R ® Ui, with a discrete

symmetry under left-right interchange, so that g^ gR, where gL^R are the SU2l^R gauge couplings. The right-handed quarks and leptons which are singlets under SU, now become 2,L doublets under SU The complete assignments of quarks and leptons are thus given by

(23) - 562 -

The electric charge becomes

Q " J3L " * V1 (24) where B and L are the baryon and lepton numbers, respectively. Note that the Ui generator now acquires an elegant physical meaning, being proportional to B-L.

After spontaneous breaking, the charged-W mass eigenstates are mixtures of WT and W_: L H

Wx a cos S Wt. i- sin $ WR ; W^» - sin $ WL + cost WR . C25)

In order to agree with observations we need m^ <\» m^, m^ » m^, and ç « 1. The last condi• tion is expected to hold if the second one is valid. Once these constraints are satisfied, the neutral current sector also does not deviate much from the standard situation. There are two Z0,s, the light one approximately satisfying m^ /(m^ cos2 8^ ^ 1 and the heavy one ac• quiring a mass m^ of the same order as m^. The observed neutral-current phenomenology is reproduced within the accuracy of the data, provided that13)

W 7 £ TttlZ , (26)

which in the minimal Higgs configuration implies that

Vrx^ z ¿10 GeV . (27) - 563 -

These bounds also ensure agreement within errors with the measured value of m^ and m^o • A precision of order II in m^ and m^o is, in fact, necessary in order to detect the deviations from the standard values if the above bounds are satisfied.

The bounds on m^ and ç that can be obtained from charged-current data depend on the mass

1 of the right-handed neutrino. If vR is allowed by phase space in p decay, then ")

WWl > 3SO GeV (28) and

^ 5 0.05- . (29)

However, the vR mass could be large, as seems theoretically more resonable, and in this case one goes back to the limit of Eq. (27), whilst ç must be small anyway [ç á 0.095 ls); also if only three families are assumed then10) ç < 0.005].

Stringent bounds on m^ have recently been obtained from non-leptonic amplitudes, which, however, necessarily include some model dependence. In particular, the K^-Kg mass difference leads17) to an important bound with the assumptions that a) the box diagram approximation is reasonable; b) the K-M mixing matrices for left and right quarks are the same, or one is the complex conjugate of the other.

Assumption (b) is true in the simplest and most interesting versions of left-right symmetric models. Barring implausible cancellations with top-quark and Higgs exchanges, one then obtains

In conclusion, left-right symmetric models are interesting and cannot be ruled out even with m and m as low as a few hundred GeV, although there are indications that the right- handed gauge bosons, if they exist, are to be searched for above the TeV region.

In the following we simplify the discussion by taking C = 0 and study two indicative cases. First, consider a heavy vR with mass equal to that of WR:

•*\ " . t31) In fact, theoretical preference goes towards heavy neutrinos with Majorana masses of the same order as the left-right symmetry-breaking mass scale. A Majorana neutrino offers a spectacular signature, since it decays with equal probability into electrons of both signs:

£<0\-*e~ + X) ~ 3(*R-*Ô+ + X) - 5*0% . (32)

We can then search for this mode even without initial electron polarization. Of course, the cross-section from polarized electrons would be twice as large. The calculated cross- sections for e~p •*• vRX are shown in Fig. 11. It can be seen that even with the demanding constraint of mVR ^ it is possible to detect WR up to a mass close to 1 TeV. Remember that WR can easily be observed at a pp? collider with /i ^ 10-20 TeV provided that < 5 TeV and that the branching ratio B(WR-* evR) is large enough. However, for m^ > Mw the direct electron signal would not be available for detection, making the electroproduction channel particularly interesting.

To illustrate the other extreme we also consider the case of a massless v^, which is of course representative of a whole range of relatively light v^'s. The initial electron polar• ization is mandatory in this case for an efficient detection of small right-handed current contributions. On the other hand, the range of observable masses is roughly doubled in this case, as shown in Fig. 12. - 565 -

SPECTROSCOPY OF THE ELECTRON SECTOR

As pointed out in the Introduction, electroproduction is an optimal reaction for discovering new particles carrying the electron lepton number. We have already met some particles of this sort in the previous section, such as the neutral heavy lepton L° or the

Majorana neutrino vR. Here we shall consider in detail the production of supersymmetric (SUSY) scalar partners of the electron and of the associated neutrino, and then turn to the production of excited electrons that would be present if the electron is composite.

A scalar lepton (ë or v) must always be produced in association with a second SUSY particle, because of R-invariance which is normally respected in SUSY models18). The second SUSY particle can either be a scalar quark (q) or a gaugino, i.e. a photino (y), a gluino (g), a w-ino, or a z-ino (W,Z). We shall consider these two possibilities successively.

We start with the associated production of scalar leptons and quarks:

e * c| (33)

The ë channel is more easily detectable because of the decay ë •+• e + y, whilst the v is expected mainly to decay into neutrals: v v + y. Therefore, in the following we only report explicit results for ë production. The calculation of the production rate from the diagram in Fig. 13 was first done in Ref. 19. We have repeated the complete calculation and we confirm the analytic results of Ref. 19 (except for the couplings of w's which have to be changed) as well as their numerical results at HERA energies. Our results are shown in Fig. 14 for mg = m~ and m~ = 90 GeV, m~ = 0. The production rate is quite large if the scalar fermions are not too heavy. Scalar electron production appears to be easily measur• able even for values of m~ larger than the maximum mass accessible by pair production at the highest energy foreseen for LEP.

We are also studying the associated production of a scalar lepton and a gaugino. If the natural expectation that y's are the lightest gauginos is respected, then the most promising channel is

e + Cj—>ê.+y * cj . C34)

This process becomes particularly important if scalar quarks are much heavier than scalar electrons and consequently the channel in formula (33) is forbidden or strongly suppressed

e

Ï.Z

M q

Fig. 13 Lowest-order Feynman diagram contributing to selectron-squark production. - 566 -

/s (TeV)

Fig. 14 Production cross-sections and event rates of a scalar electron in association with a scalar quark as a function of the ep centre-of-mass energy for various scalar masses.

by phase space. The production cross-section can be computed from the diagrams of Fig. 15. Numerical results up to HERA energies were obtained in Ref. 20. As no analytic formulae were reported there, this calculation has to be redone from the beginning in order to in• crease the energy to Ss = 2 TeV. A detailed analysis of this process and the standard background reactions (eq -*• eZq evvq and eq •+• vWq •* vveq), as well as the relevant analytical results, will be presented elsewhere. Here it can be concluded that, for m~ = 0, one can possibly detect at LEP-LHC scalar electrons of mass up to a few hundred GeV.

As a last example, we shall discuss the production of an excited electron e*. Recently an e* of about 80 GeV has been suggested21) as a possible explanation of the apparently anomalous Z° -»• e+e"y events. Independently of the outcome of this particular issue, it seems worth while to consider the possibility of excited electrons for its own sake, as a signal for compositeness. In fact, in this connection the most important lesson that was derived, under pressure from Z° anomalous decays, was that the existence of relatively light excited leptons, with masses much smaller than the typical compositeness scale, does not conflict with any experimental fact.

Fig. 15 Lowest-order Feynman diagrams contributing to selectron-photino production. - 567 -

The electroweak neutral-current couplings of the e* can be written in the form:

(35) ,1 ri

•e

2 where g = e/sin 6w, g' = e/cos 9w> T3(e~) = -1, and Y(e~) = -\, with sin 6w ^ 0.217. The effective photon and Z° couplings turn out to be given by

FR-F*F'. (36)

The electroproduction of the e goes through the diagrams in Fig. 16, which lead to

AT

Sitóle,,, COS*©* (*-W2)J V 1 ' (37)

2 Here is the quark charge; a^ = x^/2 and v^ = (T^/2) - sin 8w are the neutral-current couplings of the quark; s, t, and u are the Mandelstam variables for the parton subprocess

Fig. 16 Lowest-order Feynman diagrams contri• buting to the production of an excited elec• tron. - 568 -

and the +(-) refers to quarks (antiquarks). The numerical results plotted in Fig. 17 are obtained with the values

fr* I f f2 * 0.5" (38)

These values for the couplings in Eq. (36) are close to the upper bounds inferred from exper• imental constraints21). Taken at face value, excited electrons of masses as high as 0.5 TeV could be detected. However, it is important to keep in mind that this is only true for the maximum conceivable values of the couplings.

