Prospective Study of Muon Storage Rings at Cern

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LABORATOIRE EUROPEEN POUR LA PHYSIQUE DES PARTICULES CERN EUROPEAN LABORATORY FOR PARTICLE PHYSICS

PROSPECTIVE STUDY OF MUON STORAGE RINGS AT CERN

Edited by: Bruno Autin, Alain Blondel and John Ellis

30-47

GENEVA 1999 Copyright CERN, Genève, 1999

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ISSN 0007-8328 ISBN 92-9083-143-0 KS002503760 R: KS CERN 99-02 DE013437977 ECFA 99-197 30 April 1999

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LABORATOIRE EUROPEEN POUR LA PHYSIQUE DES PARTICULES CERN EUROPEAN LABORATORY FOR PARTICLE PHYSICS

PROSPECTIVE STUDY OF MUON STORAGE RINGS AT CERN

Edited by: Bruno Autin, Alain Blondel and John Ellis

GENEVA 1999 CERN-Service d'information scientifique-RD/988-2000~avril 1999 Abstract

muons. A high-energy muon colHde. using the decays of no arized

KEXT PAGE(S) left BLANK Contributors to this report: B. Autin", A. Bartl2), M. Beneke", R. Bennett3', A. Blondel4), A. Bueno5), R. Casalbuoni6)7), M. Campanelli5), J. Collot8), A. Deandrea9', S. De Curtis7), M. de Jong10), A. De Riijula", D. Dominici6)7), F. Dydak", H. Eberln), J. Ellis", H. Fraas12), F. Franke12), M.B. Gavela13', R. Gatto14), G.F. Giudice0, J.-J. Gomez-Cadenas15), G.J. Gounaris16), J.F. Gunion17), P. Hernandez1', P. Janot", W. Joss18), CD. Johnson0, W. Joss18), E. Keil", M. Kramer1', S. Kraml1", S. Lola", L. Ludovici19', W. Majerotto1", W.J. Murray3', G. Moortgat-Pick12', F. von der Pahlen12', V. Palladino20', J. Panman", K. Peach3', D. Perret-Gallix2", A. Pilaftsis", W. Porod2', R. Rattazzi", S. Raychaudhuri1)22), H. Ravn", F.M. Renard23', L. Rolandi", A. Rubbia5', M. Silari1', A. Strumia24', M. Vretenar", C. E. M. Wagner", J. Wells" andE.J.N. Wilson",

" CERN, Geneva, Switzerland 2) Inst. f. Theoretische Physik, Universitat Wien, Vienna, Austria 3) Rutherford Appleton Laboratory, Chilton, Didcot, United Kingdom 4) Ecole Polytechnique, Palaiseau, France 5) ETH, Zurich, Switzerland 6> Universita di Firenze, Dipartimento di Fisica, Italy 7> INFN, Firenze, Italy 8) ISN, Grenoble, France 9) Institut fiir Theoretische Physik, Universitat Heidelberg, Germany 10) NIKHEF, Amsterdam, The Netherlands '" Inst. f. Hochenergiephysik, Osterreichische Akademie der Wissenschaften, Vienna, Austria 12) Institut fur Theoretische Physik, Universitat Wurzburg, Germany 13) Univ. Autonoma Madrid, Spain 14) University of Geneva, Switzerland 15> Facultad de Ciencias Fisicas, Universidad de Valencia, Spain 16) University of Thessaloniki, Greece 17> University of California, Davis, USA 18> GHMFL/LCMI, Grenoble, France 19) Universita di Roma I "La Sapienza", Italy 20) Universita di Napoli, Italy 21) LAPP, Annecy, France 22) Tata Institute, Bombay, India 23) Physique Mathematique et Theorique, Universite de Montpellier II, France 24)INFN, Pisa, Italy

NEXT PAGE(S) left BLANK Working groups members:

NEUTRINO FACTORY STUDY GROUP:

Bruno Autin (Convener), CERN, Bruno.Autin@cern.ch Andreas Badertscher, ETHZ, [email protected] Jean-Luc Baldy, CERN, [email protected] Roger Bennett, RAL, [email protected] Alain Blondel, Ecole Polytechnique, Palaiseau, [email protected] Antonio Bueno, ETHZ, [email protected] Mario Campanelli, ETHZ, [email protected] Johann Collot, ISN, Grenoble, [email protected] Manfred Daum, ETHZ, [email protected] Yves Declais, IN2P3, Lyon, [email protected] Jean-Marie de Conto, ISN, Grenoble, [email protected] Maarten de Jong, NIKHEF, [email protected] Jean-Pierre Delahaye, CERN, [email protected] Chris Densham, RAL, [email protected] Alvaro De Rujula, CERN, [email protected] Luigi Di Leila, CERN, [email protected] Friedrich Dydak, CERN, [email protected] Curt Eckstroem, Uppsala, [email protected] Robert Edgecock, CERN, [email protected] Jean-Paul Fabre, CERN, [email protected] Alfredo Ferrari, CERN, [email protected] Jean-Marc Gaillard, CERN, [email protected] Jacques Gareyte, CERN, [email protected] Roland Garoby, CERN, [email protected] Belen Gavela, University of Madrid, [email protected] Juan-Jose Gomez-Cadenas, CERN/Valencia, [email protected] Helmut Haseroth, CERN, [email protected] Claude Hauviller, CERN , [email protected] Pilar Hernandez, CERN, [email protected] Ingo Hofmann, GSI, Darmstadt, [email protected] Jean-Yves Hostachy, ISN, Grenoble, [email protected] Colin Johnson, CERN, Colin. [email protected] Walter Joss, LCMI, Grenoble, [email protected] Robert Klanner, Universitaet Hamburg, [email protected] Kay Konigsmann, Freiburg, [email protected] Andreas Krassnigg, CERN, [email protected] Jacques Lettry, CERN, [email protected] Lucio Ludovici, INFN, [email protected] Michelangelo Mangano, CERN, [email protected] Vassili Maroussov, BINP/CERN, [email protected] Pasquale Migliozzi, CERN, [email protected] Vittorio Palladino, CERN, [email protected] Jaap Panman, CERN, [email protected] Ken Peach, RAL, [email protected] Henri Pessard, LAPP, Annecy, [email protected]

vn Werner Pirkl, CERN, [email protected] Helge Ravn, CERN, [email protected] Jean-Paul Repellin, LAL-ORSAY, [email protected] Jean-Pierre Revol, CERN, [email protected] Philippe Royer, CERN, [email protected] Andre Rubbia, ETHZ/CERN, [email protected] Roger Ruber, Uppsala, [email protected] Marco Silari, CERN, [email protected] Sasha Skrinsky, BINP, [email protected] Ulrich Stiegler, CERN, [email protected] Paolo Strolin, Naples/CERN, [email protected] Iuliu Stumer, BNL, [email protected] Bart Van De Vyver, CERN, [email protected] Andre Verdier, CERN, [email protected] Maurizio Vretenar, CERN, [email protected] Ted Wilson, CERN, [email protected] Klaus Winter, ETHZ/CERN, [email protected] Piero Zucchelli, INFN/CERN, [email protected]

vin PRECISION MUON COLLIDERS STUDY GROUP:

Ken Bell, RAL, [email protected] Alfred Bartl, Vienna, [email protected] Alain Blondel (convener), Ecole Polytechnique, [email protected] Roberto Casalbuoni, Firenze, [email protected] Guy Coignet, Annecy, [email protected] Aldo Deandrea, Heidelberg, [email protected] Stefania De Curtis, Firenze, [email protected] Daniele Dominici, Firenze, [email protected] Helmut Eberl, Vienna, [email protected] Patrick Janot, CERN, [email protected] Raoul Gatto, Geneva, [email protected] John Gunion, UC Davis, [email protected] George Gounaris, Thessaloniki, [email protected] Corinne Goy, LAPP, Annecy, [email protected] Franco Grancagnolo, Lecce, [email protected] Massimiliano Grazzini, Firenze, [email protected] Sabine Kraml, Vienna, [email protected] Eric Lanc,on, CEA Saclay, [email protected] Walter Majerotto, Vienna, [email protected] William Murray, RAL, [email protected] Denis Perret-Gallix, LAPP, Annecy, [email protected] Pascal Perrodo, LAPP, Annecy, [email protected] Massimo Placidi, CERN, [email protected] Werner Porod, Vienna, [email protected] Fernand Renard, Montpellier, [email protected] Iuliu Stumer, BNL, [email protected] David Taqqu, PSI, [email protected] Bart Van De Vyver, CERN, [email protected]

NEXT PAGE(S) left BLAMK 1 IX •""«"^""""" • •• » ••'• HIGH ENERGY FRONTIER STUDY GROUP:

Guido Altarelli, CERN, [email protected] Bruno Autin, CERN, [email protected] Alfred Bartl, Vienna, [email protected] Martin Beneke, CERN, [email protected] Roberto Casalbuoni, Firenze, [email protected] Francesco Caravaglios, CERN, [email protected] Aldo Deandrea, Heidelberg, [email protected] Stefania De Curtis, Firenze, [email protected] Daniele Dominici, Firenze, [email protected] Helmut Eberl, Vienna, [email protected] John Ellis (convener), CERN, [email protected] Hans Fraas, Wuerzburg, [email protected] Fabian Franke, Wuerzburg, [email protected] Harald Fritzsch, Munich, [email protected] Raoul Gatto, Geneva, [email protected] Belen Gavela, Madrid, [email protected] Gian Giudice, CERN, [email protected] John Gunion, UC Davis, [email protected] Manfred Jeitler, CERN, [email protected] John David March-Russell, CERN, [email protected] Colin Johnson, CERN, [email protected] Eberhard Keil, CERN, [email protected] Valery Khoze, Frascati, [email protected] Sabine Kraml, Vienna, [email protected] Magda Lola, CERN, [email protected] Walter Majerotto, Vienna, [email protected] Michelangelo Mangano, CERN, [email protected] Joaquim Matias, CERN, [email protected] Hitoshi Murayama, Berkeley, [email protected] Gudrid Moortgat-Pick, Wuerzburg, [email protected] Federico von der Pahlen, Wuerzburg, [email protected] Joannis Papavassiliou, CERN, [email protected] Werner Porod, Vienna, [email protected] Riccardo Rattazzi, CERN, [email protected] Sreerup Raychaudhuri, Bombay, [email protected] Gigi Rolandi, CERN, [email protected] Reinhold Ruckl, Wuerzburg, [email protected] Marco Silari, CERN, [email protected] Ted Wilson, CERN, [email protected]

NEXT PAGE(S) left BLAHK XI Summary

This report presents the conclusions of a six-month prospective study, encouraged by ECFA, on the physics opportunities and accelerator issues presented by muon colliders, and by extension, muon storage rings. By and large, this study was a learning process, largely inspired by the more advanced American studies, and does not claim to have produced much original work of a technical nature.

A. A THREE-STEP SCENARIO

This study group has reached a first level of understanding of the physics motivations and accelerator questions. The physics possibilities are extremely rich, and the accelerator challenges considerable, if all addressed at the same time, as for a very high energy collider. The study group proposes a three-step scenario. Each step in this scenario provides unique particle physics experiments that justify the corresponding investments in their own right, while progressively building up accelerator competence, technology and infrastructure.

1. Neutrino factory This first step involves a high-intensity proton source, a first design of a muon collector, acceleration of the muons to an energy of about 20 GeV, and a muon storage ring for neutrino production. These neutrino beams are unique in intensity and quality, allowing definitive experiments in neutrino oscillations and neutrino-nucleon scattering. The intense muon source also opens opportunities in stopped-muon physics.

2. Higgs factories Several generations of muon colliders with centre-of-mass energy in the range yfs = 100- 1000 GeV can be envisaged, once the important question of muon cooling has been answered, so as to allow high luminosities to be obtained. These machines are very compact and attractive. Muon colliders can do all the physics of electron colliders in this energy range, but they offer more. Their superior energy resolution and calibration, as well as the direct muon coupling to the Higgs boson(s), make them a tool of choice for precision studies of new particles in this mass range, should the LHC reveal their existence.

3. The high-energy frontier The maximum energy that one can envisage for muon colliders using the existing CERN infrastructure is about 7 TeV in the centre of mass. This involves a more or less straightforward extrapolation of the design of the lower-energy colliders, and again offers the physics potential of an electron-positron collider, though with superior energy resolution and some possible advantages associated with flavour-non-universal couplings. At energies above about 3 TeV, and with the present designs, the radiation induced by neutrinos at the locations where they emerge from the earth is too severe. Therefore, the high-energy step is limited at these energies if this problem is not solved. For the moment, possible solutions being advocated to go beyond this limit involve better-quality muon beams, pending progress on cooling, or careful arrangements of the site and of the locations of straight sections.

xin The development over time of these three steps would offer an extremely rich programme of physics experiments for many years, and allow for the continuous improvement of the various technologies necessary to handle high-intensity muon beams.

B. ACCELERATOR ISSUES A possible layout of a muon complex on the CERN site is shown in Fig. 1. It seems that the three scenarios would fit on the CERN site with a feasible amount of civil engineering.

'•M

Large muon collider Cvs=5TeV) 'Fast accelerator 2 in LHC tunnel (2.5 TeV)

ast accelerator 1 in SPS tunnel (400 GeV)

iggs factory (Vs = 100 GeV) v factory -~> Gran Sasso

Fig. 1: Possible layout of a muon complex on the CERN site.

The present status of the major accelerator issues may be summarized as follows. 1. Neutrino factory The muon source could be a simplified version of those envisaged for the muon collider. For neutrino beams or stopped-muon physics, the flow of muons can be continuous or bunched at high frequency, only one sign of muons needs to be produced at a time, and cooling is, maybe, not as critical. This leads to envisaging as proton source, rather than a high-energy synchrotron, a proton linac of energy 1-2 GeV, from which a beam power of up to 20 MW seems feasible. Re-use of the present LEP superconducting RF system could be envisaged for this purpose. The target on which pion production occurs is a major challenge but is probably feasible. High-field solenoids already exist, which is an important point, as the target solenoid controls the pion and muon collection efficiencies. The muon storage ring design is straightforward. Finally, muon beam parameters can be monitored with a precision of better than 1% both in intensity and in polarization.

xiv There are however many missing links in our understanding: 1 to 2 GeV protons would yield an adequate number of pions, but the collection efficiency at these energies remains to be assessed. The collection of the pions and decay muons will require a careful matching with the target area. The accelerator chain is by no means trivial, and could turn out to be quite expensive. A simulation of the whole system is the necessary next step in the design process.

2. Higgs factories For collider operation, however, the muons need to be provided in high-intensity bunches with both signs in equal numbers, and cooling is an important factor in obtaining high luminosity. This different time structure has to be kept in mind when designing the neutrino factory, and in particular the proton source. An additional bunching scheme might be necessary. Using deuterons or alpha particles as a source instead of protons should help in sign equalization at these low energies. Cooling is the crucial technology to master in this step, as the luminosity should be high enough to provide at least 1 fb"1 per year at energies of the order of 100 GeV per beam. Ionization cooling is in principle a straightforward application of the properties of interactions of muons with matter. However, its practical implementation requires ingenuity and a full simulation. It might be necessary to make precise measurements of the full six-dimensional properties of muon-matter interactions. Eventually a validation experiment will be necessary. Here again, high magnetic field technology is important: ionization cooling leads to a final emittance which is inversely proportional to the square of the magnetic field available for focusing in the last elements. The background to detectors due to decay electrons is a serious design problem, for which this study relied on the American simulations.

3. The high-energy frontier The precision muon colliders are in many ways the most demanding in terms of beam quality, and the extrapolation of the accelerator design to high energies is more or less straightforward. If the last acceleration stage were to take place in the LHC tunnel, energies of up to 3.5 TeV per beam, i.e. 7 TeV in the centre of mass, could be envisaged. Above a beam energy of about 1.5 TeV per beam, however, neutrino radiation becomes a serious concern and, unless a solution is found, will prevent energies higher than about 3 TeV in the centre-of-mass energies from being achieved.

C. PHYSICS OPPORTUNITIES

1. Neutrino factory The principal advantages of neutrino beams from a muon source are the following. The beam composition and spectrum are perfectly known. The beam energy is tunable. The presence of high-energy electron neutrinos is a unique feature. Moreover, since they have opposite lepton charges from the accompanying muon neutrinos, experiments can in principle be devised to discriminate between oscillations affecting the two types of neutrinos present in the beam. Clearly the neutrino beams from muons are ideal for a second-generation round of oscillation experiments, allowing several of the mixing angles and mass differences to be measured precisely. The prospects for CP-violation studies are marginal but not unthinkable, with progress in the statistical power of the beam or the detectors. The exact potential of these beams is still subject to large uncertainties, which would require more detailed studies, in particular to take into account the backgrounds.

xv High-intensity neutrino beams of a few centimetres in radius would come out of the muon ring, opening the way to a completely new generation of neutrino experiments, in which the traditional multi-ton neutrino detector is replaced by a small high-precision target, possibly polarized, allowing a great variety of materials and situations to be probed. Finally, stopped-muon physics would benefit from the improvement by several orders of magnitude in the available flux of muons. Flavour violation is expected to appear at a certain level of branching ratio. This aspect has not been studied in the group so far and deserves more detailed investigation.

2. Higgs factories Although the luminosities estimated in the American design are about a factor of 10 lower than those advertised in e+e~ machines of the same energy, a n+[i~ collider can cover essentially all the physics topics accessible to a lepton collider in a given energy range. In addition, it offers superior energy resolution and a larger coupling of the muon to the Higgs(es). Muons are unavoidably polarized at production and this property, being difficult to destroy, will propagate to the high-energy ring. The muon polarization can be analysed via the spectrum of decay electrons. This allows very precise energy calibration from analysis of the spin precession, from which the energy spread can also be extracted with high precision. The luminosity can be appropriately monitored using large-angle n+(J.~~ —> M+M~ scattering or radiative returns to the Z peak. If experiments were carried out at the Z peak itself, a design would have to be found for measurement of low-angle /i+M~ scattering. These properties would make such a muon collider ideal for the study of the Higgs boson. Its mass and width could be measured to a fraction of a MeV, and the cross-section can be measured with a relative precision of 1%, as can branching ratios. The full impact of such precise measurements has not yet been fully analysed. In the particular supersymmetric scenario which has been studied here, the reduction in allowed parameter phase space is considerable, even if this collider came after both LHC and a high-luminosity e+e~ collider. A fascinating possibility would be the existence of nearly degenerate Higgs bosons, e.g. the neutral H and A of supersymmetric models. The fine energy resolution of muon colliders would offer a unique separation between these resonances, possibly allowing the study of their respective quantum numbers and even interference, as could appear owing to CP violation in the Higgs sector.