5. SUMMARY AND CONCLUSIONS

The physics program for ep collisions at centre-of-mass energies of HERA and above is undoubtedly an interesting one. If a hadron collider will be built in the LEP tunnel, then ep collisions are really a must. At i/s ^ 2 TeV and for a luminosity around £ = 1032 cm-2 s-1, one can test QCD, measure the strong coupling constant, and determine the parton densities in the proton up to a scale Q ^ 1 TeV. Possible substructure of quarks and leptons can be explored down to typical distances of the order of (5 TeV)-1. New gauge bosons can be de• tected and studied for ordinary couplings up to masses of 0 (1 TeV). Finally, one can search for particles with the electron lepton number up to masses of hundreds of GeV, far above the LEP range. - 569 -

REFERENCES

1) Report of the e-p Working Group of ECFA on the study of the electron-proton storage ring project HERA, DESY-HERA 80/01 (1980).

2) Proc. Workshop on Experimentation at HERA, Amsterdam, 1983, DESY-HERA 83/20 (1983).

3) D.H. White, Proc. of Division of Particles and Fields Summer Study on Elementary Particle Physics and Future Facilities, Snowmass, 1982 (AIP, New York, 1983), p. 441. F.E. Taylor, ibid., p. 448. J.E. Wiss, ibid., p. 461.

4) For a review see, for example, G. Altarelli, Phys. Reports 81, 1 (1982).

5) R. Barbieri, L. Maiani, R. Petronzio, Phys. Lett. B96, 63 (1980). S. Brodsky and S. Drell, Phys. Rev. D22, 2236 (158ÖJ7

6) See, for example, M. Yamada, Proc. Int. Symp. on Lepton and Photon Interactions at High Energies, Cornell, 1983, (Cornell Univ., Ithaca, 1983), p. 525.

7) E.J. Eichten, K.D. Lane and M.E. Peskin, Phys. Rev. Lett. 50, 811 (1983). R. Rückl, Phys. Lett. 129B, 363 (1983).

8) R. Rückl, Nucl. Phys. B234, 91 (1984).

9) D.W. Duke and J.F. Cwens, Florida State Univ. preprint FSU-HEP 83/115 (1984) and Erratum.

10) M.A. Abolins et al., Proc. of Division of Particle and Fields Summer Study on Elementar)' Particle Physics and Future Facilities, Snowmass, 1982 (AIP, New York, 1983), p. 274. B. Humpert, CERN-TH 3817 (1983).

11) J. Bjorken, Phys. Rev. D19, 335 (1979). P. Hung and J. Sakurai, Nucl. Phys. B143, 81 (1981). H. Terazawa, Prog. Theor. Phys. 64, 1963 (1980). H. Harari and N. Seiberg, Phys. "Lett. ;'98B, 2.69 (1981). i O.W. Greenberg and J. Sucher, Phys. Lett. Î99B, 339 (1981). L. Abbott and E. Farhi, Nucl. Phys. B189, 547 (1981). H. Fritzsch, R. Kogerler and D. SchiToTöTecht, Phys. Lett. ;J14B~, 157 (1982).

12) J.C. Pati and A. Salam, Phys. Rev. D10, 275 (1874). R.N. Mohapatra and J.C. Pati, Phys.^Rev. Dil, 566 (1975). R.N. Mohapatra and G. Senjanovich, Phys. Rev. Lett. 40, 912 (1980) and Phys. Rev. D23, 165 (1981).

13) V. Barger, E. Ma, K. Whisnant, Phys. Rev. D28, 1678 (1983).

14) J. Carr, G. Gidal, B. Gobbi, A. Jodidio, C.J. Oram, K.A. Shinsky, H.M. Steiner, D.P. Stoker, M. Stroyink and R.D. Tripp, Phys. Rev. Lett. 51, 627 (1983).

15) The CDHS Collaboration at CERN.

16) L. Wolfenstein, UCSB preprint, NSF-ITP-83-178, to be published in Phys. Rev. D.

17) G. Beall, M. Bander, A. Soni, Phys. Rev. Lett. 48, 848 (1982). 18) For recent phenomenological reviews of supersymmetry see, for example, H.P. Nilles, Univ. Geneva preprint, UGVA-DPT 1983/12-412. H.E. Haber and G.L. Kane, Univ. Michigan preprint, UM-HE-TH 83-17 (to be published in Phys. Reports). 19) S.K. Jones, C.H. Llewellyn Smith, Nucl. Phys. B217, 145 (1983).

20) P. Salati and J.C. Wallet, Phys. Lett. 122B, 397 (1983).

21) N. Cabibbo, L. Maiani and Y. Srivastava, Phys. Lett. 139B, 459 (1984). See also A. De Rujula, L. Maiani and R. Petronzio, Phys. Lett. 140B, 253 (1984). - 571 -

CHAPTER XV

NEUTRINO AND MUON PHYSICS IN THE COLLIDER MODE OF FUTURE ACCELERATORS

A. De RÚjula and R. RUakl - 573 -

NEUTRINO AND MUON PHYSICS IN THE COLLIDER MODE OF FUTURE ACCELERATORS*^

A. De Rujula and R. Rückl CERN, Geneva, Switzerland

ABSTRACT Extracted beams and fixed target facilities at future colliders (the SSC and the LHC) may be (respectively) impaired by economic and "ecological" considerations. Neutrino and muon physics in the multi-TeV range would appear not to be an option for these machines. We partially reverse this

conclusion by estimating the characteristics of the "prompt" vy, ve, vT and y beams necessarily produced (for free) at the pp or pp intersections. The neutrino beams from a high luminosity (pp) collider are not much less intense than the neutrino beam from the collider's dump, but require no muon shielding. The muon beams from the same intersections are intense and energetic enough to study pp and uN interactions with considerable statistics and a Q -coverage well beyond the presently available one. The physics program allowed by these lepton beams is a strong advocate of machines with the highest possible luminosity: pp (not pp) colliders.

I. INTRODUCTION

The interactions of muons and muon-neutrinos with nucléons have not been experimentally studied with beams of energy in the TeV range. The interactions have been analysed in detail only at energies characteristic of ß-decay. Not a single v has ever been seen to

interact in a detector. These are sufficient reasons to justify a vg, v , "program" at any future high energy facility, but one can say even more.

Much of the interest of v- - and p-scattering physics resides in the study of the deep inelastic nucleón structure functions F^(x,Q2). Their measurements in light nuclei (H, D)

are still statistically limited. In heavier targets (such as C and Fe) errors in F2 are dominated by systematics and errors in xF^ are both statistical and systematic. In neutrino experiments the systematic errors are dominated by the imprecision of hadron calorimetry, _i and would decrease with energy as E 2. Errors in the measurement of the Q2-evolution of the non-singlet structure function XF3 jeopardize the cleanest tests of QCD. Very little is known about the ratio a^/a^. No experiments measuring u -»• v transitions have been per• formed. Besides testing conventional expectations, lepton scattering at higher energies could also reveal "nonstandard" physics: right-handed currents, new particle production, substructure of quarks and/or leptons, etc.1). Clearly much remains to be done in neutrino and muon physics. Two high energy hadron colliders are now seriously discussed2). The American SSC would be a 20-on-20 TeV pp collider, for which we shall assume a luminosity £• = 1033 cm-2 s_1. The European LHC, to be placed atop LEP, may be a pp or pp machine. We shall assume the LHC beam energy to be 8 TeV, and the luminosity to be 1033 (1031) cm"2 s-1 for the pp (pp) options. We allege in this paper that the production and prompt decay of charmed particles at the collider's intersection points is the source of energetic and highly collimated lepton beams, whose interest for physics is not negligible. The geometry and origin of these beams

*) A preliminary version was also included in the "Workshop on Fixed Target Physics at the SSC", Texas, 1984. - 574 - are shown in Fig. la,b, respectively. In Chapter II we derive the main characteristics (total flux and average energy) of the prompt lepton beams and compute the expected event rates at a hypothetical "standard" detector. In chapters III and IV we compare the neutrino and muon beams produced in the collider mode with the neutrino beams from a beam-dump, and with future ep facilities, respectively. Crucial to our considerations is an estimate of charm production cross sections at TeV energies. Our estimates are explained in detail in Appendix A. In Appendix B we predict the shapes of neutrino and muon beams as a function of energy and angle, and we estimate the evolution of the muon beam as it traverses an iron or soil shield.

Fig. 1 a) The colliders' intersections (here 6) as a source of lepton beams, b) Charm (<£) origin of the lepton beams at a collision point.

PROMPT LEPTON BEAMS FROM THE INTERSECTION POINTS OF FUTURE pp (pp) COLLIDERS

At the very high energies we are contemplating, the charm production cross-section ac

is expected to be a good fraction of the total pp or pp cross-section o"tot- We shall argue in detail in Appendix A, on the basis of an approximate universal scaling law of particle

a a a production, that c/ *z0-i > 10% is very reasonable conservative estimate of charm production at these very high energies. Most of the produced charmed particles (all but the very high- p,p ones) fly and will decay within the straight sections of the beam pipe. To be convinced of this, assume charm to be produced with a Feynman-x distribution (1- x)n, with n somewhere in between 0 and 5. The average energy of a charmed particle is E = E /(n+ 2) and, hence, c p the typical decay length for m = 2 GeV, T = 5 x 10"13 sees is

CD

Approximately 101 of charmed particle decays contain an (evg) pair in the final state, another 10$ contain a (yv^) pair. The production fraction of each penetrating "prompt"

a a lepton (y, vg or v ) is thus 0.1 c/ tot i 0(1$) of the total collision rate. It is on this fairly efficient way of making two lepton beams (a "leftwards" and a "rightwards" one) per collider intersection, that we shall capitalize. - 575 -

The prompt lepton beams are naturally highly collimated. Let be the average transverse momentum of the produced charmed particles. Their average production angle is

9p - = (n+ 2)/Ep. The average lepton angle 6¿ in a typical "three-body" semi• leptonic charm decay is of order (mc - mK)/(2Ec), with mR the K or K* mass. Hence, the average lepton to proton beam angle is of the order of

For = 1 GeV and n = 3

@ * (0.7 mtads) ( gTeV/E^") (3)

The angular shape of the lepton beams is discussed in more detail in Appendix B.

The "contamination" in the prompt lepton beams from the decays of other heavy flavors, such as beauty, is quite negligible: the beauty production cross-section is only a small fraction of the charm production cross-section. More surprisingly, the contamination from TT (or K) decay is also likely to be small at all lepton energies but the uninterestingly low nil• ones . To be convinced of this, assume the leading-charged-pion x-distribution to be (1 - x) , with n^ close to 4. The typical decay length of these pions is

To estimate the contamination of leptons from ir-decay in the "prompt" lepton beam, let L be the length of the colliding straight sections (after flying forward for L meters the pions will hit some material in the accelerator or the walls of the tunnel, and be lost as a source of hard leptons, see Fig. lb). The ratio R of hard leptons from pions and charm is of the order

•R = 10"*/-*=—Ï ' / ) f51

For o /atot = 10% and even for a very long straight section with L = 74 m, R is of order 10%. It goes without saying that in the SSC, whose tunnel is not predetermined, theorists see no reason not to make a couple of diametrically opposed straight beam-tube sections be several kilometers long (a small fraction of the SSC's circumference!). These collision points would then be copious sources of (u,v ) from ir decays and v's from K decays. u e - 576 -

We proceed to argue that no muon shielding preceding a neutrino experiment is necessary: all one needs is some 100 meters of soil to absorb the hadronic and electromagnetic showers from the primary collisions. Let N be the number of interaction regions in the collider. Consider a neutrino experiment placed somewhere along one of the 2N neutrino beams that the collider is tangentially producing for free. In a conventional neutrino experiment each machine burst produces zillions of muons that would completely blind the apparatus, unless efficiently absorbed and/or deflected. The muon and neutrino beams from a collider, on the other hand, are practically DC beams. Let the collider, for definiteness, be a pp machine

33 2 -1 3 with * = 10 cm" s . Assume atQt to be of order 150 mb ). The rate of pp collisions is

8 6 thus 1.5 x 10 /s. If (o /o-tot) BR(c -* yvX) is 1%, the muon rate is 1.5 * 10 /s. [For a 15(150) ns spacing between bunches this would correspond on average to one incoming muon every ^ 40(4) beam crossings.] Surely a neutrino detector can stand this rate of single muons and could even be triggered by them, should one decide to sacrifice vg physics [neutrinos are unfortunately not "tagged" since the parent charmed particle momentum is not measurable]. The magnitude and shape of the incoming muon flux, as well as the V v interactions and the high-Q2 y -»• y interactions in the "neutrino" detector also offer in• teresting physics potential.

Let us now estimate the average v and y energies in the prompt beam, and the event rates *•) to be expected in conventional-size detectors J . The main source of uncertainty in the shape of the fluxes is the longitudinal momentum distribution of the parent charmed particles. For D(D) production the least biased data are the ones from the LEBC-EHS collaboration1'), that "visually" measured charm production in pp collisions at /s = 26 GeV. Within rather limited statistics, no significant difference in the x-distributions for D and D was observed, and the cross-section was found to be compatible with the form1*)

a.

Q etc / Nw " (°T a - /.* + 0.8 (6) -z <**clpT a = (j.jto.s) GeV

The smaller n is, the harder the x-distribution of the charmed particles, the "better" (more energetic and interactive) the v and y beams. In what follows we shall refer to a conserva• tive choice n = 2 as our "optimistic" expectation for a D(D) x-distribution, and to n = 3 as the "pessimistic" choice. We shall assume F's to be produced with the same distribution as

D's. The present experimental information on Ac production is even less satisfactory than the one on charmed mesons. Charmed baryons are candidates for a "leading particle effect" since they may contain two of the parent proton's valence quarks. The qualitative exper•

imental indications are indeed that Ac's are harder than D's, with an exponent n compatible with 1, or even smaller, as suggested by certain theoretical models5). Cur "optimistic"

*) The muon flux is degraded in energy and spread in angle as it crosses the hadron shield, an effect that we shall estimate in some detail in Appendix B. For an introductory esti• mate we shall assume the shield not to be much thicker than 25 kg/cm2 (100 meters of soil or 30 meters of iron). In this case the muon flux is not seriously affected by its passage through the shield. - 577 -

("pessimistic") assumption for the Ac x-distribution is n = 0.5 (n = 1). The lepton fluxes also depend on the assumed production cross-sections and leptonic branching ratios. Table 1 summarizes the "optimistic" (fairly conservative) and "pessimistic" inputs used in our extra• polations to higher energies.

Table 1

Parameters of our models of charm production

+ + a(Ac) a(F) a(F ) a(D ) F -»• TV T n(D,D,F) n(Ac) a(D+D) o(D+D) a(F-) a(D") F + all Optimistic 2 0.5 0.5 0.5 1 2%

Pessimistic 3 1 0.25 0.25 1 11

In addition, we adopt the following semi-leptonic branching ratios for charmed particle decay6) :

3R(3)-*6^X) (7a) 3R(A->evc Xe ) ~ ~ 10 5%% (a)=0)%2)')(7b) e (7c) The D and Ac branchinî>Rg ratios (Fare centra l experimentaevX)l values -, while th157e assume.d BR(F) is the one expected from both "spectator" and "annihilation" decay mechanisms. To estimate BR(F •+ TV ) we combine the measured lifetime with the theoretical expression for the purely leptonic decay6):

(8)

= ((.? W'1 SR(F~>TVT) 1°*) /00/4eV 2 F (f ) The average vfiT) energy in a semi-leptonic "quasi-three body" decay, c sAv, of a high energy charmed particle is approximately E^S. The average energy of our lepton beams in

+ D,Ac,F •+ IvX decays is thus = Ep/(3n+6). In the decay of a fast F into T\>t the

+ average VT(T) energies are (1+ m£/mp)Ep/2. In the subsequent T v + ... decay the average

+, neutrino energy is approximately ET/3. Thus F s produce VT'S (v^'s) with an average frac• tion 0.09 (0.3) of their energy. The expected average energies (in TeV) of the different lepton beam components are given in Table 2 for the choices E = 8, 20 TeV and for our two - 578 - models of charmed particle x-distributions. The quoted values are within 201 of the naive estimates we just made, and come from more careful analytic and Monte Carlo calculations to be described in Appendix B.