3. The high-energy frontier There is no need to provide motivation here for very-high-energy exploration machines well beyond the energy range reachable at LHC, which is equivalent to about 1 TeV in the parton- parton centre-of-mass frame. Again, the muon collider has the specific feature of fine energy resolution, unlike e+e~ colliders where beamstrahlung degrades the centre-of-mass energy resolution more and more as the energy increases. There is also an obvious complementarity with e+e~ colliders for all processes with flavour-sensitive signatures, such as supersymmetric models with /J-parity violation, or for the production of excited muons and supersymmetric partners of the muon.

D. CONCLUSIONS AND RECOMMENDATIONS

The conclusions of the prospective study can be stated as follows. 1. The line of facilities using muon beams seems extremely interesting, providing a very rich physics programme for many years. 2. We suggest that ECFA advise the European particle physics community to take this option very seriously.

xvi 3. We arrive at a point where detailed design and simulation become necessary, in the absence of which the feasibility and competitiveness of muon storage rings and colliders cannot be ascertained. 4. A series of ECFA-sponsored workshops would be an appropriate forum to undertake the detailed work that is necessary to design and evaluate more completely such a project, with initial emphasis on the neutrino factory. 5. The design and even the construction of this line of machines could involve capabilities that are available in different laboratories throughout Europe. A dedicated collaboration involving European laboratories is necessary in order to go further, and could become extremely effective.

NEXT PAGE(S) left BLANK IBHH«nHBn« CONTENTS

1 FOREWORD 1

2 MUON MACHINES 3 2.1 A tentative layout of muon machines on the CERN site 3 2.1.1 Muon lifetime 3 2.1.2 Site considerations 3 2.1.3 Description of a possible layout 3 2.1.4 Special features of a neutrino factory 4 2.1.5 The precision muon colliders 6 2.1.6 Final acceleration and large collider 7 2.2 A 2 GeV superconducting linac as a proton driver for muon beams 8 2.3 Solenoids for pion collection 9 2.3.1 Introduction 9 2.3.2 Choice of conductor technology 10 2.3.3 20 T Bitter magnet 11 2.3.4 20 T hybrid magnet 13 2.3.5 Cost estimate 13 2.3.6 Conclusion 14

3 STEP 1: NEUTRINO FACTORY 15 3.1 Outline of neutrino oscillation experiments at the muon storage ring facility ... 15 3.1.1 Neutrinos from a muon storage ring 15 3.1.2 Outline of neutrino oscillation experiments from a muon storage ring ... 16 3.1.3 Appearance experiments 17 3.1.4 Background considerations 18 3.2 The mixing of three neutrino families: peculiarities, signatures and opportunities 20 3.2.1 Current motivation 20 3.2.2 Neutrino fluxes 20 3.2.3 Theoretical background 21 3.2.4 Wrong-sign muons 22 3.2.5 Matter effects 25 3.2.6 Scaling laws 26 3.2.7 T and CP violation 26 3.2.8 Summary 29 3.3 Experiments with neutrinos from muon decay 29 3.3.1 Neutrino fluxes 31 3.3.2 Long-baseline experiment 32 3.3.3 Medium-baseline experiment 37

xix 3.3.4 Conclusions 40 3.4 Neutrino scattering experiments at the muon storage ring facility 41 3.4.1 Introduction 41 3.4.2 Detector layout 42 3.4.3 Measurements 43 3.4.4 Conclusions 45 3.5 Physics with stopped muons 45

STEP 2: HIGGS FACTORIES 47 4.1 Outline of the machines 47 4.2 Overview of the physics capabilities 49 4.3 Measurements of beam parameters 50 4.3.1 Analysis of narrow s-channel resonances at fi+^~ colliders 50 4.3.2 Energy calibration by spin precession 51 4.4 Measurements of the Higgs-boson properties 54 4.4.1 Luminosity monitoring 55 4.4.2 Higgs cross-section results 55 4.4.3 Dependence upon Higgs mass 56 4.5 Consequences for Higgs-boson couplings 57 4.6 Consequences in a super symmetric scenario 58 4.7 Event generators for muon colliders 67 4.8 Squark production at the H and A resonances 68 4.9 Chargino production and decay 70 4.10 Probing CP violation in the Higgs sector of the MSSM 73 4.11 Strong electroweak symmetry breaking at muon colliders: pseudo-Nambu-Golstone bosons, very narrow and almost degenerate resonances 77 4.12 Z peak, top threshold and W threshold 79 4.12.1 Beam polarization 79 4.12.2 W and top threshold 82 4.12.3 Summary of precision improvement on electroweak observables 83 4.13 Conclusions 85

STEP 3: HIGH-ENERGY FRONTIER 87 5.1 Introduction 87 5.2 Heavy supersymmetric Higgs bosons 88 5.3 i?-violating supersymmetry 88 5.4 /^-violating contributions to tt production 91 5.5 Threshold studies: the case of supersymmetric particles 93 5.6 Implications of precision measurements 95 5.7 Strongly-interacting Higgs sector 96 5.8 Physics from extra dimensions 98 5.9 General remarks 101

xx RADIOLOGICAL HAZARD DUE TO NEUTRINOS FROM A MUON COL- LIDER 105 6.1 Introduction 105 6.2 Neutrino fluence expected from a muon collider 106 6.3 Shielding 107 6.4 Neutrino dose equivalent 107 6.5 Discussion 109

xxi 1 FOREWORD The concept of muon colliders was introduced by G. I. Budker [1, 2], and developed further by A. N. Skrinsky et al. [3]-[10] and by D. Neuffer [11]-[14]. The study of muon collider design has been under way in the USA since 1992, and, through a considerable amount of ingenuity and novel ideas, has led to a plausible design philosophy and sets of parameters for muon colliders. The Muon Collider Collaboration became a formal entity in May 1997. It comprises more than 100 physicists from 20 institutions in the USA, with the participation of three CERN accelerator physicists. The goal of the collaboration is to complete within a few years the R&D needed to determine whether a muon collider is technically feasible, and, if it is, to design the First Muon Collider. On this side of the Atlantic, the European community is blessed with the existence of a solid and ambitious project, LHC, able to explore effectively parton-parton centre-of-mass energies up to 1-2 TeV. Future options for CERN beyond the LHC, investigated in Ref. [15], include the muon collider as an interesting possibility. Because the muon collider is so original, in both its accelerator physics aspects and its physics capabilities, it seemed necessary to study it in more detail. A prospective study group, encouraged by ECFA, began its investigations in June 1998. This report describes the level of understanding reached by the participants of the study. The study was organized in three groups: neutrino physics (convened by Bruno Autin); precision muon colliders (convened by Alain Blondel); and the high-energy frontier (convened by John Ellis). This organization is somewhat different from the traditional separation between accelerators, experiments, and theory. It proved to be well suited for a good investigation of the physics possibilities, and brought out clearly the considerable accelerator challenges. The study group used many results obtained by the Muon Collider Collaboration, contained in particular in their status report [16]. There were at least four meetings of each of the three working groups, and three plenary meetings. We are particularly thankful to our American colleagues who took the time to travel and participate in our meetings, so as to share with us their experience: We thank Bob Palmer for his brilliant introduction to muon colliders; Rajendaran Raja for introducing us to cooling; Kirk McDonald for his report on the August '98 BNL workshop on muon-induced neutrino beams; and Iuliu Stumer for giving a detailed account of his studies of backgrounds. More generally, we are thankful to the Muon Collider Collaboration for giving us wide access to their working documents. The future will clearly require a dedicated effort in machine physics. The prospective study group was able to gather very precious contacts in Europe, and identified a nucleus interested in contributing to the detailed design studies and experiments that will be necessary to establish the feasibility and cost competitivity of muon machines. The technical challenges of muon colliders are certainly considerable, but the line of research that a muon-based programme would offer seems so rich that the effort to face them seems highly worthwhile. Large muon collider (\-s=5TeV)

Fast accelerator 2 in LHC tunnel (2.5 TeV)

Fast accelerator 1 in SPS tunnel (400 GeV)

jHggsfactory (vs = 100GeV) v factory —> Gran Sasso

Fig. 1: Possible layout of a muon complex on the CERN site. 2 MUON MACHINES 2.1 A tentative layout of muon machines on the CERN site B. Autin The size and shape of a muon complex are dominated by the requirement of fast acceleration. It has also to comply with the various peculiarities of an existing site. These constraints will first be reviewed and the integration of the various machines will then be described qualitatively. The figures given in this section are for illustration purposes and have not been exposed to simulation, let alone a cost or performance optimization. Some specific aspects are also discussed in Chapters 4 and 6.

2.1.1 Muon lifetime The muon lifetime at rest is 2.2 //s and its decay length (cr) 660 m. High-energy collisions may nevertheless be contemplated because of the dilation of the lifetime in the laboratory by the Lorentz factor. For an average acceleration of 1 MeV/m, the acceleration of muons from 250 MeV up to 2.5 TeV takes 8 ms over 2500 km, and 25% of the muons survive. It is at the beginning of the acceleration that the losses are the most severe. This makes the first stages (momentum-spread reduction, cooling) particularly critical.

2.1.2 Site considerations The presence on the CERN site of the largest machine in the world makes it very tempting, at least in a first analysis, to use the SPS and LHC tunnels for accommodating the accelerators which drive the muons to their top energy. It has also to be noted that the American study envisages circular accelerators to attain the final energy. Up to the Higgs factory energy, a linear structure prevails whether it is made of pure linacs or of recirculators. Moreover, the possible availability at CERN of the LEP supraconducting cavities makes it appealing to envisage a high-intensity linac as proton driver. A linear proton driver is the machine which has the best yield in terms of pions per watt and the lowest losses for high-intensity beams. This linac would also have other important applications: radioactive beams (ISOLDE), neutron spallation in conjunction with the present booster synchrotron, and accelerator driven systems (ADS) such as an energy amplifier or a nuclear waste burner. For these reasons, the proton linac should be in the neighbourhood of the CERN Proton Synchrotron (PS).

2.1.3 Description of a possible layout The general layout shown in Fig. 1 illustrates the three-step scenario. Its first part is stretched along a line which is approximately at the border of the Meyrin and Prevessin sites. It starts with a 1 km proton linac. The proton beam bombards a target from which pions and muons are collected in the transverse phase plane by a powerful focusing system and in the longitudinal phase plane by a linac which reduces the energy spread of the beam without changing the mean energy. The beam is then pre-accelerated and cooled before entering a recirculator whose shape resembles that of a 'neck-tie'. The muons are accelerated along a 500 m linac which provides 5 GeV at each passage and are sent back to the linac in arcs located at both ends. Each arc has a fixed field and there is thus one arc per energy increment. After the fourth arc (20 GeV), the beam is deflected towards a storage ring in which the muons decay along the two long straight sections and emit the two-flavour (ve and u^) neutrino beam towards the detectors. This storage ring could be oriented, for instance, towards the Gran Sasso. In collider mode, the beams remain longer in the recirculator to reach the maximum energy of 50 GeV at the end of the tenth passage in the linac, and are directed to the 'Higgs factory' which roughly occupies the location of an eleventh arc at the north-west end of the recirculator near the SPS. From the Higgs factory, the muon bunches are ejected into a fast accelerator located in the SPS tunnel up to an energy of 400 GeV, then to a second fast accelerator in the LHC tunnel up to 2.5 TeV, and finally stored in a large muon collider where they can achieve about 1000 collisions at a centre-of-mass energy of 5 TeV. Other experiments can be envisaged on the way to the highest energy, such as an intermediate collider to study the higher-mass Higgs bosons of supersymmetry, or deep-inelastic scattering using high-energy neutrinos.

2.1.4 Special features of a neutrino factory A tentative layout of a neutrino factory is given in Fig. 2. Neutrinos impose fewer constraints on the beam than colliders, and are thus a convenient first step in a muon complex. The time structure is arbitrary and one charge is sufficient. With a primary beam of protons, it is the vr+ and therefore the /^+ which is produced in greater abundance.

Linac Target |j accumulator Pre- accelerator . CO - O)

100 m Bunch rotator Recirculator

Fig. 2: Tentative layout of a neutrino factory.

Not only storage rings [17], [18] but also magnetic traps [19] have been proposed as sources of muon-induced neutrinos. The magnetic trap has an excellent capture efficiency but is limited to low energies, thus it is the storage-ring technique which will be discussed here. The most straightforward design that could be envisaged would be inspired by the front end of the Higgs factory [18], as designed by the American collaboration, adapted to a muon storage ring. This uses a 16-30 GeV synchrotron as a proton driver, leading to a low-frequency (e.g. 15 Hz) time structure. It might be worthwhile to consider another approach, taking advantage of the freedom allowed by neutrino beams, to build as simple a machine as possible to be quickly in business with the manipulation of intense muon beams. The proton driver would be a lower energy linac with a high-frequency time structure (e.g. as high as 352 MHz). Although this scheme has not been demonstrated to work, it is used here for a tentative description of what a neutrino factory could look like. The general concept is that of a fountain. The particles flow continuously from the target through the collection systems and a recirculator to the final storage ring where the muons decay into electrons and neutrinos. As a further element of simplification, it would be interesting to investigate up to what extent the RF structures can all work at high frequency and how much ionization cooling is really necessary. In this way, a minimal scheme could be set up and any further progress related to the muon colliders development would result in an increased flux of neutrinos. This scheme was not evaluated in terms of neutrino flux within the short time of the present prospective study, but a conceptual layout was outlined. The proton driver would be an intense proton linac, 10 mA at 2 GeV, based on LEP cavities as described in M. Vretenar's paper (this report). A 20 MW beam exceeds by nearly three orders of magnitude the beam power of the present CERN PS. Nevertheless, these machines have been studied in detail over several years for accelerator driven systems such as hybrid reactors or neutron spallation sources (see for instance Ref. [20]). In either case, the next step is to make a target that can stand the deposited energy over a long enough period of time. In the case of a low-frequency proton driver, resistance to mechanical shock is also required; it is believed that this would not be a problem at high frequency. The favoured technology is that of a heavy liquid metal jet [21] but the subject is so critical that there is room for other ingenuous solutions [22]. The choice of the target material is important for the production of negative pions from protons. Simulations made with MARS [23] showed that the ir~ to 7r+ ratio could be as large as 0.6 for 2 GeV protons impinging on a lead target. The ratio could become equal to 1 by using a particles or deuterons on any isoscalar target. After the target, the proton beam has to be dumped. Since there is roughly a factor 10 between pion and proton momenta, the magnetic separation of the beams is easy. The beam dump required for multi-MW beams is to be very carefully engineered. The present solution for collecting pions is based on a solenoidal system. Two types of focusing devices can be used [24]: a quarter wave transformer where the field varies stepwise between two solenoids or an adiabatic device where the field varies exponentially. The solenoid may have to produce a field as large as 20 T; its technology is described by J. Collot in Section 2.3. In the absence of cooling, the acceptance of the focusing channel is defined by the muon storage ring. Cooling would allow a larger collection angle, and, ultimately, a larger intensity. Taking a large acceptance ring such as the CERN antiproton collector as a reference, the normalized beam emittance is 6 x 10~3 m. This is the same as the emittance adopted for PILAC, a study of pion linac performed at Los Alamos [25]. For a capture radius of 1 cm at the end of the target, the collection angle is then 200 mrad for a mean momentum of 400 MeV/c and a field of a few tesla is then sufficient, but at the cost of a reduced capture yield. Comparisons should be made with other focusing devices such as magnetic horns and quadrupoles. The other factor that determines the muon yield is the momentum byte. The distributions of pions and muons are roughly the same in the momentum space and it is assumed, as a tentative figure, that pions and muons can be collected between 350 and 500 MeV/c. At the mean pion momentum, the speeds of the protons and of the pions are about the same since (3 is close to 0.945. The pion bunch-length dilation within the target is mainly due to the momentum spread of the pions. Preliminary calculations show that bunch rotation could be achieved in high-frequency cavities. It is nevertheless likely that the acceleration frequency would not be the same for acceleration and bunch rotation. The input energy to the recirculator is of the order of 1 GeV so that the muons are sufficiently relativistic to be accelerated over several passes without readjusting the phase of the RF wave. The distance at which the maximum number of muons is produced is of the order of 50 m from the source, and coincides with the entrance to the bunch rotator. This device is also assumed to work at 350 MHz, but with normal cavities which can deliver 0.1 MW/m and an energy gradient of 0.7 MeV/m for an iris radius of 10 cm and a shunt impedance of 5 MW/m. The muons are collected within an energy interval of 150 MeV, reduced to ±10 MeV after bunch rotation, while the bunch length is dilated from 24 to 180 ps. The linac length is 107 m and the longitudinal emittance 0.0036 eV s. At the end of the bunch rotator, 300 m could be occupied by an ionization cooling system. The recirculator consists of an RF straight section in which particles circulate in both directions in alternance and acquire typically 5 GeV per passage. Each time particles arrive at the end of the straight section, the beams are re-injected into the straight section by a magnetic arc adapted to the momentum to which they have been accelerated. Three such arcs are needed to reach 20 GeV. Increasing the muon beam energy simply costs more arcs. Beams are injected vertically into a small arc of the recirculator. Each arc has the shape of a 'petal'. The radius of curvature is proportional to the momentum of the particle and has been assumed to correspond to an average field of 1.2 T. The linac which occupies the 500 m straight section has an energy gradient of 10 MeV/m. It could operate at 700 MHz and be similar in design to the one developed at Fermilab for the cooling experiment [26]. In order for the bunches to be in phase with the RF wave at each passage, the arc lengths must be such that the transit time through the arc be a multiple of the RF period. There may be an extra tolerance for off-momentum particles which forces the arcs to be isochronous. The field being fixed for dipoles and quadrupoles as well, the focusing strength is different in the straight section at each passage and, in particular, it is opposite between a forward and a backward passage. The focusing of an arc must therefore begin with an F-quadrupole and end with a D-quadrupole in order to maintain the global alternating- gradient structure. More generally, the optics of a recirculator is not new and has already been successfully addressed in machines like CEBAF [27] and ELFE [28]. Last comes the muon storage ring. Here, the race-track shape is preferred to the neck-tie because it optimizes the neutrino yield which is proportional to the ratio of the straight-section length to the overall length (40%). In order to eliminate any overlap between the neutrinos coming from the pion beam and those resulting from the muon decay, the plane of the muon storage ring must be tilted with respect to the horizontal plane of the other machines. Neutrino beams emerge in the direction of the straight sections. Neutrino detectors can be situated very close to the ring, since no large background is expected. The focusing of the long straight section is such that the beam divergence is small with respect to the divergence of the neutrino beam. This means rather loose focusing (high-/3 inserts) in contrast with the packed focusing of the recirculator. This is possible because the beam emittance has decreased by the factor l//?7 with respect to the beam emittance at injection into the recirculator. Finally, the decay time in the muon storage ring at 20 GeV is 440 /xs and the revolution time is « 3.5 /is. Consequently, an accumulation system has then to be designed. The accumulation may be done preferably at the proton and/or, to a limited extent, at the muon level [29]. Accumulating protons means more particles per bunch. An example of accumulation scheme is the well-known technique of repetitive injection of an H-beam into a ring. The beam coming from the linac is deflected outwards by the field of a bending magnet of the ring and the negative ions are transformed into protons by stripping in a thin carbon foil located downstream of the magnet. The limitations are related to the heating of the foil, the emittance blow-up due to multiple scattering at each passage through the foil, the local activation of the machine due to the imperfect stripping of the ions (~ 2%) and the need for kicker magnets. The frequency multiplication technique [30] contemplated for the CLIC drive beam could be applied to muon accumulation and the experience gained with CTF3 would then be of great value.