Table 2

Average energies (in TeV) of the various components of the neutrino and muon beams

,,+ + - D -»- y v ,v„ v -*• T •*• V D ->• + F F y' e Ac - y T c y' e T D -* y~ D •+ v ,v F" -»• T -»"V y F" v e T T opt. 0.54 0.62 0.87 0.99 0.18 0.63

TLiTlL HCi pess. 0.44 0.49 0.72 0.82 0.14 0.50

opt. . 1.36 1.55 2.18 2.47 0.45 1.58

pess. 1.09 1.24 1.82 2.06 0.36 1.26

We proceed to estimate the total lepton fluxes and event rates. Let ^(ac) be the total (charm production) cross-section, let C(£) denote a particular charmed particle (lepton), and let £ be the luminosity. The lepton flux is

Leptons Ceconol ^

Here, the factor \ reflects the fact that this is the flux in one of the two beams emitted

3 by each interaction point. To estimate o"t t we use the fit )

(10)

which predicts at t = 145(173) mb at LHC (SSC) energies. With our estimate o /at t > 10% to be defended in Appendix A, we obtain

33 _2 10 QVn StC (Hb) Sec

Let us now concentrate on the number of interactions produced by the neutrino beams. The - 579 - total (charged plus neutral-current) neutrino cross-sections per nucleón should at the *•) relevant energies still be given by the approximate expression '

(12)

2 where we have used sin 6W ^ 0.21. The number of neutrino interactions per centimeter per second in a detector whose transverse dimensions are larger than the beam width (recall the small divergence of the beam) is

where p is the target density and (nucleons/gr) is Avogadro's number. To be specific, consider an L = 25 meters-long detector of average density p = 5 gr/cm3, exposed to the beam for a "working year" of Y = 107 seconds. The number of interactions in this detector, estimated from Eqs. 7 to 13 and Tables 1, 2 is given in Table 3. These estimates are obtained with the following o(C)/oc ratios, implied by Table 1:

5 SÇP, , AC/F*(F") J i / T / ' i ) 'optimistic"

The T~ leptons produced by charged current x-neutrino interactions should at these high energies be visible with a detector of modest granularity. At the LHC, and in our "pessi• mistic" model, the average decay path of a x+ is 0.7 cm, if it is produced in the chain

+ + + + F~ •* vT •*• x , and 2.5 cm if it comes from F -»• T ->• v •* x . For a T the decay lengths

+ are 0.6 cm in the chain F -»• Vt -»r~and 2.0 cm for F" -»• x" + v ->• x~. At SSC energies, these numbers would increase by the machines' energy ratio ^ 20/8.

We have mentioned that for a sufficiently short hadron shielding the prompt muon flux is practically unmodified. The shape of the y (y ) fluxes is similar to that of v (v,,) .

Thus, as in Table 3, we can easily estimate the number of y ->-vu or y -+v charged current interactions in our standard detector in a standard year. The result is given in Table 4.

Another obviously interesting quantity is the number of high momentum transfer y •* y scattering events in our standard detector. We call an event "interesting" if it occurs

*) The quoted ratio of v to v cross-sections is somewhat smaller than the one measured at present energies. To obtain it, we have used the Q2-dependent structure functions of Duke and Owens7) and we have set E, ^ 0.5-1 TeV. Table 3

Number of neutrino interactions in a "standard detector" (defined in text) per 107 seconds of running with £ = 1033 cm"2 s-1

+ vT from v from v from D v from D v from F v from F v from Ar + Total e e e e <- F" -»• T" ->• vT F~ -f x ->• vT e + neutrino (= v from D) (= v from D) (= v from F ) (= v from F") (= v from Ac) plus plus u u + interactions F + vT F" •+ v T opt. 8.4 x 10* 4.6 x 10* 6.3 x 10* 3.5 x 10* 6.7 x 10* 1.1 x io* 3.9 x 103 6.2 x 105 LHC 3 5 pess. 8.9 x 10" 4.9 x 10* 3.3 x 10* 1.8 x 10* 3.7 x 10* 2.9 x io 1.0 x 103 4.6 x lo

6 opt. 2.5 x 105 1.4 x 10s 1.9 x 105 1.1 x 105 2.0 x 105 3.3 x 10* 1.2 x 10* 1.9 x 10 SSC 3 3 6 pess. 2.7 x 10s 1.5 x 105 1.0 x 10s 5.6 x 10* 1.1 x 10= 8.8 x 10 3.1 x 10 1.4 x 10

Table 4

Number of charged-current muon-induced interactions in the same conditions as in Table 3 + + CC u -»-v if - vu u -»• V u * vu Total V + u-interactions from D from D from F from F~ from Ac

opt. 2.8 x 10* 5.2 x io* 2.1 x 10* 3.9 x 10* 2.2 x 10* 1.6 x 105 LHC pess. 3.2 x 10* 5.8 x 10* 1.2 x 10* 2.2 x 10* 1.3 x 10* 1.4 x 10s

5 opt. 8.6 x 10* 1.6 x 10s 6.5 x 10* 1.2 x 105 6.9 x 10* 5.0 x 10 SSC 5 pess. 9.3 x 10* 1.7 x 10= 3.5 x 10* 6.5 x 10* 3.8 x 10* 4.0 x 10 - 581 -

with a momentum transfer Q2 > Q2 ^ 100 GeV2: the approximate upper limit for which good data already exist. The total cross-section of interesting events for incident energy is, in the conventional notation, and upon neglect of weak effects: «KO "aa1

(14)

3

/, ^ / 100 6cV* \ ÄKVI F -I (iTeV/)

\ ' \ Qe / Ctf 100 GeV1

In the above estimate, we have used F^(0) ^ 0.4 [withJ^= (p+n)/2] and the fact that (1-y)2 approximately averages to 1/3. The number of interesting muon events in our standard detec• tor in a "year" of Y = 107 s is given in Table 5. Clearly, the rates of Table 5 are fairly large. For a dedicated muon experiment, a target much smaller than our "standard" (p = 5 gr/cm3, L = 25 m) neutrino detector may well suffice.

Table 5

Number of "interesting" (Q2 > 100 GeV2) events for conventional electromagnetic muon scattering in the same conditions as in Tables 3 and 4

+ + + + + + y y~ from D y -»• u from F y -*• y Total + + (= u" -*• y~ from D) (= y •*• y" from F ) from A y y~ y + y~ c

7 7 7 7 7 opt. 2.1 x io 1.6 x IO7 1.3 x 10 5.1 x 10 3.8 x 10 8.9 x 10 T Hr pess. 2.6 x io7 9.6 x 106 7.9 x 106 4.4 x 107 3.6 x 107 8.0 x 107

opt. 3.5 x 107 2.6 x 107 2.0 x 107 8.1 x 107 6.1 x 107 1.4 x 10s SSC pess. 4.4 x 107 1.6 x 107 1.3 x 107 7.3 x 107 6.0 x 107 1.3 x 108

All of the above considerations refer to pp machines with í = 1033 cm-2 s-1. A pp option is likely to have a two orders of magnitude smaller luminosity; all of our estimated event rates would accordingly decrease by a factor ^ 100. The prompt "free" lepton beams are a good physics reason to aim at the pp option for a collider.

III. COMPARISON OF THE "FREE" v-BEAMS WITH BEAM-DUMP GENERATED ONES

It is interesting to compare the properties of our "free" neutrino beams with the neu• trino beam that could be generated in the beam dump with which the same collider facility is necessarily equipped8). Let d be the number of times per day that the collider's beams are dumped, before proceeding to a new refilling. Let N (N-) be the number of protons (anti-

protons) dumped each time. Let Nß be the number of bunches of the collider. We shall nor• malize our forthcoming considerations to the parameters2) listed in Table 6. The extracted - 582 -

Table 6

Educated guesses of some parameters of future colliders

d N N- N P P B 13 (PP) 3 2.5 x 10 3564 LHC 13 (PP) 3 2.5 x 10 5 x 10" 108

13 SSC (PP) 3 7 x 10 6000 p's (p's) must be blown up before hitting the dump. If the cone that the blown-up beams form has an aperture of ^ 1 mrad or less, the neutrinos from the dump are sufficiently well collimated to do experiments with. The c.m.s. energy in the collisions of the extracted particles with the nucléons in the dump is ^ ^ 122 (194) GeV at the LHC (SSC). The laboratory energy distribution of the produced charmed particles (and prompt lepton beams) is the same as that of the particles produced at the pp (pp) collision points. (This is Feynman-x scaling, broken only by scaling violations in the fragmentation functions, presumably not very impor• tant for diffractively produced particles). What should be very different at lower c.m.s. energy is the charm multiplicity 0C/°"TOT- We shall estimate in Appendix A o"c/otot to be of order 2.31 (3.41) at i^i - 122 (194) GeV. Given the approximate equality in shape of the beam-beam and beam-dump generated neutrino fluxes, the simplest way to compare the two beams is to compare the normalization of the fluxes, without reference to a particular detector.