2.1.5 The precision muon colliders The Higgs factory could be built once and if the light Higgs has been discovered and its mass more precisely known. The present assumptions are a mass in the range 100-130 GeV and a width of the order of 3 MeV. The basic interest of a muon collider is the possibility of producing the Higgs in the s-channel and to measure its mass, width and cross-section with high precision. This opportunity might become reality if one can achieve sufficient luminosities for beams of tiny momentum spread 3 x 10~5. Here, three differences manifest themselves with respect to a neutrino factory. First, the beam has to be bunched; second, the two charges have to be manipulated simultaneously; and third, six-dimensional cooling is mandatory. In the scheme envisaged here, the muon beam has a time structure which is roughly the image of the proton beam structure. The bunching is thus produced at the level of the protons by an ingenious fast bunch rotation near the transition energy of a synchrotron. A preliminary experiment performed at BNL [31] proved the feasibility of the scheme for a limited number of protons in the bunch. Dedicated work has to be continued to show that it is indeed possible to compress 1014 protons in a 1 ns bunch. Within the context of the neutrino factory, the linac would work in the regime of a synchrotron injector, and, using the PS as a buncher, the proton energy would be near 6 GeV. The bunch rotator would be a new linac operating at lower frequency (around 70 MHz). The pre-accelerator of the neutrino factory would be replaced by the cooling system, for which we have so far relied heavily on the Fermilab experiment proposal [26]. It is especially important to design the cooling system soon enough to ensure that the accelerating system of the recirculator will remain adequate, and vice-versa. Once the beam has been cooled, it is accelerated in the recirculator up to 50 GeV per beam, the bunches of opposite charges being phase-shifted by vr on the RF wave and circulating in opposite directions in the arcs. In Fig. 3, the arcs are represented with the same average field as for the neutrino factory. It is likely that they will be shorter using super-ferric magnets (3 T) fed by a superconducting cable and derived from the design proposed for a very large low-field hadron collider [32]. This solution would place the last three loops in the same tunnel and save some civil engineering. The same technology might be appropriate for the Higgs factory itself.

a linac Target Cooler ju. storage ring Bunch rotator

•—• Buncher Higgs factory 100 m Recirculator

Fig. 3: Tentative layout of a Higgs factory.

As far as the collider is concerned, the study of the American collaboration is summarized in Ref. [16]. A weak point in this study is the low repetition frequency, 15 Hz, which is well adapted to a large collider but less so to a low-energy collider, where the particles decay 50 times faster. The luminosity is proportional to the repetition frequency and some innovation is required to improve it.

2.1.6 Final acceleration and large collider To reach the final energy of several TeV is more an economic than a technical problem. It is indeed rather straightforward to apply all the developments of linear colliders to muon colliders. Assuming that 40 MV/m superconducting cavities will be available in 20 years from now, a 60 km linac could feed a storage ring with both (i+ and \x~. The present approach tries to minimize the cost of civil engineering and RF investment by re-using the accelerating field over several passages. We have seen that recirculators have precisely this function, but it is not desirable to multiply the number of arcs excessively. Recent studies try to resurrect the concept of the fixed-field alternating-gradient (FFAG) accelerators [33] or to adapt achromats to a large range of momenta. The common feature of these techniques is to achieve a substantial part of the bending strength with quadrupoles: At some nominal energy, the orbit is centred in the quadrupole and the bending strength is only determined by the dipole field; at lower energy, the negative field of the quadrupole would reduce the integrated bending strength and at higher energy the positive field of the quadrupole would increase the total bending strength. Alternatively, the bending strength modulation produced by the quadrupoles might be replaced by a fast modulation of the dipole field using pulsed coils. This type of accelerator should be accommodated in circular tunnels like the SPS and LHC tunnels. In brief, the problem of ultimate energy for a muon collider is more one of optics than of acceleration. The high-energy muon collider has been thoroughly studied by the American collaboration [16] and the most important issues (detector background, final focus, isochronicity, beam stability, polarization, etc.) have been addressed if not fully resolved. The major limitation on the high-energy collider comes from neutrino radiation levels. With the present design characteristics, and on the CERN site, the centre-of-mass energy should not exceed a few TeV if one is to maintain the collider at the depth of the LHC. Hopes of solving the neutrino radiation problem rely on a reduction of the muon intensity. To maintain the luminosity with a lower current is at the cost of a reduced emittance, which requires more cooling, thus probably some technique beyond ionization cooling, and makes sense only if the beam-beam interaction is in some way counteracted by a special device. A lower emittance means more cooling and optical stochastic cooling has been proposed [34]. Beam-beam passivation [35] has been discussed for a long time and is based on electromagnetic shielding produced by the electrons of a plasma or, at the charge density of a TeV collider, by the free electrons of a metal which could be here a jet of lithium. The theory of these effects exists but no experimental application has been performed up to now. This kind of research has to be vigorously stimulated. The experience gathered with the lower-energy machines should prove highly beneficial.

2.2 A 2 GeV superconducting linac as a proton driver for muon beams M. Vretenar In the line of many ideas to re-use the LEP superconducting RF system, a proposal was made for the construction of a 2 GeV Superconducting Proton Linac (SPL) to inject H~ ions into the CERN PS [36, 37]. The purpose of this linear accelerator was to improve the beam brightness in the PS by a factor of 2, compared with the present scheme for LHC injection. The LHC could thus operate in the regime of the beam-beam limit and reach the ultimate luminosity. In fact, the spectrum of applications for an intense linac is much broader than its use as an element of the LHC injector. New generations of stopped-muon experiments and of radioactive beams for facilities such as ISOLDE become possible. Moreover, using intense beams at relatively low energy is the most economic way of producing pions in terms of particles per watt; a high-power linac is thus an excellent candidate to drive the proton beam in a muon collider or a neutrino factory complex. The accelerator is made up of a conventional drift-tube linac up to an energy of 100 MeV, a superconducting section with new low-/3 cavities up to 1 GeV, and standard LEP superconducting (SC) cavities up to 2 GeV. For the LHC needs, the linac accelerates 10 mA of H~ at the low duty cycle required by the PS. The beam is chopped at low energy to minimize capture losses. The RF cavities used in the energy range between 1 and 2 GeV, other major cryogenic components and the entire RF infrastructure can be recuperated from LEP, leading to a cost-effective machine. The main elements to be constructed are the 100 MeV room-temperature linac, new SC cavities and cryostats from 100 MeV to 1 GeV, the focusing and diagnostic equipment and the cryoplant. New civil engineering is needed for a 900 m long tunnel and an equipment gallery. Pulsed operation is likely to be needed for muon colliders, as well as for LHC, but continuous-wave (CW) operation may be interesting for a neutrino factory; extra cooling power has then to be installed. With an adequate 100 MeV CW injector, this linac could deliver a continuous beam of protons. Assuming a 10 mA beam current at 2 GeV, the beam power is 20 MW and the proton flux 6 x 1016 p/s, or more than three orders of magnitude over the present PS intensity. Expenditure for extra cooling power can be distributed in time to match the needs for increased flux. Few modifications to the SPL basic design are required for CW operation. A second proton injector (a particle source and an RFQ accelerator up to 2 MeV) has to be built and connected to the main linac by a switching magnet to operate in parallel with the H~ low-duty-cycle injector. The room-temperature linac cavities have to be specifically designed for CW operation and the cryogenic power will need to be nearly tripled because of the additional RF losses. The SC cavities and the RF systems are perfectly adapted for running CW with 10 mA current, as they do now for LEP, but energy consumption increases to 70 MW. A key concern is the radiation safety for a beam power of 20 MW. In order to allow hands-on maintenance, losses in the linac have to be kept below 0.5 nA/m: a challenging figure that requires sophisticated collimation systems and a careful control of beam-halo formation. The large aperture of the LEP SC cavities is an advantage in this respect, because most of the halo particles are transported to the end of the linac and dumped into the target area where radiation issues are specifically addressed. Table 1 summarizes some of the parameters of the SPL in the CW mode of operation.

Table 1: Superconducting-proton-linac parameters in the continuous-wave mode of operation.

Beam current 10 mA Energy 2 GeV Beam transverse emittance 0.6 /jm, rms, normalized Beam-energy spread ±2 MeV, total {y/ha) Bunch length 24 psec, total (y/Ea) Linac length 900 m Overall RF power 34 MW Number of klystrons 43

RFQl chopper RFQ2 DTL SC - Low P SC-LEP2 Isolde target v-factory

0.05 1000 2000 Energy [MeV]

10m 100m 372m 407m

Fig. 4: Schematic layout of a possible proton driver based on superconducting RF cavities.

2.3 Solenoids for pion collection J. Collot, W. Joss 2.3.1 Introduction In this section, we will briefly present a conceptual study of a pion collector based on the utilization of high-field solenoids. As depicted in Fig. 5, the pion production target is housed in

9 the bore of a 3 m long solenoid. Pions released by the target freely spiral towards the solenoid exit edge, where they are focalized into the decay channel by a transition magnet (not described here) if their helical curvature radius is smaller than a quarter of the bore diameter. This condition sets a limit on the transverse momentum of the collected pions, which reads

PT (GeV) < 0.075 $(m) B(T) . (1) If at the end, one desires to put forward a proposal of a magnet feasible in the close future with as little R&D investment as possible, the status of the high-field-solenoid technology [38], which will be succinctly reviewed in the following paragraphs, roughly dictates that one should remain below 20 T in a bore diameter of 10 cm over a total length of 3 m. Such a solenoid would collect pions with a maximal transverse momentum of 150 MeV.

0 =- 10 cm

solenoid

Fig. 5: Sketch of the pion collector.

2.3.2 Choice of conductor technology High-field magnets are in principle most economically built by making use of superconductivity. However, as can be seen in Table 2, of the two common superconductors currently procurable on a large scale, only NbaSn allows a 20 T field to be reached. As a matter of fact, Nb3Sn solenoids generating up to 21 T are today commercially available. But at high fields, the obtained critical current density of NbaSn superconductors is rather small, and consequently the magnet dimensions are at present far too small (<£ < 5 cm, 1 < 50 cm) for our needs. High-temperature superconducting magnets, which might improve this situation in the future, are not expected to be launched on the market for five years.

Table 2: Main features of available superconductors.

Superconductor Tc(0 T) Tc(ll T) Bc2(1.8 K) Bc2(4.2 K) NbTi 9.5 K 4.2 K 14.0 T 11.0 T Nb3Sn 18.0 K 10.4 K 25.5 T 23.2 T

On top of these limitations, a superconducting magnet, if used alone, may suffer from the large radiation doses which will result from the intense proton-beam interaction in the target. In contrast to superconducting magnets, resistive solenoids exhibit no fundamental field limit. In practice however, their maximal field is technologically limited by the complexity and

10 then the cost of both the d.c. power supply and the water cooling system needed to operate the magnets. For a given power P, the field generated in a resistive solenoid with a bore diameter $ is given by ±Bm=GM (2) where • p is the electrical resistivity of the conductor. • A is the filling factor which corresponds to the fraction of the volume occupied by the conductor. • G is the dimensionless Fabry factor which depends on the geometry and the current distribution of the magnet [39]. As already derived by Maxwell, G is maximal and equal to V/3TT/2 for an infinite cylindrical magnet with A = 1. Being run at ambient temperature, and since they are basically made of Cu and some insulating material, resistive magnets are much less sensitive to radiation. Based on these considerations, we have examined two configurations: • a pure resistive 20 T solenoid of the Bitter type, • a 20 T hybrid magnet consisting of a 12 T Bitter magnet inserted in the bore of an 8 T NbTi superconducting solenoid. All the characteristics of the magnets that will be presented in the two following paragraphs were derived from the experience acquired by the Grenoble High Magnetic Field Lab (GHMFL) in constructing and operating high-field solenoids [40].

2.3.3 20 T Bitter magnet The Bitter technique [38] is currently the easiest way to build a long high-field resistive solenoid if no severe constraint on the field homogeneity is required. In addition, since the main materials which are used in this technique are copper, Kapton and water as the cooling medium, Bitter magnets can certainly withstand the radiation doses generated in the proximity of the pion production target. The structure of a Bitter magnet is presented in Fig. 6. Such a solenoid is built by stacking thin (~1 mm) Cu discs interleaved with insulating Kapton foils. The Cu discs are made electrically-open by punching narrow radial grooves. Windows in the insulating Kapton foils, azimuthally localized near the radial grooves, assure the electrical connection of adjacent Cu discs. To force the current to spiral through the coil, the Cu and Kapton discs are periodically rotated. Holes are punched in the discs so as to form channels - when the coil is assembled - through which high-resistivity water is circulated to cool the magnet. To keep the mechanical stress induced by Lorentz forces in the solenoid below the elastic limit of Cu (especially at low radius where the current is maximal, since I(r) oc 1/r), the proposed 20 T magnet is composed of two coils (Fig. 7) connected in series. The operation of this solenoid at 20 T would need a d.c. power supply of 60 MW and a refrigerating system forcing the circulation of 750 1/s of water with a temperature rise of 20 K across the magnet. A 24 MW d.c. power supply is in operation at the GHMFL. Based on this experience, a 60 MW power supply appears technologically feasible.

11 cooling water

current

Bitter plate

insulation

cooling hole •contact area

housing

tie rod

bottom end plate

current BITTER MAGNET

Fig. 6: Structure of a Bitter magnet.

= 3m

R4 = 415 mm

R3 = 133.5 mm R2= 129.5 mm

Fig. 7: Sketch of the 20 T Bitter magnet.

12 2.3-4 20 T hybrid magnet The interest in using a superconducting magnet comes from the huge saving in electricity consumption it brings. As shown already, a standalone SC magnet does not appear as a viable solution yet. This is why our proposal is to place a Bitter magnet in an SC outsert. In such a solution, the Bitter magnet, if it is thick enough, would also act as a radiation screen for the SC solenoid. Now, if we want to limit ourselves to well-mastered technologies which are today 'on catalogues', we are compelled to use NbTi at a maximum field of 8 T because of the large radius of the SC bore. Our proposal, which is schematically drawn in Fig. 8, is based on an extension in length of the 8 T NbTi magnet which is being built by Oxford Instruments under a contract signed with GHMFL in the context of the 40 T hybrid magnet project [40]. The 12 T Bitter magnet could simply be an optimized version of the device which was described in the previous section. Since the power dissipated in a resistive magnet scales as B2, a 22 MW d.c. power supply will be sufficient to run the Bitter magnet at 12 T.

L = 3m

NbTi • H T - I.SK

B = 12T P = 22 MW

>j = 100mni

Nb'li

Fig. 8: Schematic view of the 20 T hybrid solenoid.

2.3.5 Cost estimate The cost estimates which are given below have been prepared with the help of GHMFL. At this stage, they have to be taken as indications for determining the most promising configuration for further studies. To estimate the electricity consumption cost, a total of 70 months of continuous operation and a price of electricity of 37 CHF/MWh have been assumed.

20 T Bitter magnet Item Cost Scaling law (MCHF) Magnet 3 oc weight d.c. supply and cooling system 25 txLB2 Electricity consumption 110 oc LB2 time Total 138

13 20 T hybrid magnet Item Cost Scaling law (MCHF) Bitter magnet 3 oc weight SC magnet + cryogenics 13 oc L d.c. supply and cooling system 7 « ^Bitter Electricity consumption 35 K LBBitter time Total 58

2.3.6 Conclusion At present, technical solutions exist to build a 3 m long, 20 T solenoid. Among the configurations briefly presented here, a hybrid solution using an 8 T SC outsert and a 12 T Bitter insert seems to be the cheapest configuration if one takes into account the cost of the electricity consumption. Such an SC magnet could be ordered from industry. In addition, the technology to build the Bitter magnet is available at GHMFL. Further studies are needed to optimize the geometry with respect to the performance of the pion collector. An investigation of the radiation doses behind the Bitter magnet and their consequences in the SC outsert has also to be done.

14 3 STEP 1: NEUTRINO FACTORY The neutrino sector of the Standard Model has always been considered fascinating and attractive. With the advent of strong experimental indications for neutrino oscillations, and with the prospects of studying extra-galactic neutrinos in the not too distant future, the case for a continued experimental neutrino programme has become, if anything, stronger. In line with its long-standing tradition and with its expertise in experimentation with neutrinos, CERN should take on a significant part of this experimental neutrino programme, as one pillar of its long-term scientific programme. With a view to contributing to the discussion of how a long-term experimental neutrino programme at CERN could look, this chapter draws attention to the physics opportunities which are offered by the high-intensity neutrino fluxes originating from the decay of muons circulating in a muon storage ring. As already mentioned, such a complex, called a 'neutrino factory', could be an interesting step in an R&D programme towards a /x+/z~ collider. The description of the physics opportunities and, even more so, of the underlying accelerator complex is, at this early stage, sketchy and incomplete. Yet it is hoped that sufficient interest is raised so that further in-depth studies will be encouraged and pursued. As mentioned in Ref. [41], the additional possibility of high-intensity neutrino beams from pion decay would be opened by the high-intensity proton source. It would imply acceleration of the protons to higher energies and involve a proton synchrotron. Only the neutrino factory based on muon beams is described in this report, and is designed to provide a second generation of experiments at Gran Sasso.

3.1 Outline of neutrino oscillation experiments at the muon storage ring facility J. Panman 3.1.1 Neutrinos from a muon storage ring The muon storage ring (see Fig. 2) is fed with muons originating from ir decay. Pions could be produced by the high flux of 2 GeV protons accelerated by a proton linac. The acceptance of muons can be increased by a cooling system. The captured and cooled muons are accelerated to any desired momentum up to 20 GeV or somewhat higher1, and then injected into the muon storage ring, whose straight sections serve as a decay path. The direction can be chosen to point toward the Gran Sasso or other positions. Muons in a storage ring have a well-defined momentum, and no other particles are stored along with them. Thus, when /x+ are stored, the decay

delivers a pure beam of equal numbers of v^ and ve with a perfectly calculable energy spectrum, depending only on the muon momentum and the polarization of the circulating beam. There is no opposite-sign background. Similarly, a beam of pT will give an equal number of u^ and ue. In the following, a fj,+ beam will be assumed unless otherwise specified. The momentum of the muon beam can be chosen to match the experimental requirements. The energy spectrum of the fM's peaks close to the muon energy, while the energy spectrum of the ise's is softer, peaking at two thirds of the muon energy. Since the muon beam is monochromatic, the neutrino spectra do not exhibit the large tails towards high energies which are present in wideband beams produced by n decays. Besides the excellent knowledge of the spectrum, the absolute number of neutrinos can be calculated with high precision, since the number of circulating muons is easily measurable. 1 Optimization of the muon beam energy is beyond the scope of this study.

15 With a given geometry of the storage ring, a fixed fraction of the muons decay in the direction of the experiment (up to 40%), independently of their momentum. The decay electrons are swept away by the field of the bending magnets, and the background of low-energy neutrons and photons arising from electromagnetic cascades can be shielded. 'Nearby' experiments at the two ends of the storage ring, with rather moderate transverse dimensions, are well conceivable. There is a large degree of flexibility in the design of the storage ring, allowing various detector locations. In fact, different straight sections can be used to point simultaneously to different experiments located at optimum distances from the decay region. Figure 9 shows the expected v^ flux at the Gran Sasso from muon decay in the muon storage ring.

o 20 -

0 2 4 6 2 4 6 8 E (GeV)

Fig. 9: Fluxes and lepton spectra (taken from Ref. [18]) in a detector 732 km downstream of a muon storage ring source with circulating unpolarized muons of 10 GeV. The number of muon decays is 7.5 x 1O20, of which 25% point to the detector. The upper plots show the (anti)neutrino spectra, the lower plots the charged-lepton spectra for charged-current interactions.

3.1.2 Outline of neutrino oscillation experiments from a muon storage ring With the advent of experimental evidence for neutrino oscillations, and therefore the likely existence of a CKM-type unitary mixing matrix between three weak eigenstates (fe, v^ and vT) and three mass eigenstates {v\, ^2 and ^3), the experimental challenge is to determine the four independent parameters of this Dirac neutrino mixing matrix, together with the two associated independent differences of masses squared (Amf2, Am^). Of course, Nature may have even more surprises in store such as sterile neutrinos and the like. The neutrino factory described above lends itself naturally to the exploration of neutrino oscillations between all neutrino flavours with high sensitivity to small mixing amplitudes sin2 20

16 and small differences of masses squared Am2. The observables are listed in Table 3. Here, 'NC/CC denotes the ratio of 'short' to 'long' events in a calorimetric detector, where the penetrating muon of charged-current v^ events gives rise to 'long' events, whereas all neutral- current events as well as charged-current ue events give rise to 'short events'.

Table 3: Neutrino oscillation studies at a neutrino factory from a fj,+ storage ring

Oscillation Type Measured quantity

l/e <-> Vx disappearance energy spectrum, 'NC/CC' Ue V^ appearance 'wrong-sign' muons ve «-> vT appearance r events

VfJ, <"> Vx disappearance energy spectrum, ' NC/CC'

v^ <-» i>e appearance 'wrong-sign' electrons Up <-» VT appearance r events

The neutrino factory permits a precise determination of neutrino oscillation parameters, with a very significant improvement as compared with earlier experiments with accelerator neutrinos. The particular strength of this neutrino beam is its background-free flavour composition, the ease of the absolute normalization, and the free choice of the momentum of the muons in the storage ring. In particular, the energy can be chosen high enough so as to be above the r-production threshold or conversely low enough to remain below charm-production threshold. In the following, a possible programme of neutrino oscillation measurements is discussed. Of course, this cannot be exhaustive but can be regarded as an initial exploration of the potential. We also indicate briefly options in other fields of neutrino physics. In neutrino oscillation experiments it is of primary importance to know the initial composition of the neutrino beam. In a beam produced by muon decay, the two neutrino types have different leptonic charge and flavour. Therefore, even in the presence of oscillation, the charge of the lepton produced in charged-current interactions is a unique tag of the initial neutrino flavour. Thus in a beam produced by pT decay, a negatively charged lepton originates from the i/p, while a positively charged lepton originates from the v%. In the absence of oscillation one expects charged-current reactions with pT and e+ in the final state. However, the presence of fj,+ or e" would signal oscillation phenomena [18].

3.1.3 Appearance experiments

An experiment capable of identifying muons and determining their charge is sensitive to ve <->• v^ and ue <-> vT oscillations (via the r~ —> JJT decay) in the appearance channel, and u^ <-> vx oscillations through disappearance. Of course, also ve <-> i/x oscillations can be measured in the disappearance channel even if the electron charge is not determined. The importance of charge discrimination of the leptons has recently been underlined for short-/medium-baseline experiments in Ref. [42], and for long-baseline experiments in Ref. [43]. A detector which has muon and electron identification without charge determination, provides the opportunity to search for neutrino oscillation phenomena by comparing the rate of Vp charged-current events with ue charged-current events. In the presence of v^ <-> vx and/or ^e <-* vx oscillations, a good disappearance measurement is the ratio of electrons and muons [44].

17 However, because of the beam composition with equal numbers of muon and electron neutrinos, without charge determination such a measurement would be quite insensitive to v^ <-> Pe oscillation.

1 1 1 1 1 11 1 I 1 1 1 1 II E ' ' 1 ' "F [0 GeV/c ; muons -1 0 - 20 GeV/c muons t > [ > <

—•=»

-2

-4

0 -

-5 I i I 1 I 11 I I I 1 I 1 1 i j i

-4 -3 -2 10 10 10

Fig. 10: Typical sensitivity of a vT appearance experiment utilizing the FM beam or ve beam from muon decay. The curves give 90% CL limits for an exposure in a beam generated by 3 x 1021 muon decays, of which 25% point to a detector with 1 kt fiducial mass, situated in the LNGS. The detector is assumed to have 25% (10%) efficiency

for tau detection for the neutrinos from the decay of 20 (10) GeV muons. The sensitivities for uT appearance in

ve <-> vT and P^ «-> vr oscillations are similar and not shown separately

The availability of a copious source of high-energy electron neutrinos is unique to the neutrino factory. This opens up the possibility to perform u^ <-» vr oscillation experiments with a sensitivity similar to v^ <-> vT experiments. The charge of the decay daughter of the r selects the oscillation mode (i/e «-> vT versus v^ <-> uT). With the capability of charge measurement of the outgoing leptons, the 'wrong-sign' muon or electron can signal u^ <-> ue or ve <-> v^ oscillations. Also r decays can produce 'wrong-sign' leptons and therefore the detection of these leptons can also indicate v^ <-> vT or ve <-> uT oscillation. Detection of the decay kink and/or kinematical analysis of the event can disentangle these different possibilities. The intrinsic limitation in this method is given by the charm-production process, which has a relatively large cross-section in neutrino scattering. Furthermore, a detector at a larger distance would provide the same Am2 sensitivity at maximal mixing with a reduced background. 2 Figure 10 gives an estimate of the accessible range for v^ <-• vT oscillations in the sin 26 versus Am2 plot, assuming that r decays are measured without background, with 25% (10%) efficiency for the neutrinos from the decay of 20 (10) GeV muons, in a detector of 1 kt fiducial mass, situated in the LNGS.

3.1.4 Background considerations A discussion of the potential sensitivities is not complete without a study of the experimental backgrounds. For a given value of Am2, background considerations are essential in the determi-

18 nation of the best value of L/E, and in particular for the choice of the muon beam momentum. The discussion outlined below would need to be quantified in order to fix this important parameter. As mentioned above a measurement of the rate of leptons of opposite charge is a powerful tool for appearance experiments. In Table 4 the possible appearance channels are compiled, together with their most dangerous backgrounds. Charm production, which can also generate leptons with the opposite charge, is expected to be reducible by a large factor. It is possible to have a crude estimate of the size of the problem. Charm production occurs in 5% of events in the energy range of these beams (a few tens of GeV). Rejection by detection of the primary lepton reduces the remaining background to about 0.005. A reasonable estimate for kinematical rejection of charm decays is again a factor of ten. The estimated order of magnitude of the background is then 5 x 10~4. The background is larger in processes where + charm is produced by neutrinos rather than antineutrinos (i/e in beams from fi decay, or i/M in beams from /x~ decays). A weaker rejection is to be expected in charm production by electron- type neutrinos compared to muon-type neutrinos. This is due to the more difficult experimental task to veto electrons compared to muons. Combining these arguments, the detection of ue <-> vT oscillation in a beam from fj,+ decay is expected to have the lowest background.

It should be noted that the i/e <-> u^ and PM <-» ue channels can be studied at neutrino energies below charm threshold, and can therefore be studied free of this particular background. The inconvenience of this approach is the low neutrino intensity to be expected at these energies. An experimental background is also present in the form of leptons with mismeasured charge. This effect can be at the per-cent level in iron-core magnets, and potentially much lower in air-core spectrometers.

Table 4: Appearance channels and their backgrounds (charges assumed for a beam from n+ decay).

Channel Signal Potential background Ve <-» I/pi n~ charm production byl7u f e <-> l/T r~(with decay into \i ) charm production by iv i>M <-> ve e+ charm production byi/e + + Vfi *-* &T r (with decay into e ) charm production by ve

So far, the sensitivity of the experiments made possible by a neutrino factory has been characterized by a contour in the sin2 26 versus Am2 plot in a two-flavour mixing scenario. How- ever, given the strong experimental indications, in particular for solar neutrino and atmospheric neutrino oscillations, one is unavoidably led to consider the more general case of three-flavour mixing. It is in this area that the well-defined and background-free neutrino beam originating from a muon storage ring, in conjunction with the possibility of reversing the polarity, shows its full power, as recently emphasized in Ref. [43]. The point is that contrary to the case of two- flavour (i.e. i/fj, <-• ux) mixing, in a three-flavour mixing scenario there are generically ue <-> v^ oscillations at long baselines. Consequently, the measurement of the charge of final-state muons gives an extremely powerful appearance measurement via 'wrong-sign' muons, with no need for r identification. Furthermore, CP-violation effects may not be out of reach. As a consequence, the prospects of building a magnetic neutrino detector with a fiducial mass in the 10 kt range should receive due attention.

19 3.2 The mixing of three neutrino families: peculiarities, signatures and opportunities B. Gavela, P. Hernandez and A. De Rujula 3.2.1 Current motivation Indications of atmospheric neutrino oscillations [45] have rekindled the interest in accelerator experiments that could study the same range of parameter space. The results of SuperKamiokande are interpreted as oscillations of muon neutrinos into neutrinos that are not ve's. Roughly speaking, the measured mixing angle is close to maximal: sin2 26 > 0.8, and Am2 is in the range 5 x 10"4 to 6 x 10~3 eV2, all at 90% confidence. The solar-neutrino deficit is interpreted either as MSW (matter enhanced) oscillations [46] or as vacuum oscillations [47] that deplete the original i/e's, presumably in favour of i/^'s. The corresponding mass differences (10~5 to 10~4 eV2 or some 10~10 eV2) are significantly below the range deduced from atmospheric observations. Currently envisaged terrestrial experiments have no direct access to the solar mass range(s). The inevitable conclusion of a description of atmospheric and solar neutrino data as two independent two-by-two neutrino-mixing effects is that the only hope to corroborate the atmospheric results with artificial beams is based on long-baseline experiments looking for r appearance or /i depletion. The often-discussed long-baseline experiments — such as MINOS [48] or a CERN to Gran Sasso [49] project — would have difficulty in covering the entire parameter space favoured by SuperKamiokande. If the same data are analysed in a three-generation mixing scenario, the conclusions are very different: Long-baseline experiments searching for ve <->• v^ transitions regain interest, since these oscillations (even if primarily responsible for the long-distance solar effect) will in general also occur over the shorter range implied by the atmospheric data. We analyse the potential of a neutrino factory in a three-generation scenario [50]. A recent analysis of the SuperKamiokande data [51] favours slightly higher values of Am2: good news for current long-baseline projects and for the physics potential of a neutrino factory. To be specific we consider as a 'reference set-up' the neutrino beams resulting from the decay of n^ = 2 x 1020 /Lt+ and/or yT in a straight section of an E^ = 20 GeV muon accumulator ring pointing at an experiment with a 10 kT target, some 732 km downstream, roughly the distance from CERN to Gran Sasso or from Fermilab to the Soudan Lab. Many of our results are for the 'reference baseline' L = 732 km, but we specify the scaling laws that interrelate different energies and distances.

3.2.2 Neutrino fluxes 2 The neutrino fluxes at a neutrino factory have simple analytical forms . Let y = EvjE^ be the fractional neutrino energy. For unpolarized muons of either charge, and neglecting corrections of order m? / E2 the normalized fluxes of forward-moving neutrinos are

2 Fu^(y) ~ 2y (3-2y)e(y)e(l-y), 2 FVefiM - I2y (I-y)&(y) 0(1-y), (3) and, for each produced neutrino type, the forward flux from n^ muon decays is

dNu 2 K(y) • (4) dydS ?~o TX m ,1?

2We expect the i/-beam divergence to be dominated by the p-decay kinematics [18].

20 The above expressions are valid at a forward-placed detector of transverse dimensions much smaller than the beam's transverse size ~ Lmtl/{2Etl). In the absence of oscillations, one can use Eq. (4) and the charged-current inclusive cross- 38 2 sections per nucleon on an approximately isoscalar target {av ~ 0.67 x 10~ Ev cm /GeV, <7;j ~ 0.34 x 10~38 Ejj cm2/GeV [52]) to compute the number of neutrino interactions. For the reference set-up and baseline described above, one expects some 2.2 x 105 fj,~ (1.1 x 105 /z+) and 9.6 x 104 e+ (1.9 x 105 e~) events in a beam from \i~ (A*+) decay [18]. In our calculations we make a cut Eu > 5 GeV to eliminate inefficiently observed low-energy interactions. This affects the quoted numbers only at the few per-cent level.

3.2.3 Theoretical background

In a three-family scenario the mixing between ve, v^ and vT is described by a conventional Cabibbo-Kobayashi-Maskawa matrix V relating flavour to mass eigenstates. For Dirac neutri- nos3 and in an obvious notation,

C12C13 C13S12 S13 \ /^l\ — C12S13S23 Ci2C23el

2 Let us adopt, from solar and atmospheric experiments, the indication that |Am 2| -C |Am23|, which Barbieri et al. [53] have dubbed the 'minimal scheme'. Though this mass hierarchy may not be convincingly established, the minimal scheme suffices for our purpose of delineating the main capabilities of a neutrino factory. Atmospheric or terrestrial experiments have an energy range such that Arn^L/E^

~~22 22 2 = sin (0(02323)) sinsin (20(201313)) sinsin~~

~~2 2 2 P(ve —* vT) = cos (023) sin (20i3) sin ( ) V ^ / 2 2 sin (2023) sin ( —^ ] , (6) with 2 Am L~~

Note that for #13 = 0 the probability P(^M —> vT) reduces to the familiar expression for the mixing of the second and third generations, while the other probabilities in Eq. (6) vanish. The approximate analysis of the SuperKamiokande data by Barbieri et al. [53] results (for the range of Am^ advocated by the SuperKamiokande collaboration) in the restrictions 023 = 45 ± 15° and #13 ~ 0-45°, with a preferred value around 13°. Fogli et al. conclude [54], after a more thorough analysis and with equal confidence, that #13 < 23°, while their range of 2 Am 3 is a little narrower than the one obtained by the SuperKamiokande team [45]. We shall present results for the range of angles advocated in Ref. [53] and the range of masses of Ref. [45], simply because these are the widest ranges.

~~3 Extra phases appear in the Majorana case, but their effects are of order mvjEv.~~

~~21 All mixing probabilities in Eq. (6) have the same sinusoidal dependence on Am| L/Ev, entering into the description of a plethora of channels:~~

~~+ fe —> ve —* e disappearance, i'e ~* ^ ~* A4"1" appearance, + + + + ue —> i>T —> r appearance (r —* /x ; e ), ^ ""* ^ ~> M~ disappearance,~~

~~i/M —» i/e —> e~ appearance,~~

~~^ —*• vT —* r~ appearance (r~ —• /x~; e~). (8)~~

~~The 'wrong-sign' channels of /x+, r+ and e~ appearance are the good news relative to the (misleading) results of a two-family analysis, for which the only appearance channel would be that of T~ .~~

3.2.4 Wrong-sign muons The three-family mixing scenario brings to the fore the importance of appearance channels such as those leading to wrong-sign muons, for which there would be no beam-induced background at a neutrino factory, unlike for other types of neutrino beams. We present results for a 90% statistical sensitivity reach; the physics backgrounds will be briefly discussed later. 2 2 In Fig. 11 we show the sensitivity reach, in the [sin (023), Am 3] plane, for various values of 0i3, for L = 732 km, for our reference set-up and for stored \x~. We have chosen to illustrate the disappearance observable A^ = N[fi+ + /x~] (i.e. the total energy-integrated number of muon events), and the appearance measurement N[fi+] (the effects of the small fj,+ contamina- + + + tion from ve —y vT oscillations, r production and T —> /i decay are negligible). Figure 11 conveys the benefits of muon-charge identification: For stored n~ the observation of /i+ appearance is very superior to a measurement (such as the depletion of the total number of muons) in which the charges of the produced leptons are not measured. This is true for all 0i3 bigger than a few degrees. This angle is very unconstrained by current measurements. Note that the SuperKamiokande domain would be covered for any sin2(0i3) > 3.6 x 10~3 by the appearance channel, while the disappearance measurement would fall short of this motivating goal (The latter remark may be somewhat qualified by recent SuperKamiokande data [51] indicating slightly larger Am2 values). In Fig. 11 we show results only for stored //". The wrong-sign muon results are slightly superior for the polarity we do not show: If it is positive, and for equal numbers of decays, the unoscillated numbers of expected electron events (and of potential wrong-sign muons) are roughly twice as numerous. The muon-disappearance results, on the other hand, are slightly weaker for a /i+ beam. In Fig. 12 we show the sensitivity reach, in the [sin2(0i3), Atn^] plane for the extremal values of 023 ~ 30°, 45° allowed by the SuperKamiokande data. The overall conclusion of an analysis in terms of the mixing of three generations is that the capability of detecting 'wrong-charge' muons would be extremely useful in giving access to 2 the study of a large region of the (0i3, 023, Am 3) parameter space.

~~22 10~~

2 Fig. 11: Sensitivity reach in the plane [sin 023, Am|3] at 90% confidence, for our reference set-up, a (i -decay beam and L = 732 km. Matter effects are taken into account. The discontinuous lines correspond to the appearance observable N[n+] at #13 = 40,13,5°, and the full lines correspond to the disappearance observable

~~iVM at Qi3 = 0,40°. The rectangle is the approximate domain allowed by SuperKamiokande data.~~

Fig. 12: Sensitivity reach in the plane [sin2 613, Am.23], at 90% confidence, for the same conditions as in Fig. 11. The continuous (dashed) lines correspond to #23 = 45° (30°). The lines covering the most (least) ground are + for the appearance (disappearance) observable N[[i ] (ATM). The rectangular domain is the approximate region allowed by SuperKamiokande data.