The number of leptons of type A produced by all of the dumped protons is

Z <»(.£-*» o» UT ~UR SGL »(e-/) . NR 2L where we have counted only the most energetic leptons, produced in the decay of the charmed particles created in the "first generation" proton interactions in the dump. The time- averaged ratio of the beam-dump flux to the beam-beam flux of Eq. (11) is given by

^(faea», du^) 365-pi (16) TT lÓ^secs ttft

Substituting the parameters of Table 6 and the quoted cross-section ratios, we obtain

N (17a) 2JA(- r V"»"(Luc)

(ssc) -»14)1^)1^) (17b) - 583 -

This means that, on average, the beam-dump v-beam is ^ 3(10) times more intense than the beam-beam v-beam in the pp versions of the LHC (SSC). In the pp version of the LHC this intensity ratio would increase to ^ 0(300): The beam-beam generated beams are in this case of rather low intensity. The transverse size of the beam-dump generated v-beam at a detector is bound to be bigger that what could be achieved with a beam-beam generated beam. For a sufficiently wide detector, the number of v interactions per year can be estimated by multi• plying the numbers in Table 3 by the corresponding flux ratios of Eq. (17). The result of this exercise for the total number of neutrino interactions per year in our standard (p = 5 gr/cm, L = 25 m) detector is 1.7 x 106 (1.2 x 106) at the LHC in our optimistic (pessimistic) model. With our assumption N^(pp) = N^fpp), these numbers apply to the pp version of LHC as well. At the SSC, the number of interactions is an order of magnitude larger, to wit 1.8 x 107 (1.3 x 107). It would clearly be nice to be able to afford this more expensive version of neutrino beams. An interesting remark concerns the number of neutrino interactions per extracted bunch in our standard detector. To obtain it, divide the number of interactions per year by 365/TT (days in a physicist's year), by 3 (the assumed value of d: dumps a day) and by Nß, specified in Table 6. The results are of the order of 1, 36 and 7 for the pp, pp versions of the LHC, and for the SSC, respectively. In the last two cases we may have been contemplating too large (I) a neutrino detector, unless one can extract the beam by fractions of a bunch.

The beam-dump generated beams have, in spite of their favorable intensity, several short-comings that we now discuss. A first, easily solvable problem of the beam-dump gener• ated beams is the following. The decay length of a charmed particle at the relevant energies is of order 12 cm (30 cm) at the LHC (SSC), see Eq. (1). This is larger than an interaction length L in a solid target of density p:

Thus, the first few interaction lengths of dump ought to be made of thin, well separated slabs, to let the charmed particles decay.

A second (unsolvable?) problem concerns the number of hard muons produced per extracted bunch:

10* (LHC,pp)

These numbers are so enormous that a costly muon shielding (or several kilometers of soil) are certainly necessary downstream of any v-detector. In addition, many slow muons are generated by the decay of "slow" secondary pions in the dump's interslab spaces. Detailed physics with these abrupt spills of muons is certainly out of the question. A possible solution may be to "dump" the beam on an internal gas-jet target. - 584 -

Another interesting question is the comparison between the necessary beam dump that we have just discussed and a .hypothetical "dedicated" beam dump experiment. Let the collider be operated as a dedicated proton accelerator for N^ hours/day, and let these protons be dumped in the dump. Assume the collider to accelerate protons in this mode at a rate of

= 1011* p/minute, where "D" stands for "dedicated to dumping". The ratio of dedicated (D) to necessary (N) neutrino fluxes from the dump is

7> ?0 (4-s--io/Wf) Lkt 1 (20) 1 lO * p's mi**' n 30 ( *-\O lNf) SSC

For our standard choices of parameters, a one hour a day dedicated running produces 80(30) times more neutrino events at the LHC (SSC) than the necessary beam dump. The total numbers of neutrino events per standard year per standard detector for N^ = 1 (and our other "standard" choices of parameters) is summarized in the following table. Clearly the dedicated

Table 7

Comparison of the numbers of neutrino events (per standard year and detector) in various scenarios

Necessary Dedicated Beam-beam beam dump beam dump

5 8 opt. 6.2 x io 1.7 x 106 1.4 x lo LHC (pp) 8 pess. 4.6 x 105 1.3 x 106 1.0 x lo

opt. 1.9 x 106 1.8 x 107 5.4 x 108 SSC pess. 1.4 x 106 1.3 x 107 3.9 x 108 beam dump is the best (though most expensive) option for neutrino physics, while the beam- beam generated muons are the only useful ones for physics (unless an extremely slow extraction of protons is feasible).

COMPARISON OF THE COLLIDER'S MUON BEAM WITH OTHER FACILITIES

The very intense prompt muon beam from a collider can be used for the study of u-nucleon scattering at large Q2, as indicated in Table 5, that refers to total number of events with Q2 > 100 GeV2. Since Q2 is a measure of the "depth" to which the interacting particles are analyzed, it is also interesting to compare different facilities in terms of expected cross- sections and number of events in various ranges of Q2. The results of such a comparison are summarized in Fig. 2, which we proceed to explain.

In Fig. 2a we compare the cross-sections for e+p -*• e+X and u^N5-* u+X scattering in bins of Q2 [jf = (p+n)/2]. The (ep) results refer to the parameters of the HERA machine and those of a hypothetical ep collider in the LEP tunnel (E = 100 GeV, E= 8 TeV). The cross- + P sections for the (u JV) results are averaged over the "pessimistic" prompt muon fluxes that we have computed for the LHC and SSC machines in Appendix B. All calculations include the - 585 -

33 2 1 J?pp= 10 cm" s"

J/'„ = 1032 cm"2 s"1

a) b)

-e*(100 GeV) • p(8 TeV) SSC In*. PESS)

'—i e*[100 GeV) • p!8 TeV)

HERA le*)

i HERA (e*)! I i il -I—l_U I L i-J , u 1 10*

2 2 a2 (GeV2) O IGeV )

Fig. 2 Unpolarized neutral current cross-sections and event rates at various facilities.

weak and electromagnetic effects of the standard SU(2) x U(l) model and employ the Q2- dependent structure functions of Duke and Owens7). The cross-sections for ep colliders extend to higher values of Q2 than those of the "secondary" p>T collisions since the center of mass energy of the former is higher. This effect is partially compensated by the fact that the "effective luminosity" of the u>P collisions on a sufficiently long target is very high. This is shown in Fig. 2b, where we compare number of events in Q2-bins for a standard year of running (107 sees). The ep event rates are obtained with a luminosity of 1032 cm-2 s whereas the yj^ results correspond to a pp luminosity of 1033 cm-2 s-1 and our "standard" target (p = 5 gr/cm3, L = 25 m). We have not reduced the muon flux by the effect of the hadron shield, which may diminish the rates by a factor of two. The conclusions from Fig. 2b are clear. The dedicated ep colliders are superior in terms of possible statis• tics at the highest values of Q2, the most interesting domain for possible "new physics". But the high statistics of scattering at lower Q2 may permit the search for very rare events. Also, nuclei are unlike protons, muons may be different from electrons, and fixed target experiments are definitely complementary to the ones at a collider.

SIM1ARY AND CONCLUSIONS

We have argued that the "free" prompt muon and neutrino beams from future pp colliders are sufficiently intense, energetic and collimated to be of interest to physics. We believe - 586 - that their potential ought to be considered when choosing the characteristics of these machines. The most obvious example is the choice between pp and pp options: we vote for pp.

The physics that can be explored with the prompt muon beam from a pp collider compares favorably with that of approved or hypothetical ep colliders, at all but the highest values of Q2 > 1000 GeV2, as can be seen in Fig. 2b.