The previous considerations are based exclusively on statistical sensitivities. The backgrounds to a wrong-sign muon signal are associated with the numerous decay processes that can produce or fake such muons. Pions masquerading as muons can be ranged out with great efficiency, particularly in competition with the generally energetic primary muon from the leptonic

23 vertex. Muonic charged currents are not the most threatening background, since one would also have to miss the right-sign muon. Electronic charged currents may singly produce charmed particles, but the decays of the latter lead to muons of the 'right' sign. In any case, the background from charm production and subsequent muonic decay can be easily suppressed or studied by lowering E^ below the canonical 20 GeV we have been using. At one quarter of the stored muon energy the statistical appearance sensitivity would be reduced by a factor of 2, while charm production would be almost completely kinematically forbidden (This is an extreme example, in that it might jeopardize muon recognition.) Neutral-current events in which a hadron decays into a muon early or straight enough are presumably the main hazard. Experience with NOMAD — admittedly not a coarse-grained very large device — demonstrates that an 'isolation' cut in the transverse momentum of the muon candidate relative to the direction of the hadronic jet is extremely efficient [55]. In these events, an additional cut of the missing transverse momentum (carried mainly by the outgoing neutrino in the neutral-current leptonic vertex) relative to the muon plus hadrons would also help. Even detectors as coarse-grained as MINOS [48] or NICE [56] have jet-direction reconstruction capabilities and could implement similar cuts. Without a specific detector in mind and considerable simulation toil we cannot answer the question of how large the above backgrounds would be. A question that we can answer is how small they would have to be not to interfere with the signal. For our standard set-up and an 5 20 unoptimized E^ = 20 GeV, there would be a grand total of a few 10 events for nM = 2 x 10 fx decays at L = 732 km. To compete with a limiting appearance signal of a few wrong-sign muons may be difficult. At some 10 times larger L the low-mass edge of the sensitivity domain would change very little, as shown below in Eq. (13) and Fig. 13, while the background would be reduced by two orders of magnitude: a level at which it would not represent a challenge. The overall optimization of the signal-to-noise ratio is a multi-parameter task that we cannot engage in at this stage.

~~10 r~~

Fig. 13: Sensitivity reach in the plane [sin2 #23, Am^] at 90% confidence, for our reference set-up, a jx -decay beam and L = 732 and 6000 km. The discontinuous (continuous) lines correspond to the appearance (disappearance) observable N[n+] (N[fi+ + n~\). We chose #13 = 40° for appearance, 813 = 0 for disappearance.

~~24 3.2.5 Matter effects~~

Of all neutrino species, only ve and ue have charged-current elastic scattering amplitudes on electrons. This, it is well known, induces effective 'masses' (i = ± 2 Ev A, where the signs refer to ue and ve and A = \/2GY ne, where ne is the ambient electron number density [46]. Matter effects [46, 57] are important if A is comparable to, or bigger than, the quantity Ajk = Amx/(2£v) of Eq. (7) for some mass difference and neutrino energy. In the minimal scheme Am^ is neglected relative to Am^; the question is the relative size of A and A23 c± A13 (We assume 2 /S.17123 = m3 — m to be positive, otherwise the roles of neutrinos and antineutrinos are to be inverted in what follows.) 13 For the Earth's crust, A ~ 1CT eV. For a typical neutrino energy Ev = 12 GeV (the 2 3 2 average ve energy in the decay of E^ = 20 GeV muons), A ~ A23 for Am 3 = 2.4 x 10~ eV . This means that A » A23 for the lower Am2 values in Figs. 11 and 12, while the opposite is true at the other end of the relevant mass domain. Thus, the matter effects are dominant in the most relevant portion of the domain of interest: the lower mass scales. Yet, as we proceed to show, matter effects are practically irrelevant (except in the analysis of CP-violation effects) in long-baseline experiments with L < 3000 km. They only begin to have a sizeable impact at even larger distances4. Let us define the following:

2 2 B = ^/[A23 cos(2013) - A} + [A23 sin(2013)] (9) and sin(2 0M) = A23 sin(20i3)/£ , (10) where 9M is to be taken in the first (second) quadrant if A23 cos(2#i3) — A is positive (negative). The transition probability governing the appearance of wrong-sign muons is, in the minimal scheme, in the presence of matter effects, and in the approximation of constant ne [58],

2 2 P(ve -* Vll) ~ 4, sin (20M) sin (B L/2) , (11) which, for A = 0, reduces to the corresponding vacuum result: the first of Eqs. (6). For sufficiently small BL/2, it is a good approximation to expand the last sine in Eq. (11) and to use Eq. (10) to obtain 2 2 P{v* - ^) ~ 4 sin (2013) [A23 L/2] , (12) which coincides with the expansion for small A23 L/2 = Am^ L((4.EV) of the vacuum result in Eqs. (6), even when matter dominates and B ~ A (at a distance of L = 732 km, A L/2 ~ 0.2). In practice, and after integration over the neutrino flux and cross-section, the above ap- proximations are excellent in those parts of the disappearance sensitivity contours of Figs. 11 and 12 that are roughly 'straight diagonal' lines of slope —1. There, S23 sin(2#i3) Am^ is approximately constant. In this region the results with and without matter effects are indistin- guishable and (for an equal number of events) the sensitivity contours from ^e —> v^ and ve —> v^ transitions would also coincide. For sufficiently large Am2^, matter effects are negligible. In Figs. 11 and 12 this occurs in the portions of the limits that are approximately 'straight vertical' lines, for which the oscillating factors in Eqs. (11) and (12) average to 1/2. All in all, only the wiggly regions in the sensitivity boundaries distinguish matter from vacuum, neutrinos from antineutrinos. The differences are not large (factors of order two). All of the above also applies to the disappearance-channel results shown in the same figures. 4This refers to the approximate assessment of sensitivities, not to the analysis of eventual results: In the Sun or on Earth, Nature may well have chosen parameter values for which matter effects are relevant.

25 3.2.6 Scaling laws The preceding discussion was made in the context of the relatively 'short' long baseline of 732 km and for E^ = 20 GeV. How do our results scale to other distances and stored-muon energies? (the neutrino-factory scaling laws differ somewhat from similar ones for neutrinos from ix and K decay). We are considering detectors at a sufficiently long distance (or otherwise sufficiently small in transverse dimensions) for the neutrino beam that bathes them to be transversally uniform. For a fixed number of decaying muons (independent of E^) the forward neutrino flux varies as E^L~2, see Eq. (4). The neutrino cross-sections at moderate energy are roughly linear in the neutrino (or parent-muon) energy. For L < 3000 km, sin2(AL/2) ~ (AL/2)2 is a good approximation (better than 25% and rapidly deteriorating for increasing L) and the vacuum- like result of Eq. (12) is applicable. Entirely analogous considerations apply to the probability P{vn ~* uy)i whose explicit form in the minimum scheme [58] we have not written. All this implies that the 'straight diagonal' parts of the appearance contours in Figs. 11 and 12 scale as S23 sin(2#i3) Am2^ oc E^ ' , with no L dependence. For L > 3000 km, this sensitivity (still in the approximation of constant ne) is weakened by an extra L-dependent factor so that, for any distance, the appearance sensitivity at the low-mass end scales as

1/2 523 sin(2013) Am|3 oc E~ (AL/2)/\sin(AL/2)\ . (13) For the straight vertical parts of the appearance boundaries in Figs. 11 and 12 the oscillation O Icy probabilities average to 50% and the scaling law is S23 sin(2#i3) oc LE^ For a disappearance channel the putative signal must compete with the statistical uncertainty in the background and the E^ and L dependence are not those of an appearance channel. Moreover, the scaling laws for our /V[/i+ + /z~] contours are not very simple functions of the mixing angles. For L < 3000 km their straight diagonal portions in Figs. 11 and 12 scale up and down as Am2 oc E]/A L~ll2. The straight vertical parts of these limits move right and left as sin^ oc L1/2 E^ . For L > 3000 km the scaling laws for disappearance are more involved. In Fig. 13 we compare results for L — 732 and 6000 km. Only the disappearance channel at large sin2 9 benefits from the larger distance. For the more attractive wrong-sign /i-appearance channel there is no advantage to a very long baseline.

3.2.7 T and CP violation The beams from a hypothetical neutrino factory would be so intense and well understood that one may daydream about measuring the CP-violating phase 8 in the mixing matrix of Eq. (5). Standard-Model CP-violation effects, as is well known in the quark sector, entail an unavoidable reference to all three families. They would consequently vanish in the minimal scheme that we 2 have been considering, insofar as the mass difference Am 2 is neglected. With the inclusion of this difference the parameter space (two mass gaps, three angles, one CP-odd phase) becomes so large that its conscientious exploration would, in our current nescient state, be premature. We will simply give some examples of the size of the effects that one could, rather optimistically, expect. As we shall see, the truly serious limitation is the small statistics inherent to appearance channels. CP-related observables often involve the comparison between measurements in the two charge-conjugate modes of the factory. One example is the asymmetry [59]

~~Ji-ai i P(Pe~~

26 which would, in vacuum, be a CP-odd observable. The voyage through our CP-uneven planet, however, induces a non-zero A^ even if CP is conserved, since ve and Pe are differently affected by the ambient electrons [60]. The T-odd asymmetry [61]

~~,T - p(v* -» vv) ~ p(^ ~»v e) P(l/e is 'cleaner' than ^4£f, in that a non-zero value for it cannot be induced by matter effects. But~~

Aj^ is very difficult to measure. In a /x~-generated beam the extraction of Piy^ —• ve) requires + a measurement of electron charge, the e + e~ number involving also P{ve —> u&). It is not easy to measure the electron charge in a large, high-density experiment.

In a neutrino factory, A^ would be measured by first extracting P(i^ —• ve) from the + produced (wrong-sign) pT in a beam from fj, decay and P(ve —* i'/*) from the charge-conjugate beam and process. Even if the fluxes are very well known, this requires a good knowledge of the + cross-section ratio cr(PM —> ^ )/cr(z^ —> n~), which may be gathered at a shorter-baseline sta- tion. To obtain the genuinely CP-odd quantity of interest, the matter effects must be subtracted with sufficient precision. We have computed the genuine CP-odd asymmetry in matter,

Aelt(6)=A^(S)-A™(0)} (16) in which the matter effect is subtracted, at L — 732 km, with a fixed neutrino energy Ev — 7 GeV with maximal CP violation, 5 = 90°, and with various parameter values chosen in their currently allowed domains. We find that for values of Am|i as small as the ensemble of solar neutrino experiments indicate, the CP-odd asymmetries are only sizeable, of the order of 1% to 10%, in a small domain of parameter space. To decide whether that region is amenable to empirical scrutiny, a first question to explore is the relative size of the measured and the theoretically subtracted terms. For the subtraction procedure to be useful #23, #13, Am^ and the density profile traversed by the beam must be known with sufficient precision for the error in the subtracted term not to dominate the result. At the distance of L = 732 km this is not a problem: The subtractions are small enough that a precision of a factor of two in their determination would suffice [50]. A second question on the observability of CP violation is that of statistics. In practice, for our reference set-up, there would be too few events to exploit the explicit Ev dependence of the CP-odd effect. To construct a realistic CP-odd observable, consider the neutrino-energy integrated quantity TOP where the sign of the decaying muons is indicated by asubindex, N[fi+] (N[fj,~\) are the measured + number of wrong-sign muons, and iV0[e ] (JVo[e~]) are the expected number of i>e(fe) charged 5 current interactions in the absence of oscillations . The genuine CP-odd asymmetry is Ae^ (5) = ^ejT(^) ~ ^ejF(O)) the flux and cross-section weighed version of the asymmetry Eq. (16).

As an illustration, in Fig. 14 we give the signal over statistical noise ratio for |^e/i(±7r/2)| as a function of distance for our standard set-up, for E^ = 10 and 20 GeV, sin2 #12 = 0.5, 4 2 Amj2 = 10~ eV and 613 = 13°. The number of 'standard deviations' is seen not to exceed ~ 2 at any distance. Moreover, for very long baselines, the relative size of the theoretically subtracted term A^ (0) increases very

~~sIn the analogue energy-integrated T-odd asymmetry, the T-even contributions to its numerator do not cancel, because of the different energy distributions of ve and fM in the beam.~~

27 rapidly, as shown in Fig. 15. We have examined other parameter values within the limits of the scenario we have adopted for neutrino masses and mixing angles6. As an example, increasing Am^ to 6 x 1CT3 eV2, with the other parameters fixed as in Figs. 14 and 15, increases the maximum number of standard deviations to ~ 3.5 (at L ~ 3000 km), but the size of the theoretically subtracted term at that distance increases by an order of magnitude relative to its value in Fig. 15.

~~L/(103Km)~~

Fig. 14: Signal over statistical uncertainty in a measurement of CP asymmetries as a function of distance, with the continuous (dashed) lines corresponding to E^ = 20(10) GeV. CP violation is maximal and sin2 #12 = 0.5, 4 2 Ami2 = 10~ eV , 6*13 = 13°. The lower four curves describe ^te^(±7r/2) over its statistical error. The upper two curves are vacuum results for the same CP phase(s).

~~4.5 L/(103Km)~~

Fig. 15: Ratio of the subtracted term A^(0) relative to the genuine CP asymmetry Ae^(Tr/2), as a function of distance, with the continuous (dashed) lines corresponding to E^ = 20(10) GeV. The CKM parameters are as in the previous figure. 6The CP-violation effects are much bigger for the larger mass differences that become possible if the results of some solar neutrino experiment are disregarded. We have not pursued this option.

28 The conclusion is that, if the neutrino mass differences are those indicated by solar and atmospheric observations and the physics is that of three standard families, there is little hope of observing CP violation with the beams and detectors we have described.

3.2.8 Summary The inevitable conclusion of a description of atmospheric and solar neutrino data as two independent two-by-two neutrino-mixing effects is that the only hope to corroborate the atmospheric results with artificial beams is based on long-baseline experiments looking for r appearance or fj, depletion. If the same data are analysed in a three-generation scenario, the conclusions are very different: Long-baseline experiments searching for ve <-> v^ transitions regain interest, since these oscillations (even if primarily responsible for the long-distance solar effect) will also occur over the shorter range implied by the atmospheric data, unless the mixing angle #13 is artificially set to zero.

We have studied v^ <-» ue oscillations in the context of a neutrino factory. Rather than concentrating on the v^ —> vr process, the observation of which is notoriously difficult, we have outlined the possibilities opened by experiments searching not only for an unexpected e//u production ratio, but very preferably for the appearance of wrong-sign muons7: y^ in a beam from decaying \X^. We have not dealt in detail with the problem of backgrounds. A neutrino factory may provide beams clean and intense enough not only to corroborate the strong indication for neutrino oscillations gathered by the SuperKamiokande collaboration, but also to launch a programme of precision neutrino-oscillation physics. The number of useful observables is sufficient to determine or very significantly constrain the parameters #23 and #13 and Am^ of a standard three-generation mixing scheme. Only if the neutrino mass differences are much larger than we have assumed would a neutrino factory serve to measure the remaining mixing parameters of the very clean neutrino-mixing sector. It is instructive to compare the current programs to measure the CKM mixing matrices in the quark and lepton sectors. Considerable effort is being invested, sometimes in duplicate, to improve our knowledge of the quark-sector case, mainly via better studies of B-decay. Even though non-zero neutrino masses are barely established, the neutrino sector of the theory can be convincingly argued to herald physics well beyond the Standard Model [62]. It is in this perspective — with dedicated B-physics experiments and beauty factories in the background — that a neutrino factory should be discussed. Whether by itself, as part of a muon-collider complex, or even as a step in its R&D, a neutrino factory seems to be a must.

3.3 Experiments with neutrinos from muon decay A. Bueno, M. Campanelli and A. Rubbia In the last few years there has been growing interest in studying the technical feasibility and the impact on physics of a muon collider with high-intensity beams [16]. Muons decaying in this machine are a continuous source of both muon and electron-like neutrinos [18] via the following relation8:

M~ -* e~£e*V (18) 7In principle, but not in practice, the search for wrong-sign electrons would be equally useful. 8In this paper we always refer to the decay of negative muons. The same considerations are obviously valid in the case of positive muons.

~~29 Between production and detection, neutrinos oscillate with a certain probability. The probability for neutrino oscillations is given by~~

2 2 2 P{EV) = sin IB sin (1.27Am -^-) , (19) Ev where B is the mixing angle between the two neutrino flavours, and Am2 is the difference of the squares of the neutrino masses. Let us consider three possible cases of mixing between two neutrino flavours.

1. Pure Up <-» uT oscillations: In this case there will be disappearance of Up neutrinos, with oscillation probability P, given by Eq. (19). If we define as $^ the initial Up flux, the flux after the oscillation #f. will be

~~^ = *lMx(l-P). (20)~~

The ue component of the beam remains the same, since in this case neutrino electrons do not oscillate. The ve beam, however, provides a way to predict at the far detector the initial Vp flux. In the muon rest frame, the distribution of muon neutrinos and electron antineutrinos is precisely predicted by the V-A theory:

~~J2iy n 2 1/11 =p[(3 - 2x) + (1 - 2x)PpCos8) , (21) dzdfi 4TT 12x2~~

where x = 2Ev/mfi, Pp is the average polarization of the muon beam, and 9 is the angle between the momentum vector of the neutrino and the mean angle of the muon polarization. In a muon collider, the beam polarization can be carefully measured via the spectrum of the electrons from muon decay; thus the spectra of the two components of the neutrino beam, and so the ratio of the fluxes reaching the far detector, can be known with good accuracy.

Pure Up —> us oscillations: The Vp flux and spectrum are exactly the same as for the V V\x *-> T case, and also the ue beam is not affected. It is possible, however, to discriminate between Vp —* us and Vp <-> vr oscillations, since the ratio of neutral current to charged interactions is different in the two cases.

Pure Vp <-* ue oscillations: In this case, also electron antineutrinos would oscillate into Up, with the same probability as the Up <-+ ue oscillation. If we call this probability P [given as above by Eq. (19)], the final flux will be composed of four neutrino types:

*„„ = $j,M x (1 - P) , (23)

~~H = K~e x P , (24) $„„ =^xP, (25)~~

*ve = $k x (1 - P) . (26)

The total detected flux $^ + $^ + $j,e + <3>i7e in this case would be the same, i.e. equal to the initial flux. The antineutrinos coming from the oscillation would produce leptons of opposite sign with respect to neutrinos from the beam, so a magnetic detector with charge-discrimination capability would be able to study in detail this kind of processes. This is the topic of the medium-baseline study, that is presented in detail in Section 3.3.3.