The "free" neutrino beams are energetic and intense enough to deserve utilization, but the more expensive beams from beam dumps equipped with muon shielding are considerably more intense, as can be seen in Table 7. - 587 -

APPENDIX A

CHARM PRODUCTION CROSS-SECTIONS

Our estimates of prompt lepton fluxes depend linearly on the total cross-section a. for charm production in pp (pp) collisions at = 0.1 to 40 TeV. Unfortunately, both the exper• imental and the theoretical scenario on charm production even at the energies available in today's accelerators are fairly confusing. The situation (as of July 1983) is summarized9) in Fig. 3. The data are spread over more than an order of magnitude and are sometimes incon• sistent. The theoretical models1though allegedly inspired in the same theory (QCD), show a similar or even larger spread. A glance at Fig. 3 suffices to imagine what the spread of the theoretical predictions would be, if they were to be extrapolated two or three orders of magnitude up in energy, to the regime of interest to us. We are faced with an interesting situation in which we can neither trust theory nor heavily rely on experiment. Our naive way out is explained in this Appendix.

tOOOG

SPS/FNAL ISR

1000

5 100

( COM 7» — FRI 78 CAR 79 000 82 HAZ M 10 BRO 80c o Direct teptons • e|i coincidences DD tpNl • ÏÏ\ tpN) WMVAw Single e

t W////// Lepton pairs

10 20 30 40 50 60 70 »0 90 /s [GeVl

Fig. 3 Summary of experiments and models of charm production in pp collisions (from ref. 9). - 588 -

In Fig. 4 we have summarized some data for the multiplicities = a(pp •+• i)/°tat °f

11 CT different particles i = IR,K,D,p,Ac in pp collisions ), n^ = a(pp -»• i)/ tot/ The few data points on charm multiplicities that are shown are either directly measured in pp collisions, as for the ISR data, or extracted from measurements in nuclear targets with an assumed A^3 dependence (as advocated by Halzen5) whose "data" we have borrowed). The trend of multi• plicities as a function of energy for particles of different masses follow curves that are not dissimilar. To make this statement more precise, we have drawn Figs. 5 and 6. Fig. 5a shows fits of the form11) = a^ + b^ ln s + c^sz, for i = IR*, K1, p. The most naïve expectation based on dimensional analysis would be that the production cross-section for a particle of mass m^ is proportional to m72. That this is approximately correct at high energy becomes apparent in Fig. 5b, where we have plotted m2. Obviously this expec- i tation cannot be correct close to the different production thresholds s^. Moreover, m?a(pp •* i) is dimensionless, and may be expected to be a function of a dimensionless variable.

|| 10

_

-2 1

01 *- 0.1 V us- 9-' / / / / / / / / / /° sp 0.01 I I /° at_t I O a > < I of t '

i * Ac D 0.001 " DO

I I i I I I I I I ' I i I I II I I I I Mill I 1 I i I I I I I 101 102 103 10fc s [GeV2]

Fig. 4 Particle multiplicities as a function of energy in pp collisions (IR,K,pyp and ch from ref. 11). - 589 -

:

10» 10° r :

S" NT1 3 vr'h- ^^^^ a) • Y-/ b)

:// K/ / 7 y 2 2 log,0 (s'/l GeV ) log10 (s/1 GeV ) 1 i i i i i i i / i i i i i i i 1.2 1.6 2.0 2.4 2.8 3.2 3.6 1.2 1.6 2.0 2.4 2.8 3.2 3.6

10° : —

c)

v 10"' exp. fits extrapolation - /I i\ n 7 K"

log10 [(s-STHl/m-j] i i i i i i i i 12 3 4 5 6 7 9 10

Fig. 5 a) Fits to some of the particle multiplicities of Fig. 4. b) Multiplicities times the square of the produced particle's mass. c) Same as (b), plotted as a function of the variable defined in Eq. (Al).

/s in GeV

c 10 20 50 100 500 103 5 103 104 5 10* I I I 1 1 1 I I i s 3 4 5 10 50 100 500 103 5 W3 104 III I 1 I 1 1 1 1

2 n 3 5 10 10 500 103 ill 1 II UA5

fei* fe^ (SSC) (LHC) laiU

10*

2 x= (s-sTH)/m

Fig. 6 Comparison of pion, strange particle and charm multiplicities in pp collisions in terms of the approximate scaling law of Eqs. (Al). - 590 -

In Fig. '5c we "cure" these problems9) by plotting m? as a function of x = (s- s^p/m2. The multiplicities that in Fig. 5a were displaced by orders of magnitude in the vertical and/or horizontal directions have now considerably coalesced, and show a striking similarity in their shape. We have "detected" a rough universal scaling law for the production cross- sections in pp collisions of particles of different masses '

mi

x«x.= (s-s;H)/m¿ where f(x) is a particle-independent universal function, normalized by construction to vanish at threshold: f(0) = 0. Clearly, this scaling law could not be expected to be better than it is: we compare particles with specific charges, neglect all reference to resonances, spin, isospin, etc. But the scaling law13), when extended to charm production in the next paragraph, \ is presumably better (it is at least more predictive) than what is shown in Fig. 3. In Fig. 6 we apply the previous considerations to "total" cross-sections for pion produc• tion, strange particle and charmed particle production. The curve labelled "IT" is

3 + + ( /2)m^fJ + 3, we have estimated the TT° multiplicity to be the average of TT

3 2 + and TT~ multiplicities. The curve labelled "S" is ( /2)m , an estimate of the total strange particle production multiplicity, multiplied by m£. The estimate is based on a simple counting of the three-body (i.e. pp -*• pAK*) and four-body channels (i.e. pp •*• ppK K~)

that are dominant at relatively low energy. The points for AcD and DD production are those of Fig. 4, multiplied by m^ and plotted in terms of the corresponding x (see Eq. Al). The points labelled "C" are underestimates of total charm cross-sections: the sum of the aver•

ages of the ÄcD and DD points in the same Figure (we have neglected F production, that in our naïve world would be <\< \ of D production: there are two types of F's and four types of D's, and irip ^ m^). The point labelled D(e+e~) is a guess5) based on the measured D multiplicity in e+e~ annihilation well above threshold, and transferred to a pp energy scale by assuming

2 + se££(pp) ^ s(e e~). The dashed line labelled (%) is an estimate of the pion mul• tiplicity at very high energy, and corresponds to a fit containing a (log)2 teim. The dotted line is an extrapolation of the lower energy fit to the pion multiplicity, whose dominant

term at high energy is a simple logarithm. A recent measurement of 3/2 by the UA5 collaboration is also shown. In estimating charm production at future colliders we shall

conservatively use the dotted line. It corresponds to values of ^c/°tot of 11% and 13$ at

a the LHC and SSC collider energies, respectively. The values of o /at t t the same machine's beam-dump fixed target energies are 2.3 and 3.4$. Notice that our extrapolation in energy of the charm production cross-section is a very long shot. But in the sense of our scaling law in terms of x ^ s/m?, the extrapolation from the UA5 point (for which m^ = m^) to the x-values relevant to charm production at future colliders, is much more modest.

We conclude that a 10$ charm production "efficiency" at future colliders is a conser• vative estimate, that is unlikely to be wrong by more than a factor of 2 to 4, either way.

*) Here we shall not dwell on possible improvements12) of these naïve expressions (e.g. the substitution of m¿ by the transverse mass in the definition of x) nor on the comparison of m? for different reactions (pp,7rp,Yp,vp ...). - 591 -

APPENDIX B

NEUTRINO AND MUON FLUXES

In this Appendix we give more detailed results for the prompt lepton fluxes as a func• tion of energy and angle. The corresponding average energies are used in Chapter II to esti• mate the number of events per year in a standard detector.

Let c(x), with x = E /E , by the Feynman-x distribution of a given charmed particle in __ c P PP(PP) collisions. We adopt normalized distributions of the form:

CtX) = (l-x)"' /(** I) (Bl)

Let L(y), with y = E^/Ec> be the longitudinal momentum distribution (in an "infinite" momentum frame) of a given lepton i, in the decay c -»• Si + X (£, = v ,v ,u). For a "three- body" fundamental decay such as c •*• u v^s and in the approximation m^/m2

Í Z~

We do not give here the exact expressions for mg f 0, which are more cumbersome. Let

z. = E0/E be the longitudinal momentum fraction of the lepton in the chain pp->- X' + c(c-* í,+ X). The normalized flux of the lepton beam is then

4^-- fee*) Uy) Sl*jL-xy)dxdy (B3) CÍ2. y

for which it is easy to obtain explicit analytical expressions. A good approximation of the effects of mg ¿ 0 tions to Eq. (B2) 2 effects of mg ¿ 0 is to introduce the quantity ß = m*/(m-nrp and make the following corree- f Zp> -GfiY ^¡iHy3 far l=ju,e (B2c) L(y) (B2d) fy-spy* tifa* ferX-^e

We compute the normalized total fluxes of a given lepton type by summing the individual fluxes we just described (that correspond to a particular charmed particle D, F, A ) with the assumed - 592 - relative weights of particle production given in Table 1. We have checked the above analytical results against a Monte Carlo calculation (with mc = 2 GeV, mg 0.5 GeV) that proceeds along similar lines, and which we shall heavily rely upon for the computation of the angular spread of the beams.

Figure 7 exhibits our results The neutrino fluxes are presented as zydN/dzv or EvdN/dEv, which is a measure of the distribution of events as a function of energy The muon fluxes are shown as dN/dz^. The calculation of the fluxes proceeds along similar lines and involves an extra convolution (or Monte Carlo step) in the case of the "fast secondary" VT'S,

F -»• VTT(T v^X). We do not give the (rather obvious) details of this calculation. It is clear from Fig. 7 that the lepton fluxes are still considerable at energies that are a good fraction, say 40$, of the machine energy E .

Fig. 7 Neutrino and muon fluxes as a function of z = E(lepton)/E(proton) •

In Fig. 8 we give Monte Carlo results for the angular spread of the lepton beams, as a function of the angle 9 between the lepton momentum and the proton beam direction. For neu• trinos we show Ev(0v)dN/d cos 6^ which represents the event distribution at a detector, as a function of angler while for muons we give dN/d cos 6u, a measure of the number of muons in the beam as a function of angle. We investigate various assumptions on the x-distribution of the parent charmed particles and use a Gaussian pT distribution with = 1 GeV. Even if were to be doubled, the beam divergence is of order 1 mrad. At 100 meters from a collision point these beams could be intercepted by a target of very modest transverse dimen• sions. - 593 -

- F*—«T 11) . T (-•VTI2) . X)

n (l-Xpil3

b)

' L i

- L H

vT(2)

; «,(1) ¿1

1 1 1 1 12 3 4

e»T Imrad)

Fig. 8 Angular shapes of neutrino and muon fluxes corresponding to = 1 GeV.

The shape of the muon beam given in Fig. 7 refers to muons as they come from a collider's interaction point. But the muons are degraded in energy and intensity as they cross the hadron shield, or a certain amount of soil. We have estimated these effects, but not the additional angular spread induced by muon interactions prior to a detector. A fair approxi• mation to the energy loss of a muon in a material of density p and atomic number of weight (Z,A) is given by1")

d£ (B4)

Muons with TeV energies are more than minimum ionizing, due to the effects of bremsstrahlung, pair creation and nuclear interactions. Eq. (B4) is an approximation to what is theoretically and experimentally known about these effects. Let E^ be the energy of a muon that has trav•

elled a distance L through a certain material. On the average the original energy E0 of that muon is, according to Eq. (B4)

(BS)

Let dNo/dEo = (Eo) be the original muon flux. The muon flux after an L-meter voyage through a dense medium is

(B6) - 594 -

In Fig. 9 we shew the percentage of produced muons

that survive after a voyage of L kilometers in typical soil material (p = 2.5 gr/cm3, Z = 10, A = 20). Since the beam is narrow and the original flux of muons is of the order of 106/s (for £ = 1033 cm-2 s_1), problems of radiation safety cannot simply be forgotten. Because of statistical fluctuations that we have not taken into account, the number of muons at relatively large L is underestimated in Fig. 9. Figure 10 exhibits the shape of the muon flux after different depths of soil. The results are given in terms of energy (rather than energy fractions) for the LHC and the SSC, since Eq. (B4) does not exactly "scale". Again, the high energy tails of these distributions are underestimated, as a result of the neglect of fluctuations.

In Fig. 11 we show the shape of muon fluxes after a modest number of meters of iron, a possible material for a hadron shield. For L < 100 meters, the extra angular spread of the beam should be smaller than its natural width. This time we give results in terms of a scaling variable z^, rather than the actual energy for the two machines. For the "short" iron shields we are considering the breakdown of scaling implied by Eq. (B4) is negligible in the comparison of SSC and LHC energies. As can be seen from Fig. 11, the muon beam is still quite intense after a few tens of meters of iron shield.

L (km) in soil

Fig. 9 Fractional number of muons as a function of depth as they travel in soil. - 595 -

Fig. 11 Same as Fig. 10, in an iron shield. - 596 -

REFERENCES

1) G. Altarelli, B. Meie and R. Rückl, Physics of ep-collisions in the TeV energy range, CERN preprint TH. 3932 (1984), see these proceedings. 2) Details on the machine design of the LHC and SSC can be found in these proceedings.

3) A. Martin in the Proceedings of the 21st International Conference on High-Energy Physics, Paris 1982, ed. by P. Petiau and M. Porneuf, Les Editions de Physique (Paris, 1982); R.N. Cahn, Theoretical Perspectives on Elastic and Total Cross-sections at the SSC, LBL preprint, LBL-17432 (1984).

4) M. Aguilar-Benitez et al., Phys. Lett. 123B (1983) 103.

5) For a review, see e.g. F. Halzen in the Proceedings of ref. 3.

6) R. Rückl, Weak decays of heavy flavours, CERN preprint (1983), to be published in Physics Reports C.

7) D.W. Duke and J.F. Owens, Q2 dependent parametrizations of parton distribution functions, Florida State University, preprint FSV-HEP 83/115 (1984) and Erratum.

8) For a recent discussion of high energy beam-dump-generated neutrino beams, see E.L. Berger, L. Clavelli and N.R. Wright, Phys. Rev. D 27 (1983) 1080.

9) D. Drijart et al., Contribution to the High-Energy Physics Conference, Brighton (UK), 1983.

10) The theoretical models of Fig. 3 are from the following references: COM 78 - B.L. Combridge, Nucl. Phys. B151, (1978) 429. FRI 78 - H. Fritzsch and K.H. Streng, Phys. Lett. 78B, (1978) 447. CAR 79 - CE. Carlson and R. Suaya, Phys. Lett. 81B, (1979) 329. ODO 82 - R. Odorico, Bologna preprint IFUB 82/3 (1982). MAZ 82 - P. Mazzarrti and S. Wada, Bologna Prep. IFUB 82/9 (1983). BRO 80 - S. Brodsky et al., Phys. Lett. 93B, (1980) 251. 11) See e.g. G. Giacomelli and M. Jacob, Phys. Rep. 55 (1979) 1 and references therein. The parameters of the fits in Fig. 5 are taken from A.M. Rossi et al., Nucl. Phys. B84 (1975) 269. 12) A. De Rújula and R. Rückl, to be published.

13) A similar scaling law in terms of s/m| (see Fig. 5b) used to predict charm multiplicities from Kg multiplicities has been proposed by S. Geer et al., EP Internal Report 83-08, CERN, 1983.

14) See e.g. A. De Rújula et al., Phys. Rep. 99 (1983) 341 and references therein. - 597 -

CHAPTER XVI

PROSPECTS OF THEORETICAL PARTICLE PHYSICS

G. 't Hooft - 599 -

PROSPECTS OF THEORETICAL PARTICLE PHYSICS

Gerard 't Hooft, Institute for Theoretical Physics, Utrecht, The Netherlands.

The Organizing Committee has asked me to report to you on what is to be expected in the future of theoretical particle physics. Apparently they know that I have a direct telephone line to an alien civilization whose scientific development is far ahead of ours. I had not used it for a long time, but I decided to overcome my pride, pick up the hom, and dial a number. I got a man from the constellation Centauri on the line; he immediately asked whether the planet Earth is ready to become a member of the intergalactic Common Market. I said No, we were still having some domestic problems, I just wanted to ask him some questions, and proceeded: 'How far is your scientific research?' - '10* years. ' This made me very curious. 'Then I have a lot to ask.' - 'What about? ' 'Particle physics.' - 'Please ask, you'll learn from it!' Well, there I was. How do you start? I began hesitatingly, by uttering an excuse. I said 'Wait a minute, it is not that simple, your paradigm is probably very different from ours!' He was quiet for a moment. - 'What is a paradigm? ' 'Well,' I said, 'this is something I read in Thomas S. Kuhn. It is something like the whole collection of preconceptions and ideas, methods and procedures that you learn and then teach at school.' - 'I think I understand' he said. 'Well, in that aase our paradigm is that of "truth", and our method is called "logic", and —. ' I interrupted. 'No, no, that is the whole point. According to Kuhn there are many forms of "truth" and many different sorts of "logic" which can be incommensurable. Any paradigm will sooner or later end up in a crisis, as Kuhn says, and then a revolution will come, over• throwing the old paradigm, replacing it with a new one, just like political systems.' - 'J do not understand' said my man from Centaurus. 'That cannot happen if you stick to truth and logic. ' I realized that this was going to be a pointless discussion. So I finally took the courage to ask my first real question: 'How does one quantize gravity?' (because this seems to be the most important question of present-day theoretical physics). - 'That is the wrong question' was his reply. And then he started to ask me questions. At first I thought he wanted to know what our pres• ent level of understanding is. But some questions were utterly trivial, crazy, or senseless - and he kept insisting that I be precise in my answers. Then there were some extremely difficult ones. None of these were questions I had ever thought of asking before. And always, somehow, the answer was at hand. Sometimes only a little thinking was needed. At some point he suggested 'Imagine turning on your LEP machine, or a pp collider. Suppose it tells you that —' The amazing thing was what all these questions did to me. The answers always were the only possible answers. But somehow they taught me thousands of years of the theoretical physics of the future. - 600 -

Then he interrupted. 'lou understand that we are not letting you get away with all this knowledge. According to your own philosophies it will cause bloody revolutions on Earth. We are very peaceful. I will now erase your memory. ' And before I could protest he had all my new understanding erased. I do not even remember the questions he asked. The empty spaces were replaced by arguments that would convince me that the whole conversation had not taken place at all, but that I had made it up just to make a point at this meeting.