30 If no charge identification is available, it is possible however to exploit the different cross- section between neutrinos and antineutrinos to get some hint for this kind of process. Let's call R the ratio between neutrino and antineutrino cross-sections: _ qfo CC) R~^cc)- (27)

The fluxes of ue and v^ are equal at production, but since the energy spectra are different, the number of neutrinos reaching the far detector is slightly different for the two flavours. We assume this effect to be negligible, and we set $), = $^e = $ (deviations from this behaviour can be anyway computed for a more accurate estimation). Thus, the number of interactions for the different neutrino flavours would be: :P , (28)

Ne{E) = NVa+Nffa = AxP + Ax(l- P)/R , (29) where A is the product of the flux times the neutrino cross-section. The ratio between the two flavours is still dependent on P: N» 1-P + P/R „ 2-P K Ne P + (l- P)/R ~ 1 + P ' ' where we have assumed the factor R = 2, independent of energy. The above equation allows us to derive the oscillation probability, with no assumption in the initial neutrino flux. Without charge assignment the interpretation of an observed deficit in terms of v^ disappearance or fM <-> ue oscillations is not straightforward, and the ambiguity could be solved by considering data from other experiments (as usually done in the interpretation of the SuperKamiokande results) or studying the modification in the j/bj = E^/Ev distribution due to the different polarization of the antineutrinos produced in v^ «-> i/e oscillations.

3.3.1 Neutrino fluxes The muons are produced in the decay chain of hadrons behind an appropriate target and are subsequently captured, cooled, accelerated and stored in a ring where they are left to decay. The muon yield is determined by several parameters. If a continuous proton source is assumed, the total number of muons is given by the total proton yield times the average pion yield per proton, times the muon yield per pion, so that the total number of muons accelerated is given by the following relation: AT — /V y V . y V , y/

22 where Np is the proton yield per second. We assume that it corresponds to 10 protons per year. Based on muon-collider studies we assume about 0.6 pions per proton, half of which can produce useful muons, and 0.25 muons per pion survived, cooled and accelerated, thus resulting in about 0.1 muons per proton. Overall, a total muon production above 1021 muons per year could be achievable. Let us remark that the requirement on cooling should be less stringent than that for a high-luminosity muon collider, where overlap between two high-density beams is required, and this should increase the overall muon yield. We assume that the total muon flux can be improved by a factor of 2 with respect to the figures quoted above. Running the experiment for five years, a total of 1022 muons could in this case be reached. In the following sections we will consider the cases of a medium-baseline experiment with charge discrimination, and a long-baseline experiment without charge discrimination. We consider it experimentally challenging to build a detector with electron-identification and charge- discrimination capabilities, with a mass of a few kilotons.

31 3.3.2 Long-baseline experiment 2 In the region with full mixing and Am vx disappearance mode will be limited by the knowledge of the neutrino flux. In fact, since the oscillation probability shows a l/E2 dependence, the oscillated events are all concentrated in the low-energy region, and it is difficult to observe any shape distortion due to the oscillation. So, the only visible effect is a deficit in the total number of neutrinos observed. The integrated oscillation probability in this case is

f P(E)$Vli(E)dE (Am2L): (32) showing a quadratic dependence on Am2. In long-baseline experiments performed using a pion beam, the problem of the flux uncertainty has been addressed by the use of a near detector; this solution having the disadvantage that the solid angle covered by the two detectors is not the same, thus requiring a non-trivial extrapolation from the near to the far flux [63, 56]. The neutrinos directed towards the Gran Sasso would travel the distance between the two laboratories (732 km), to be detected in one of the large pieces of apparatus installed there. We consider the ICARUS [64] detector as a target, with its final mass configuration of 4.8 kt. In this scenario we profit from a very good energy resolution for electrons, and excellent electron-muon separation capabilities.

~~The total number of u^ and ve charged-current interactions in ICARUS as a function of the muon-beam energy is shown in Table 5, considering unpolarized muon beams.~~

~~Table 5: Charged-current rates in the ICARUS detector for neutrinos produced by the decay of 1021 muons, at different muon beam energies.~~

~~Muon Energy v^ CC events ue CC events (GeV) 2.5 560 240 3.5 1540 660 4.5 3280 1410 5.5 6000 2570~~

~~The energy spectra for the two types of neutrino at the various values of the muon energy are shown in Fig. 16.~~

~~32 10 3~~

~~: : E, - 5.5 GeV 2 10 i E, - 4.5 GeV i E, = 3.5 GeV : 1~~

~~10 r E, = 2.5 GeV~~

~~1 : " i 1 , , !,,,,!,, , i 1 , , , , 1 . , ' . , 1 , , 12 3 4 5 Energy (GeV) 5 E» = 5.5 GeV •Z » 4.5 GeV E, = 3.5 GeV 10 r = 2.5 GeV~~

~~: 1 ; 1 , , 3 4 5 Energy (GeV)~~

Fig. 16: Energy spectra of «/M (upper plot) and i/e (lower plot) interacting in the long-baseline experiment via charged-current processes for muon energies of 2.5, 3.5, 4.5 and 5.5 GeV (1021 muons, 4.8 kt).

~~We have assumed the neutrino charged-current interaction cross-section to scale linearly with the energy even in the very low-energy part of the spectrum:~~

~~38 2 a(ye) = = 0.67 x l(T cm £(GeV) ,~~

dt a(i7e) = a(z7e) = 0.34 x 10- W£(GeV) . The relevant point is that for the energies considered here the cross-sections for electron and muon neutrinos are the same. We consider now the results that could be achieved by the experimental set-up described above, without a near detector, in the case of pure v^ —> vTja oscillation. For the different values of muon-beam energy, the oscillation probability as a function of the parameter Am2 is shown in Fig. 17. In the region of small probabilities, the dependence of this quantity on Am2 is quadratic, as seen from Eq. (31). Also quadratic is the dependence on the neutrino energy, so the low- energy beam has higher oscillation probability with respect to the high-energy one. In the Am2 region of interest, between 10~4 and 10~3 eV2, the oscillation probability is between 1% and 10%, and a similar or better sensitivity is needed for observing the oscillation signal. If the energy shape of the oscillated events is not considered, and only a counting experiment is performed, as is the case for the small-Am2 region, the statistical error is just given by the total number of muon neutrinos observed: AAL 1

~~33 t tI-~~

~~/ /// \ / \ / / ' / / / / / /~~

~~/ / / / 10 / / / / / / / / / / / /~~

~~/ / IiiIiir -2 i i 10 -4 10 10 10 Am2 (eV2)~~

~~Fig. 17: Average integrated (over the full energy spectrum) oscillation probability of as a function of Am2 for muon energies of 2.5, 3.5, 4.5 and 5.5 GeV (curves from left to right).~~

The total error on the oscillation probability has to account also for systematic effects. The main systematic effect comes from the knowledge of the flux. Without the near detector, this is given in first approximation by the statistical error on the number of electron neutrinos detected in the far detector. Other sources of systematics are corrections due to the muon polarization, and from uncertainties in electron and muon identification efficiencies: AP

The contribution of the first two components of the total error, of purely statistical nature, is plotted in Fig. 18 as a function of the integrated flux. Even in the most favorable case, this error never falls below 2%, and it is assumed that the other sources of systematics, indicated by S in the above expression, are controlled to a better level, so they are neglected in the total error estimation. Being of only statistical nature, the total error decreases as the square root of the total flux. If a near detector is built, the statistical error on the number of ue detected becomes negligible, but then systematic effects due to the extrapolation from the near to the near detector become relevant. The error is also inversely proportional to the square of the beam energy, for the combined effect of the increased neutrino cross-section, and of the larger number of neutrinos reaching the far detector as an effect of the Lorentz boost. Since, as seen before, the oscillation probability decreases with the square of the beam energy, at first approximation the sensitivity of the experiment is independent of the energy.

~~34 22 10 10 Muon Flux~~

~~Fig. 18: Total relative error (oscillation plus control sample) as a function of the total muon flux.~~

From the curves shown it is possible to see that for the low-energy beam the oscillation probability is equal to the la error in the case of 1022 muons for values of Am2 around 4 x 10"4 eV2. The above discussion is based on the fact that at low oscillation probabilities the oscillation occurs in the low-energy part of the spectrum, where statistics are limited. At higher values of Am2, however, more information can be extracted from the energy distribution of the detected neutrinos, in addition to the total flux, since in this case the characteristic oscillation pattern can be seen. As an example, the spectra of detected i7e, v^ with and without oscillations, and their ratio are shown in Figs. 19 and 20 assuming a value of Am2 of 2.2 x 10~3 eV2 (central value suggested by the SuperKamiokande result) and 1.0 x 10~2 eV2 (value suggested by Kamiokande and Soudan), and considering the smearing due to the resolution of the ICARUS detector. The oscillation patterns are clearly visible. All considerations so far have been made in the assumption of maximal mixing. When smaller mixing angles are also considered, two-dimensional oscillation contours can be extracted. For the final result we consider the two cases of integrated fluxes of 1021 and 1022 delivered muons. The 90% contours, for 2.5 and 5.5 GeV muon beams are shown in Fig. 21. It can be seen that, while in the 'low'-intensity scenario the covered area reaches values of Am2 of about 10~3 eV2, for the high-intensity case the sensitivity goes to about 6 x 10~4 eV2, thus covering at 90% C.L. all the range indicated by the atmospheric neutrino results. As an exercise, the value of a muon storage ring has been evaluated with a set of much more restricted assumptions, for an experiment aimed at investigating a region of higher mass differences.

~~35 co co •£40: _..J" ,—J' 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 v events (ICARUS, 1021 \L) GeV ve events (ICARUS, 10 V ) GeV e §80^~~

~~20 0. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 V|1 events (ICARUS, • events (ICARUS, 10 V) GeV §0.8 --f-4-~~

~~0.2 •-K 00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 v (oscillated) events (ICARUS, 102V) GeV v (oscillated) events (ICARUS, 1021 u) GeV~~

Fig. 19: Energy spectra of detected ue [upper plot], Fig. 20: Energy spectra of detected ve [upper plot], non-oscillated (solid line) and oscillated i/^ (dots) non-oscillated (solid line) and oscillated v^ (dots) [middle plot], and the ratio of the two [lower plot] for [middle plot], and the ratio of the two [lower plot] for 1020 muons of 5.5 GeV and Am2 = 2.2 x 10"3 eV2. 1020 muons of 5.5 GeV and Am2 = 1.0 x 10"2 eV2.

~~: 'I I 1 ' 1 I ' : : M Ge V Ge V Ge V Ge V in in - • g in _ 1 CN~~

~~, I,.... m c\i ' i~~

~~10 - /~~

~~CM / /^Kamiokande- CD _ / ^ /~~

~~10 - *•• — — - - ~~~

~~10 - 90% V - V x Super-Kamiokande 1 i , i i 10 0.2 0.4 0.6 0.8 sin229~~

Fig. 21: 90% C.L contours for a disappearance experiment with a total flux of 1021 and 1022 muons, compared to the SuperKamiokande 90% C.L. contour. The full line is the limit for 5.5 GeV muon beam and 1022 muons, the dashed bold line is for 2.5 GeV beam and 1022 rnuons, the dashed line is for 5.5 GeV beam and 1021 muons, and the dot-dashed line is for 2.5 GeV beam and 1021 muons.

36 3.3.3 Medium-baseline experiment As an exercise, we consider an experiment that could be performed with a muon storage ring of a first generation assuming that the PS as it exists now is used as a source, that no cooling is performed and that muons are only accelerated to 7 GeV. The existing CERN-PS machine is able to accelerate 2.5 x 1020 p/yr at an energy of 18 GeV. We assume that only 0.04 /x/p will be trapped and accelerated into the storage ring. For comparison, the Muon Collider Collaboration expects to reach a yield of 0.3 ///p. With our assumption, the total number of muons accelerated is 1019 /x/yr. We consider that after four years of running, a total of 4 x 1019 /J. will have decayed inside the storage ring. The muon energy is set to 7 GeV in order to obtain a relatively low- energy neutrino beam. We have computed the event rates assuming an unpolarized muon beam. The NOMAD detector target has a total mass of 2.6 t. It is currently located in the West Area, pointing to the direction of neutrinos from the present WANF beam. Since neutrinos from the PS would arrive at a large angle with respect to the present orientation of the detector, we assume that it can be moved from the West Area and operated at a different position. This also gives the possibility of increasing the beam line, thus lowering the background whilst keeping the oscillation signal constant. The point with largest distance from the PS conceivable on the CERN site is at the Prevessin laboratory, close to the North Area. The estimated distance from the PS is about 3.6 km (see Fig. 22).

~~Prevessin site~~

~~CERN sites~~

~~Fig. 22: Schematic overview of the CERN sites.~~

The muon-beam energy is set to 7 GeV in order to obtain a relatively low-energy neutrino beam. We compute the event rates assuming an unpolarized muon beam. The event rates for 19 an integrated intensity of 4 x 10 ^x are shown in Table 6. The energy spectra of v^ and i>e charged-current events are shown in Fig. 23. For comparison, we give the expected number of oscillated events for full mixing and various relevant Am2 parameters.

~~37 Table 6: Neutrino event rates assuming the NOMAD detector (2.6 t) as a target. The muon beam has an energy 19 EIX = 1 GeV and the integrated intensity is 4 x 10 ^. The baseline is L = 3.5 km.~~

~~No oscillations Vn CC events 11600 ii- + z?e CC events 5070 e With oscillations Am2 = 1 eV2, sin2 2(9 = 1~~

~~ue CC events 6600 e- v^ CC events 3300 /x+ With oscillations Am2 = 0.4 eV2, sin2 29 = 1~~

~~ve CC events 1580 e" L>H CC events 910 M+ With oscillations Am2 = 0.2 eV2, sin2 26 = 1 ve CC events 430 e~ Dp CC events 260 M+~~

~~> 700 1 ' ' ' ' " ' : Mein | RMS 1.239 ° 600 ALLCHAN 5 500 h § 400 L~~

~~300~~

~~200~~

~~100~~

~~A , , • ,. .n?2rj '•'.•'••• i"',' j . . ., 1 , . . , 1 , , , •~~

~~Fig. 23: Predicted muon neutrino and electron antineutrino charged-current event energy distribution for an integrated statistics of 4 x 1019 muons.~~

Let us concentrate now on the specific case in which a detector with charge-discrimination capabilities is available. In this case the oscillated events exhibit quite a clear signature, i.e. in the case of ue oscillations, ue neutrinos would appear, while an unoscillated beam would

~~38 contain only ue. Charge discrimination in the detector will trivially separate the two types of neutrino components:~~

~~+ ve + N —> e + X intrinsic beam component, (33)~~

~~ue + N -» e~ +X oscillated. (34)~~

~~In the case of Pe —> v^ oscillations, Vp. neutrinos would appear, while an unoscillated beam would contain only v^.~~

~~v^ + N —> fj,~ + X intrinsic beam component, (35) ^fj, + N -> [i+ + X oscillated. (36)~~

We stress that this experiment would for the first time address CP conservation in the lepton sector, since the transition v^ <-> ue and its CP-conjugate v^ —> ve would be analysed at the same time. The event selection is based on the identification of leading final-state electrons or muons, and looks for opposite charges than the one expected in the unoscillated beam components. We carried out the study of signal efficiency and background estimations using a full simulation of the events and the reconstruction packages currently used in NOMAD. All selection cuts are applied on the reconstructed quantities. For the electron final state, the following backgrounds are the dominant ones. + • Charge confusion: i/e + N -> e + X -* 'e~' + X. • Asymmetrically-reconstructed conversions or Dalitz decays: i/£ + N —> i/£ + X and

• Misidentified hadrons: V£ + N —> vt + X and h~ —> 'e~'. The NOMAD detector is well suited to search for electron charged-current events. The electron identification is good and well understood. Charge separation of the leading electron is also very well known. Charge confusion arises primarily from early bremsstrahlung with the leading photon converting asymmetrically into an e+e~ pair where the e~ is lost. This process is rare and the simulation gives in the low-energy region a contamination at the level of one in ten thousand. An important source of background for the electron search comes from Dalitz decays and 7T° conversions (where the 7 converts close to the primary interaction vertex). Those non-prompt electrons, embedded in the recoiling hadronic system, are in general less isolated than the prompt ones. Hence, an efficient rejection of this background is obtained by demanding that the electron candidate have the highest transverse momentum in the event. Additional discrimination is achieved by means of a lower cut on the measured electron momentum. Remnant backgrounds, owing hadron misidentification, can be reduced to a negligible level by comparing the reconstructed electron momentum (tracking) with the associated measured energy (calorimetry). Table 7 summarizes the results obtained for electrons, when normalized to 4 x 1019 muons. For an overall 35% electron detection efficiency (ee-), the expected background is well below one event. For the muon search, we use the standard muon identification algorithm used in the NOMAD experiment. It has a momentum threshold of about 3 GeV imposed by the requirement of reachability of the muon chambers. After the cuts listed in Table 8, the detection efficiency + for fi (eM+) is 50%. The background contamination for the ve —> v^ oscillation search is negligible. The small punch-through background is completely suppressed by a kinematical isolation requirement, since a misidentified muon will come from the jet.

~~39 Table 7: Summary of detection efficiencies and expected backgrounds for a vM <-> ue oscillation search.~~

~~ve CC (%) ^ CC Vp, NC PeCC ve NC Initial 100 11600 3867 5070 2028 Candidate highest Py 59 196 99 1922 35.2 Pele > 2.5 GeV 41 4 2.1 1503 0.4 Calorimetry 35 0 0.7 1360 0.4 Charge 35 0 <0.2 <0.2 <0.1~~

~~Table 8: Summary of detection efficiencies and expected backgrounds for a ve oscillation search.~~

~~ve -> ^ CC (%) ^ CC ^NC ue CC uG NC Initial 100 11600 3867 5070 2028 Candidate highest PT 65 3874 2.5 0.5 0.4 Charge 65 2 1.1 0 0.18 Isolation 50 <0.1 <0.2 0 <0.1~~

In the case of a positive signal, the simultaneous use of both channels provides a test of CP conservation in the leptonic system. In the case of a negative result, combining both channels assuming CP conservation, the 19 90% C.L. limit on v^ <-> i/e oscillations, for a total flux of 4 x 10 muons, can be obtained from the following: 2.3 4 v M = 3.5 x 10" . (37) ' 11600 x ee_ + 5070 x eM+ This corresponds to a limit on the mixing angle for large Am2 of

sin2 26 < 7 x 10"4 90% C.L. (38) and Am2 > 2 x 10 2 eV2 for maximal mixing. The 90% and 99% C.L. exclusion contours are shown in Fig. 24, along with the LSND positive solution, the current limits from NOMAD, CCFR and reactor experiments, and the expected limit from MiniBOONE. The LSND solution is well covered by the sensitivity obtained in our study. At the 99% C.L., the limit on the mixing angle at large Am2 is sin2 29 < 1.4 x 10~3. We can reach 1.7 x 10~3 at the 3a level, a value still below the allowed LSND solution at the 99% C.L.