The message should be clear — if only you knew exactly which questions to ask, you could make tremendous progress in understanding our physical world. The answers are always logical and straightforward. But the nature of the questions depends on one's imagination, intuition, habits, culture. And that is what I would call a paradigm. If a paradigm is overthrown it is because a new set of questions are the vogue.

Not only must the questions be correct. They should also be put in the right context — and asked at the right moment. Democritus, for instance, with his atom theory, had found the right answer. But the question was not right — it was premature by 2000 years! The Greeks should not have worried about the separability of matter. They still had to learn how to combine their philosophies with accurate observations and measurements. By proposing a heliocentric system, Aristarchos had found the correct answer to a question that was premature as long as one did not dare ask whether the heavenly bodies perhaps fol• low simple equations of motion.

The question is more important than the answer. Galileo had a theory for the tides that was incorrect. But by asking the question whether perhaps these tidal movements could be explained by the movement of Earth among the other bodies in space, science advanced further than the backlash caused by an incorrect answer.

And so it is that theories themselves, and the logics of their arguments, are rarely overthrown by revolutions and replaced by other theories. Rather, they are incorporated in new theories. This is what happened to Newton's theories of forces and accelerations when relativity theory arrived, and again when quantum mechanics was invented. Without Newton there would have been no Einstein and no Schrödinger. The new theories were to a large extent limited by the requirement that for large masses and low velocities Newton's laws ought to remain valid.

It is this process that I expect to continue in the future. In particular, the theory of elementary particles is an edifice made of many solid bricks: one of these is Newton's theory. On top of that there are the relativity theories by Einstein and a brick called 'quantum theory'. One of the newest bricks is gauge theory and renormalization.

Having lost my paranormal telephone connection I will now try to reconstruct some of the questions that particle physicists must put to both theorists and experimenters.

This is not as easy as it would have been 20 years ago. The renormalizable gauge theories that we have now work excellently. In principle we could accurately describe the dynamics of our world up to a tremendous energy scale of around 1020 GeV, without any ap• parent mathematical inconsistency. Even quantum chromodynamics may well come under control as our computers become faster and the programs smarter. What should we ask?

One problem is that all our renormalizable gauge theories work so well. But there is an infinite set of varieties, each with a bunch of free parameters which can each take any - 601 - value within a certain range. Just because they are all logically impeccable (or so it seems) we are faced with the fundamental problem of how to choose between them. This is why theorists are urging experimenters to look at the highest attainable energies, just to find out which choice nature itself made.

In the meanwhile we theorists have a pastime which consists in devising our own 'guidelines for gods'. Why could one gauge theory be better than another?

De GVTsibus non est disputandum. However, on contemplating the arena of gauge theories, one indeed finds that some are far more pleasing and probable than others. Now, most the• orists will prefer their own definition of the concept 'naturalness1. But it will not de• viate very much from the following credo: 'A theory is unnatural if a disproportionately accurate fine-tuning of otherwise unrelated physical parameters is necessary to reproduce a world even approximately resembling our own. ' We will not call a fine-tuning dispro• portionately accurate if the parameters involved are related by some symmetry, which may be broken by a tiny effect. The strength of this requirement is that all theories of particles that are considered to be more or less established today — such as quantum electrodynamics and chromodynamics — clearly satisfy this requirement. Curiously, it becomes more and more difficult to satisfy it at higher energies. The SU(2) x U(l) theory, so beautifully sup• ported by the discovery of the W and Z, is only natural up to about 1000 GeV. To get natu• ralness beyond that level we need something more or something new. A mathematically more convenient way to formulate naturalness could be:

Whenever a parameter or combination of parameters n is small,

hi « i , then the theory must have some enhanced symmetry in the limit

n •*• 0 .

For instance, the combinations

2 o -, m -i m T e 1 e 1 ¥ _ 1 = Jir 137 ' m Ï836" ' m2 32 ' p m * P

correspond to separate photon conservation, chiral symmetry for electrons, and chiral sym• metry for quarks, respectively.

At present, theorists have two options for resolving the naturalness problem beyond the 1000 GeV barrier. These are two competing theories:

i) Supersymmetry. Every particle may have a supersymmetric partner separated from it by not much more than 1000 GeV. What is required is a global supersymmetry, either direct or to some extent spontaneously broken. Loaal supersymmetries may be relevant only at the Planck scale. It is usually argued that they automatically yield a global supersymmetry below the Planck scale. But this is not obvious. After all, in gauge theories local gauge invariance usually does not produce a spontaneously broken global symmetry with the same algebra, a fact that in my opinion is not always sufficiently emphasized. Although these theories are extremely elegant and fundamental, they may perhaps not be right. One reason for concern is the complete absence of obvious supermultiplets. - 602 -

ii) Technieolour. The idea here is that several of the particles that we today conceive of as being point-like are actually composites. In particular the Higgs particle should be composed of a fermion-antifermion pair. Algebraically this idea is attractive. The new binding force could be much like chromodynamics but 1000 times stronger, hence the word technicolour. One problem here is that several levels of new local symmetries and breaking patterns are needed in order to explain the Higgs-Yukawa forces that generate the quark and lepton masses. Thus the term 'extended technicolour' is coined. The naturalness barrier is pushed from 1000 GeV to perhaps 100,000 GeV but not much beyond. We could take a modest attitude and consider this as acceptable for the time being. Experimentally the way to distinguish between our two options is to detect a Higgs particle. In the supersymmetric theories the Higgs is elementary — therefore fairly light and comparable to W and Z. In the technicolour scheme the Higgs is probably beyond 1000 GeV and is barely detectable as a wide resonance.

An extremely important aspect of particle physics is its role in modern cosmology. The 'early history' of the first picoseconds is determined entirely by the kind of dynamics as• sumed at correspondingly high energies. A single-run experiment has been performed for us at infinite energies but the data are extremely difficult to interpret. At best the evidence we get is highly indirect. Here, too, we have several varieties of the naturalness problem: Why is the universe approximately isotropic? Why are there no magnetic monopoles? Why is the cosmological constant as small as it seems to be? — it seems to be zero.

This finally brings me to the subject of quantum gravity. It may seem to you that this is a subject for dreamers, not physicists, but you may well be mistaken. I am certain that here my partner from Centaurus asked many questions of the 'What if —?' kind. My own pet theory gives a non-local relationship between the physical phenomena in inertial frames and accelerated frames. Non-locality is probably what is needed in order to explain away the cosmological coupling constant. One may perhaps ask what happens if two particles are sent to a black hole, just to meet and collide one millimetre away from the horizon. In the centre-of-mass frame the collision has tremendous energy, approaching infinity if the point of collision approaches the horizon. Thus the 'black-hole-tron' may be the ultimate par• ticle collider of the (distant) future.

Another intriguing question is to compute corrections to forward scattering cross- sections that are due to the gravitational effects. Contrary to the present trends, we find an increase of the cross-section proportional to E2, and the gravitational Bom term entirely dominates all other forms. Unfortunately it is not clear what to do with this observation. The importance of asking these questions, however, is not that one day we might be able to do such experiments, but rather that quantum gravity must be the cornerstone of any respect• able unified model of matter.

If you look at the past, then the theories of the dynamics of matter invariably turn out to be pretty unique. There are no alternatives as elegant and simple as those which were found to be the blueprints of nature. My long-term extrapolation is that this will continue to be the case for our future theories: they must be unique. But just as in the past, theorists are by far too dumb to be able to reconstruct our blueprints without the help of experiment. So, paradoxically enough, we need the new and bigger machines just to help us find the questions, arguments, and answers that will explain how we could have anticipated all those data without any experiment at all! - 603 -

The currently proposed machines will tell us which of the two main theoretical ideas, supersymmetry or technicolour, is closer to the truth (if any). Whatever will be the out• come and whatever the hints for our next series of questions, I am confident that the result will be extremely exciting physics.

It is even possible to imagine that eventually there will be an end to theoretical physics — that is, the complete set of fundamental physical laws may be found one day. But regardless of whether this will turn out to be true or not, the end is certainly not in sight.