~~3.3.4 Conclusions We have performed a study of the capabilities of neutrino beams coming from muon decays, to test two open problems of neutrino physics.~~

~~40 this study (99%C.L.) <—» ve 90% C.L. LSND: 90% and 99% regions~~

~~10 10 10 sin2 20~~

Fig. 24: Predicted negative limits at the 90% C.L. and 99% C.L. for this experiment compared to the expected MiniBOONE 90% C.L. limit for neutrino-oscillation appearance. Negative results from previous NOMAD, CCPR, BNL-776 and reactor experiments are also shown.

The SuperKamiokande result, allowing the possibility of very small Am2 for neutrino oscillations, presents strong challenges to the experiments willing to explore this region of the parameter space. The method presented here, is based on disappearance of v^ coming from a muon beam. Given the layout of the accelerator, a near position could be placed on the surface, opposite the far laboratory. Since a built-in control sample of ue coming from the same muons can be exploited for normalization, the experiment can however be performed without requiring a near detector, and in this configuration it has the potential to reach in a clean way the low-Am2 region suggested by the atmospheric neutrino results. Using a detector with charge-identification capabilities, it is possible to perform a medium-baseline experiment in the appearence mode. We have shown that with the performances of the present PS accelerator, and with the possibility of recycling parts of an already existing detector (NOMAD), it would be possible to perform an experiment to increase the present limits on v^ — ue oscillations. The area in the parameter space indicated by the LSND result can be fully covered, with a sensitivity comparable to that of the MiniBOONE experiment, but with a completely different approach.

3.4 Neutrino scattering experiments at the muon storage ring facility M. de Jong 3.4-1 Introduction In the following section we concentrate on deep-inelastic scattering. Therefore we take 250 GeV beams, similar to studies done with muon beams. The exercise shows that neutrino beams can provide fundamentally new measurements with comparable quality. Some of the measurements can be initiated at considerably lower momenta, e.g. at 25 GeV. The scaling laws are such that the spot size can be equal (the detector can also be a factor 10 closer to the decay region), while the event rate is lower by a factor 10 because of the lower neutrino cross-section.

41 In order to investigate the prospects of a neutrino programme at the future muon collider, it is useful to review the characteristics of the present neutrino experiments. Existing high- energy neutrino beams are produced in two steps. First, high-energy protons are immersed on a production target. The produced pions and kaons are focused before they pass through a decay tunnel. In this tunnel, pions and kaons can decay into a muon and a muon neutrino. Owing to other decays, there is an unavoidable and not well-known contamination from other neutrinos and antineutrinos. At the end of the decay tunnel, hadrons and muons are removed by an absorber. After passing this absorber, the neutrinos enter the detector area. The finite lifetime of the pion (kaon) and the inherent divergence of the neutrinos limit the effective flux on a physics target. The small flux of these neutrino beams and their large size require detector set-ups based on heavy targets. This spoils the physical measurements through nuclear effects, non-isoscalarity corrections and (relatively) poor detector resolution. The cross-section of the process v^ + N —> \x + X can be written in the most general form as

GFMNEU r , _ Myxy _ y ] 1 dxdy IT [WiH y 2EV where x is the Bjorken scaling variable and y the elasticity. The functions F\, F2 and F3 describe the structure of the target nucleon and depend only on x and Q2 (—Q2 is the invariant- mass squared of the four-momentum transfer). They are in principle different for neutrons and protons and for neutrinos and antineutrinos. The third structure function appears only in the cross-section for weak interactions. Its contribution changes sign between neutrinos and antineutrinos. The average of the nucleon structure functions xF^ — (xF^ + xF£)/2 for neutrino and antineutrino scattering can be attributed to the valence quark distribution in the nucleon and the difference the strange sea. The Q2 dependence of the structure functions can be used to test perturbative QCD and to determine the strong coupling constant as. The total deep-inelastic cross-section has been measured for neutrinos and antineutrinos incident on iron with a systematic uncertainty of about 5%, primarily due to the uncertainty in the flux measurement.

3.4-2 Detector layout Detectors can be located at the end of each straight section of a muon storage ring, detecting neutrinos from a short decay tunnel. This is in contrast with the conventional neutrino beams originating from pion and kaon decay. A schematic layout of a muon storage ring with a neutrino detector is shown in Fig. 25.

~~Detector R~~

~~Fig. 25: Schematic layout of a muon storage ring with a neutrino detector. A minimal length d guarantees a sufficient distance between the detector and the bending magnets.~~

42 The flux F of neutrinos incident on a physics target is related to the length L of the straight section as follows: 1 oc 2nR + 2L (L/2 + d)2 ' The first factor corresponds to the fraction of muons decaying in the straight section towards the neutrino detector. The second factor describes the focusing of the neutrino beam. The muons in the storage ring have a well-defined momentum. Their decay delivers a pure beam of equal numbers of v^ (p^) and Pe (ve), the properties of which are calculable. The distribution of the energies and the impact points of the neutrinos originating from an unpolarized beam of muons with an energy of 250 GeV in a straight section of 100 m is shown in Fig. 26. It can be seen that the average neutrino energy is half of that of the muon beam and that the flux is concentrated in a beam of a few centimetres. The fraction of neutrinos passing through a target with a radius of 5 cm is about 75%. The length of the straight section can be optimized to the requirements of the experiment.

~~0.015 -~~

~~50 100 150 200 250 2 4 6 8 10 ENERGY (GEV) IMPACT POINT (CM)~~

Fig. 26: Distribution of the energies (left) and impact points (right) of electron neutrinos incident on target. The integral of each distribution is normalized to unity. The impact point is with respect to the central beam line. The length of the straight section is chosen to be 100 m for muons with energies of 250 GeV.

The possibility of a 'close-focus' neutrino beam combined with the high intensity is new. Detectors can be built around moderately sized targets using detection techniques developed in other fields of high-energy physics. New designs of neutrino detectors and targets are therefore necessary.

3.4-3 Measurements The close-focus neutrino beams from a muon storage ring make high-statistics measurements possible for a wide range of physics targets. The number of interactions Nfa^N —> fiX) is estimated to be

~~X "MUONS X /DECAY /TARGET X 4 • 10 X p x \EV) ,~~

43 where iVMUONS is the number of muons produced, /DECAY is the fraction of muons decaying in the straight section towards the physics target, /TARGET is the fraction of neutrinos passing through 2 the target, p is the surface density of the target expressed in gr/cm and (Ev) is the average energy of the incident neutrinos expressed in GeV. With 1020 muons of 250 GeV, 108 neutrino interactions can be recorded in a liquid-deuterium target with a length of 3 m and a diameter of 10 cm. For comparison, the CERN wideband neutrino beam would yield about 104 neutrino interactions per 1020 protons. Precise measurement of xF^ for neutrinos and antineutrinos is of immediate interest. It will provide accurate information on the valence quarks as well as the strange sea. In principle, the measurement of the integral J(dx/x)xF^ could provide the most accurate value of as. The GLS sum rule relates this integral to the number of valence quarks in the nucleon up to a correction proportional to as. Such a determination of as is insensitive to nuclear effects and small x uncertainties. Measurements of sin2 #w at the heavy-target experiments suffer from experimental systematic uncertainties in distinguishing charged-current from neutral-current events. This can be avoided with a different design of the neutrino detector. The aim is to identify the electrons and muons resulting from charged-current interactions of i>e (^e) and v^ (y^) respectively. In this design, the moderate size of the physics target is significant. The electroweak mixing angle sin2 #w could be determined with a precision equivalent to that of the W mass. Charm production in deep-inelastic neutrino scattering is related to the strange sea in the nucleon:

^ d(x>Q)|V ax A large fraction (~ 10%) of the produced charm decays into a muon which can be detected efficiently. In order to determine the strange sea, the value of Vc& is usually taken to be equal to that of Vus. This assumes unitarity of the CKM matrix. On the other hand, the difference between charm production induced by neutrinos and antineutrinos eliminates the contribution from the strange sea. The cross-section is then proportional to the valence d-quark distribution and to V^d only. The absence of small x contributions reduces the systematic uncertainty due to the unknown c-quark mass. In addition, high-resolution vertex detectors can be used to tag the decay topology of the produced charm particles. The value of V^d could be determined accurately, perhaps as well as Vus. With such an accuracy, the measurement of Vc<\ tests the unitarity of the CKM matrix. No data exist on deep-inelastic neutrino scattering from polarized targets. Deep-inelastic muon-scattering experiments have been performed at CERN with polarized targets by the Eu- ropean Muon Collaboration (EMC) and the Spin Muon Collaboration (SMC). The observation by the EMC that little of the nucleon spin is carried by the quarks resulted in the so-called ;spin crisis'. This observation has been confirmed by the SMC and other experiments. With the neutrino beams from a muon storage ring, high-statistics experiments on deep-inelastic neutrino scattering from polarized targets are possible. The unknown spin structure fuctions g\ and gy, of the proton and neutron can be measured for neutrinos and antineutrinos. The average of the nucleon structure functions g% = (g% + g%)/2 for neutrino and antineutrino scattering can be attributed directly to the polarization of the valence quarks and the difference from a polarized strange sea. As for muons, the Bjorken sum rule relates the integral f dx(gf — #") to the ratio of the axial and vector couplings in the neutron decay. The combination of deep-inelastic muon-scattering and deep-inelastic neutrino-scattering experiments provides a test of the flavour SU(3) symmetry for the three lightest quarks.

44 3.4-4 Conclusions The neutrino beams originating from a muon storage ring can be used to study interactions of neutrinos with matter. Future high-statistics and high-precision measurements of neutrino interactions can improve our current knowledge of electroweak and strong interactions. For example, new experiments could determine the CKM matrix element Vccj to a precision comparable to that of Vus and the electroweak mixing angle to a precision equivalent to that of the W mass. Neutrino scattering from polarized targets would be within reach.

3.5 Physics with stopped muons A. Blondel The availability of an unprecedented flux of low-energy muons at the exit of the muon cooler would open opportunities for muon physics in its own right [65]. Violations of lepton flavour conservation, already indicated by the neutrino oscillations, are expected at some level in muon physics. They also arise from slepton loops in supersymmetry as soon as sleptons have a non-degenerate spectrum [66]. The physics of this programme could cover experiments such as « search for /i —> e-y and ji -» eee decays; • search for the lepton-flavour-violating muon conversion fj,N —* eiV; a improved measurements of muon properties (muon lifetime, gyromagnetic anomaly g^ — 2, Michel parameters, and electric dipole moment); • study of muonic atoms and of muon capture. Other possible applications of low-energy muons, such as catalysed muon fusion, would also be worth investigating. Most of these experiments have timing requirements (long spills preferred) that should be easier to meet if the muons originate from a proton linac rather than from a synchrotron which is naturally bunched.

45 4 STEP 2: HIGGS FACTORIES A. Blondel Taking advantage of the experience gained running intense muon and neutrino factories, the community could envisage the construction of muon colliders, starting with intermediate energy colliders of limited dimensions aimed at precision measurements. It is impossible at this moment to define the exact parameters and goals of these precision machines, since they will depend to a large extent on the physics panorama. Should a light Higgs boson (up to m^ = 140 GeV) be discovered at LEP, Tevatron or LHC, the study of its properties at a muon collider would be ideal, and readiness to design and build that machine will be precious. As will be seen in the following chapters, the heavier Higgses H and A of supersymmetry would offer a natural scale as well, should they exist. This section starts with considerations on the performance and design of muon colliders. Here again the designs proposed by the American Muon Collider Collaboration are considered as baseline. The emphasis is placed on the compatibility between the neutrino and muon factory on one hand and the muon colliders on the other. After an overview of physics capabilities follows a more detailed description of one of the key arguments in favour of muon colliders, the extraordinary beam-energy calibration. Then an evaluation of the precision with which the Higgs-boson properties could be measured is given, followed by implications on the Higgs coupling determinations. The benefit from precision measurements of the Higgs-boson properties is then considered in a particular supersymmetric scenario, and compared with what could have been learned from hadron and e+e~ colliders. The H and A resonances could really provide exciting physics when stop or sbottom production is considered, or if CP-violation effects occur in the Higgs system, as shown in the following two sections. The more classic production of charginos is also considered. Finally, the precision muon collider(s) could certainly perform precision physics at the Z peak, W and top thresholds, with the help of beam polarization which is described in the corresponding subsection.

4.1 Outline of the machines A. Blondel and E. Keil Parameters of the muon colliders are given in Table 9, from Ref. [16]. They correspond to the specific choices of the proton source: a 16 GeV synchrotron operating at 15 Hz. With respect to the muon beam of a neutrino factory, the muon collider differs in three important respects. • Both /x+ and pT must be used at the same time, preferably in equal or nearly equal numbers. Production of a large number of n~ has led the authors of Ref. [16] to envisage their production by rather high energy protons on heavy targets. A possible alternative, which would be an interesting line of study, would be to use deuterons or alpha particles as projectiles, ensuring isospin symmetry by construction, and avoiding the need for high- energy protons and/or heavy targets. This might have practical advantages for the design of the driver and of the target. The lower-energy beams produce as many or even more pions per unit of driving-beam power, and in a more restricted phase space. However, the feasibility of efficient particle collection at these low momenta remains to be demonstrated. • The muon beams must have a small emittance. This requires cooling to a much larger extent than for the neutrino-beam application. Ionization cooling is considered the most likely method. It involves a succession of dB/dX light material absorbers embedded in strong-focusing magnetic fields and of accelerating RF sections. Although cooling rests on the rather well-known properties of muon interactions with matter, the feasibility and performance of an actual implementation remain to be demonstrated.

47 The muon beams must have a large bunch population to ensure adequate luminosity. This requires accumulating particles in a few bunches, hence the relatively low repetition rate. The comparison of the repetition rate to the muon lifetime (see Table 9) shows that, especially for the low-energy muon colliders, there is a large amount of freedom in the repetition rate, from a few Hz up to almost 1 kHz for a 100 GeV centre-of-mass collider.

Table 9: Baseline parameters for high- and low-energy muon colliders. Higgs/year assumes a cross-section 5 x 104 fb; a Higgs width T = 2.7 MeV; 1 year = 107 s. From the Muon Collider Collaboration [16] CoM energy (TeV) 3 0.4 0.1 p energy (GeV) 16 16 16 p/bunch 2.5 x 1013 2.5 x 1013 5 x 1013 Bunches/fill 4 4 2 Rep. rate (Hz) 15 15 15 1A> (Hz) 32 240 960 p power (MW) 4 4 4 /i/bunch 2 x 1012 2 x lOi2 4 x 1012 fj. power (MW) 28 4 1 Wall power (MW) 204 120 81 Collider circum. (m) 6000 1000 350 (B) (T) 5.2 4.7 3 Sp/p(%) 0.16 0.14 0.12 0.01 0.003 3 10 6-D e6,N i™) 1.7 x 10-i° 1.7 x 10" 1.7 x 10-i° 1.7 x 10-i° 1.7 x 10-1° Rms en (IT mm-mrad) 50 50 85 195 290 P* (cm) 0.3 2.6 4.1 9.4 14.1 oz (cm) 0.3 2.6 4.1 9.4 14.1 ar spot (fim) 3.2 26 86 196 294 a$ IP (mrad) 1.1 1.0 2.1 2.1 2.1 Tune shift 0.044 0.044 0.051 0.022 0.015 „ effective "•turns 785 700 450 450 450

~~Luminosity (cm"^"1) 7 x 1034 1033 1.2 x 1032 2.2 x 103i 1031~~

~~Higgs/year 1.9 x 103 4x 103 3.9 x 103~~

The parameters of a precision muon collider can be discussed by inspecting its luminosity L averaged over the muon lifetime. It can be written as follows, assuming that the cycle time is long compared to the relativistic muon lifetime:

~~m*£*). (39)~~

The first bracket contains natural constants: the muon lifetime at rest To, the muon charge e, and the permeability of free space (J,Q. The rate 7VM at which muons are stored describes the features of the muon source. The last bracket contains the parameters of the circular muon collider: beam-beam tune shift £, muon energy 7, and amplitude function at the interaction point f3±. The fraction containing the bending radius p, the magnetic dipole field B and the circumference C gives the average field (B). In deriving (39), we have assumed that muon cooling makes it possible to achieve the beam-beam tune-shift parameter £. Because of muon decay, the storage rate is smaller than the production rate. If the storage rates for /i+ and /j,~ are different, the smaller value enters into (39). We assume that the muon production rate is proportional to the power of the proton beam, with a relatively weak dependence on the proton energy that is a free design parameter.

48 The average luminosity L in (39) does not depend on the number of bunches in the precision muon collider, which is a free design parameter. Few bunches, ideally a single one, have the advantage that their normalized emittance is larger, that the requirements on the cooling system are less stringent, and that there are only a few, ideally one, collision points around the circumference, apart from the interaction point. They have the disadvantage that the peak proton power on the target and the bunch population are high. The advantages of few bunches are the disadvantages of many bunches, and vice-versa. Hence, the proton source must deliver protons on target at intervals of several milliseconds, corresponding to a few relativistic muon lifetimes. The duration of a beam pulse must not be longer than the revolution period in the muon collider: For operation with one bunch, it must be much smaller. These requirements are met by a linear proton accelerator, pulsing at a rate of some 100 Hz with beam pulses of a few microseconds at most. The driver energy and repetition rate are the result of an optimization. The muon capture, cooling, and acceleration sections must operate at the same rates, and bring the muon beams to the energy of the precision muon collider. Although the size of the muon colliders is very small, the accelerator (possibly a recirculator) that brings muons to the operating energy is larger, since in addition to the bends it must include RF sections. A preliminary design for a precision muon collider has been worked out in Ref. [16]. The size of these colliders is comparable to that of the CERN PS. The main difficulty is associated with arranging the beam-optical modules needed to achieve the small values of bunch length as and amplitude function /3± at the interaction point in such a small machine. A very important quality of the muon collider is the possibility of exchange in the cooling stage between transverse and longitudinal emittance, leading to reduced energy spread. This can be achieved by introducing an absorber of adequately designed variable thickness in a dispersive section. This leads to a possibly very small energy spread, a precious quality for study of narrow resonances, and a mandatory property for the possible operation with polarized beams. Of course this is achieved at the expense of luminosity (see Table 9).

4.2 Overview of the physics capabilities A. Blondel In general a muon collider can do everything that an e+e~ collider could do. On the negative side for the muon collider, one finds it difficult to provide a very high luminosity. This is essentially constrained by the proton power on the target, by the capability one has to cool the beams further, and finally by the eventual possibility to circumvent the beam-beam tune shift. The figures given above represent the present understanding of the muon collider performance and are typically a factor of 10 or more lower than the corresponding ones for electron colliders. An improvement would clearly be welcome! In addition, the operating range of a muon collider is rather narrower than that of an electron linear collider: In addition to the usual scaling law in E2, the luminosity of a muon collider for a given circumference of the collider ring increases linearly with muon energy, due to the dilatation of muon lifetime, leading to a scaling law in E3. One is led to envisage more than one precision machine, for example one Higgs and Z factory, then one for top threshold or heavy Higgses, etc. Much of the infrastructure should remain the same, though. Muon colliders offer, on the other hand, two major advantages with respect to the electron colliders. The first one is the almost infinitely precise knowledge of the beam-energy spectrum, examined in some detail in Section 4.3. This is a determining factor in the study of thresholds and narrow resonances, which are used to make precise measurements of particle masses, widths

49 and cross-sections, from which couplings to the muon can be derived. In contrast, electron linear colliders are faced with the serious problem of beamstrahlung, a phenomenon which not only induces a loss of centre-of-mass energy resolution, but is difficult to monitor precisely. To take an example, the present TESLA design leads to an average energy loss of between 1 and 3% with a corresponding energy spread. This energy spread dilutes thresholds and resonances. The shift of several GeV in centre-of-mass energy has an intrinsic uncertainty that it is hoped can be reduced to the level of a few per cent of its value, still several tens of MeV, which will limit intrinsically all measurements of particle masses and widths. The other highlight of physics with muon colliders is the well-known fact that the Higgs boson(s) couple to muons with a strength proportional to the muon mass squared, leading to usable cross-section for fJ,+^~ —> h, as long as the lightest Higgs mass lies below the W-pair threshold. The fact that the Higgs mass(es) and width(s) could be measured with a precision of a few hundred keV is probably extremely important, although the full impact may not have been realized yet. It appears from the investigations that have been performed so far, that, in the few scenarios considered, it reduces the available parameter phase space by several orders of magnitude. If they are ever made, these measurements could well have a similar historical importance to the precise measurements of the Z line shape at LEP. This is true of the Standard Model case with one Higgs boson, and would become truly fascinating if there were two more Higgses, possibly of different CP quantum numbers and interfering, as in most Higgs doublet models, in particular in supersymmetry. Finally, the muons are simply different from electrons, and would couple to different partners if these existed. This brief overview underlines the complementarity between electron and muon colliders, and the probable extent of the loss if muon colliders were never to exist. The topics presented in this section give a few examples of physics results that are specific to muon colliders, and that could not be obtained otherwise. It has been realized during this short prospective study that the possibilities are very rich, and would certainly deserve further detailed studies.

4.3 Measurements of beam parameters 4-3.1 Analysis of narrow s-channel resonances at /i+/x~ colliders A. Blondel, R. Casalbuoni, A. Deandrea, S. De Curtis, D. Dominici, R. Gatto and J.F. Gunion The possibility of analysing narrow s-channel resonances, the Higgs in particular, is one of the special features of muon coliders. This problem is very similar to the analysis of the Z resonance. For a given decay channel, the resonance is characterized by three parameters: the mass, the total width and the peak cross-section, itself proportional to the product of the muon (initial- state particle) branching ratio BR for R —> fi+n~ by the branching ratio of the resonance to the final state considered. One of the simplest ways to determine the parameters of an s-channel resonance is through a three-point scan. However, in the case of resonance widths comparable with the energy spread of the beam, OE-, one needs a very careful determination of the energy spread itself. This is the case for instance for the Standard Model Higgs boson: for mi, ~ 100 GeV, Fh = 3 MeV. It is advocated that, by exchanging energy spread for transverse momentum in ionization wedges in the cooling stages of the accelerator, it should be possible to reduce the energy spread to the 5 small value aE/E = 3x 10~ . These measurements impose stringent constraints on the knowledge of the beam parameters. The measurement of the mass requires precise knowledge of the absolute energy scale, while the measurement of the width and cross-section require excellent knowledge of the energy

50 spread itself. In fact, as shown in Fig. 27, the relative errors on the width F and on the branching ratio BR for R —> /z~V~ are about three times Acr^/crg, for T « UE- This result can be obtained by evaluating the errors induced on the determination of F and BR from a given error 5a E- It turns out that, in the narrow-resonance approximation, the induced errors are independent of BR and depend only on the ratio T/CTE [67]. This result holds for any energy distribution of the beam characterized by an energy spread OE- AS an example, the results of Fig. 27 have been obtained by using a Gaussian distribution. From this we see that given 5a E, an improvement can be obtained either by reducing as itself (by a reduction in the luminosity), or by trying some different method.

~~ABR 0.40 0.40 BR~~

~~0.20 - - 0.20~~

~~0.00~~

~~- -0.20~~

~~-0.40~~

~~Fig. 27: The relative errors on BR and F are given as functions of T/CTE for different choices of SCTE/PE-~~

In the absence of knowledge of the energy spread, one could still measure the integral of the cross-section as a function of centre-of-mass energy , which is independent of as, and proportional to the product F-BR, and obtaining BR from the ratio of the peak cross-sections measured in fi+fi~ —> R —• ^+/x~ and in /J,+fJ,~ —> R —• all, which is also as independent. This leads to a considerable loss of precision, since the fi+fi~ decay mode is not the most abundant one, and by far. However, it will be shown in the following that the beam-energy sprectrum can be determined with essentially unlimited precision by study of the decay products of the muons, so that a muon collider will allow the determination of both F and BR with unsurpassed precision.

4-3.2 Energy calibration by spin precession A. Blondel Because of the weak decay, muons produced in pion decays are 100% polarized. The average longitudinal polarization (i.e. muon helicity) is about 28%. The muon spins will precess in electric and magnetic fields that are present during cooling and acceleration, but the muon spin tune v — the number of additional spin precessions happening when the muon makes a complete turn — is very low: v = (40) 2 mM 90.6223(6) " Its value is 0.503 at the energy corresponding to the Z peak. It has been estimated that a longitudinal polarization of about 20% will resist all muon handling up to the injection into the collider. Higher polarization could be obtained by a selection of fast or slow muons in

51 the pion decay channel, at the expense of course of some luminosity. The presence of low- beam polarization will have to be taken into account for physics analyses, but as we will see, polarimetry is probably very easy, and a powerful tool for beam parameter measurements, as described in Ref. [68]. Added here are a possible polarimeter design and a discussion on the measurement of the energy spread itself. Polarimetry is provided by the electron energy spectrum, which is a measure of the muon longitudinal polarization. The angular distribution of decay electrons in the muon centre-of-mass is , d N „ = 7Vx2[(3 - 2x) - V{\ - 2x) cos 6} , dxdcos# so that for each decay-electron energy in the lab frame, the rate depends on the muon longitudinal polarization, as shown in Fig. 28. The momentum analysis of decay electrons could be performed in a polarimeter such as that shown in Fig. 29. The detection of electrons would be best done using direction-sensitive detectors with good timing resolution, such as gas Cherenkov detectors followed by lead-glass calorimeters to provide a cross-check. It can be seen that for an electron momentum of 42% of that of the muons, the asymmetry vanishes. This would be a good region in which to monitor the muon flux. Polarization is best monitored using the high-energy region. Selecting the fractional momentum bite of 0.6 to 0.8 retains 13% of decay electrons with a polarization analysing power of 0.33. If the polarimeter is able to catch 1 m of decay length at a 50 GeV muon ring having a total circumference of about 300 m, about 1.7 x 106 electrons are collected at every turn for a beam of 4 x 1012 muons.

~~positron spectrum in u+ decay 1~~

~~-0.2 asymmetry j decay spectum, P=+1 I decay spectum, P=-1 -0.4 i~~

~~10 15 20 25 30 35 40 45 50 Positron energy (GeV)~~

~~Fig. 28: Energy spectrum of positrons from 50 GeV /i+ decays, for two ;U+ polarizations. The asymmetry between the two helicities is also plotted.~~

~~52 Muon polarimeter electron , detectors~~

~~First magnet after straight section~~

~~Fig. 29: Possible set-up of a muon polarimeter. Decay electrons of different energies can be filtered by angular analysis, using slits in the shielding, in the first bend after a straight section.~~

~~As muons circulate in the ring, the polarization precesses in the plane of the ring, so that, at turn T after injection, [PL + iPx] (T) oc j~~

2 P{T) = pinit e-^-¥) , i.e. a Gaussian decrease with time-constant Analyses of such spectra show that for a 50 GeV beam with OE/E = 10~3 and 20% polarization, these parameters can be determined for each muon fill with a statistical precision of: AE/E = 2 x 10~6 (AE = 100 keV) for the energy, Aa^jE — 2 x 10~6 for the relative energy spread, AP = 3 x 10~4 for the polarization itself.

~~For a beam-energy spread of O~E/E = 3 X 10~5 these numbers become:~~

~~AE/E = 10"7 {AE = 5 keV) for the energy, AOEJE = 5 x 10~7 for the relative energy spread, AP = 10~4 for the polarization itself.~~

~~The errors are smaller in this case since the polarization survives longer.~~

~~53 x 10'' CO 0.39~~

~~"coo Q. > 0.38 (5~~

~~0.37~~

~~CO C O) W 0.36~~

~~30-40 GeV positrons initial muon polarization = 0.2 3 0.35 energy spread oE/E=10"~~

~~200 400 600 800 1000 Turn number~~

Fig. 30: Oscillation with turn number in a fill of the number of electrons in the energy range 30-40 GeV for 50 GeV muons (normalized to the total number of muon decays during the given turn). The oscillation amplitude is a measure of the beam polarization, its frequency a measure of the beam energy, and its decrease with time a measure of energy spread.

Systematic errors would be dominant. Clearly the beam-energy measurement error will be dominated by the present error on (g — 2)/2, which is 7 x 10~6. It could also be affected by residual beam oscillations. The error on the measurement of polarization will be dominated by the calculation of the exact momentum acceptance of the device, taking into account the beam parameters. The energy spread will be affected by possible time dependence of the other beam parameters such as emittance, by time-dependent backgrounds, and by other possible sources of depolarization. More precise estimates would require a detailed design and simulation of the device. On the whole, however, given that a year will count more than 108 muon fills, it seems quite certain that the energy spread can be known with a relative precision of better than 1% of its value, even if it is as small as crgfE = 3x 10~5. The abundant number of decay electrons can presumably also be used to monitor the total muon intensity, with a precision limited by acceptance and background estimates, but presumably much better than 1%. Beam Current Transformers have similar precisions. Finally, the measurement of other beam parameters, such as beam emittances, should be accessible to devices such as wire scanners, taking advantage of the fact that muons do not interact much with matter.

4.4 Measurements of the Higgs-boson properties W. Murray The scan of the Higgs boson is one of the most important goals of a muon collider. If the Higgs is below the WW threshold then it can be directly measured nowhere else, but the fine energy spread and large s-channel Higgs coupling to the muon allow this unique possibility.

54 For a Higgs mass of 110 GeV/c2, for example, the width is around 5 MeV. We therefore need to have a spread in the beam energy of the order of 0.003%, or better in order not to smear out the resonance. This is discussed in Refs. [69] and [70], and limits the luminosity to of the order of 1031 cm~2s~1. This in turn corresponds to a production rate of a few thousand Higgs bosons per year. To estimate the physics potential, a very crude simulation of a detector was used; essentially a generator-level smearing of charged and neutral particles with the performance of a typical LEP detector and with all particles below 20° removed to approximate the shielding. No background was allowed for, and b-tagging was taken, very optimistically, from an NLC pixel proposal with a pixel layer at 2.5 cm, such that 80% of b-quarks, 6% of c-quarks and 0.2% of light quarks are counted as b's. Then ^/x, qq(7) and Higgs events were generated using PYTHIA 6.120 [71], and classified 'experimentally' as radiative return to the Z, di-muon, and high s' uds-, c- and b-quark events. The number of events in each class was used to fit the luminosity and h —> bb and h —> 'other' cross-sections simultaneously.

4-4-1 Luminosity monitoring There is no need for a dedicated luminometer for Higgs physics. This is demontrated using the example of a 110 GeV/c2 Higgs. The measurement of luminosity can be made without using small-angle \x\x scattering, because within the main detector acceptance, assumed to be 20° to the beam, there is a 380 pb /x/u. cross-section. Hadronic returns to the Z can also be used to measure luminosity, and will have an accepted cross-section of around 280 pb. These together are significantly larger than the total cross-section for Higgs production, predicted by PYTHIA to be 25 pb, and than the 200 pb of hadronic events at full beam energy. Even a perfect knowledge of the luminosity only reduces the h —• bb error by 3%. Figure 31 shows the statistical error on a luminosity of 1 pb-1, which is typically 5%. It falls dramatically as the centre of mass drops to the Z resonance, and rises for high energies as the event rates fall.

~~Fitted luminosity error~~

~~l.ii.l I.IMI 100 110 120 130 140 150 160 170 180 190 2 Mh,GeV/c~~

~~Fig. 31: The fitted error on the luminosity versus Higgs mass.~~

4-4-2 Higgs cross-section results If the Higgs mass is known to around 100 MeV/c2 before operation starts, a coarse energy scan, in perhaps 5 MeV steps, will have to be made to locate it. After that the line shape can be scanned in detail, and an example is shown in Fig. 32.

~~55 JO a. 30 llOGeVHiggs X t 25 PYTHIA -6-.12Oi X m 20 • • • Fitted, 10pb"!/point 13 x D 15~~

-5

~~109.98 109.99 110.01 110.02 110.03 2 x beam energy, GeV/c'~~

Fig. 32: The production cross-section for pairs of b-quarks from a 110 GeV/c2 Higgs boson as a function of beam energy. Dots are generated by a fitted Monte Carlo corresponding to 10 pb"1 of events, and the continuous line is the simulated cross-section. The line shape is given by PYTHIA 6.120, and no spread in the beam energy is allowed for.

The figure was produced from the fit described in the previous section. PYTHIA 6.120 [71] incorporates a muon structure function, but the implementation of the structure function does not perfectly control shifts in the beam energy of less than one part in 104, i.e. 10 MeV in this case, which may explain the small shift in the peak position. The b-tagging capabilities are clearly important. If the actual results are worse than those assumed here, the cross-section measurement suffers rapidly. The fitted errors, ±3 pb from 10 pb"1 h —> bb and ±10 pb from 10 pb"1 for h —> other, do not depend strongly on the cross- section, because of the large background. The nearby Z resonance may be useful for detailed understanding of the detector performance. To use these measurements to extract the mass and width requires precise knowledge of the beam energy, and in fact control as well. This has been addressed in the previous section.

4-4-3 Dependence upon Higgs mass The [A/J, —> h —> bb cross-section is shown in Fig. 33. It falls quite rapidly as the centre-of-mass energy rises, because of the increasing width and reducing bb decay fraction. The peak cross- section drops by an order of magnitude at the W+W~ threshold, and the bb branching fraction also drops, and the results in other channels must be obtained to get a complete picture. The error on the cross-section falls as the energy rises. The initial rapid drop is because it is not possible to completely separate Higgs and real Z + 7 production, especially when the 7 energy is low. The very large bb cross-section swamps the Higgs signal. The ratio of cross-section to error tells us where we can make the best measurement of the bb rate with 1 pb"1. This is a little misleading, as the increasing Higgs width would in practice allow a higher luminosity for higher Higgs masses, but this would not change the plot dramatically. We must also investigate the precision in other decay modes.

~~56 •X> 1 10 =-~~

~~100 MO 120 UO 140 150~~

~~10 r~~

~~, , , i I i i , i I i i 100 1 (1 120 130 140 150 1 ;~~

~~: 2 - • «- • * •~~

~~- •~~

~~, , , , , , , , i 100 110 120 130 140 150 M. , GeV/c2~~

~~Fig. 33: The Higgs to bb cross-section, error and their ratio, from 1 pb 1 of data.~~

4.5 Consequences for Higgs-boson couplings G.J. Gounaris and F.M. Renard The potential of a muon collider for testing the Higgs-boson couplings is investigated in Ref. [72]. This study applies to a light Higgs boson (m^ < 2Mw); for larger Higgs masses the increase of the total width and of the backgrounds forbids high-precision tests. We have first checked that the integrated /i+/ix~ luminosity required for improving the measurements of the Higgs branching ratios in e+e~ —* hZ at an LC of 100 fb"1 varies between a fraction of a fb"1 and a few fb"1, depending on the Higgs decay mode. In order to quantify, in a gauge-invariant way, the meaning of testing the Higgs boson couplings, we have added to the Standard Model Lagrangian a set of new physics terms expressed in terms of dimension-6 SU(3) x SU(2) x U{\) operators Ol which produce anomalous Higgs boson couplings, namely the eight bosonic CP-conserving ones called 0$I^0BW_J 0B$, 0W$, 0ww, 0BB, 0*2! 0GG; the four bosonic CP-violating ones 0BW, 0WW> 0BB, 0GG; and the x fermionic operators &i\. Each of them contributes with a coupling constant g eS. We have collected the constraints on these various coupling constants that are expected to be established from searches at the various colliders (LEP, SLC, TEVATRON, LHC, LC), anticipated to run before the fi+fj,~ collider. We have computed their effects on the Higgs partial widths, total width and branching ratios. We have then established the minimum luminosity L(fj,fj.) required in order for the muon collider to improve the aforementioned constraints. We have again found (see Table 10 and Fig. 34) that for most of the operators (except for 0$,i and 0$ 2) a few fb"1 is required with measurements of the branching ratios. In the case of 0BW> 0wwi 0BB and their CP-violating partners the results depend on whether the 77 mode at an LC will have run before the /i+/^~ collider. In this case the required luminosities

57 lie in the range of 10-20 fb 1. Otherwise a fraction of a fb * would be sufficient. We have also shown that the measurement of the total Higgs width at the level of 10% is required in order to improve the constraint on 0$^-

~~Table 10: Required ji+\i~ luminosity in fb"1 for rrih = 130 GeV (The numbers between parentheses correspond to the constraints imposed by a 77 mode at an LC.)~~

~~(a) CP-conserving operators 0*i 0BW 0B* 0W* 0ww 0BB 0*2 0GG 413 12(27) 164 53 0.7(27) 0.3(32) 1. 0.8~~

~~(b) CP-violatinj; and fermionic operators 0BW 0ww 0BB 0GG 0bi(A = 5O TeV) 0^ i(A = 500 TeV) 0.2(21) 15(36) 2(26) 3 0.7 1~~

~~10 'E r- 10 " i i ; Fig. la : Fig. lb [% — O,,(ZZ) 10 ' r / , / 10 i L. A~~

~~\-v-0B,(Z7) 1 10 3 fr J 10 t / •' / /~~

~~10 i * r oBB, 0B.. 0W* yy( // — 1 0 • fr 1 . 4 - - -—-'-'" L 10 L. 77(LC) - f : 10 i k \— 1 10 I o.iTT 0.12 0.14 0.16 0.10 0.12 0.14 0.1(5 nih (TeV) mh (TeV)~~

~~Fig. 34: /U+/L* luminosity needed to improve the constraints on the CP-conserving operators (only the most efficient channel is indicated).~~

We notice that the values of the new physics scales to which these constraints correspond lie in the range of several tens of TeV in the case of the bosonic operators. This is a domain where many theoretical models expect such effects to show up. As far as fermionic operators are concerned, a luminosity of 1 ftr1 would allow us to test fermionic scales of the order of 60 and 500 TeV for 0bi and 0Mi, respectively.

4.6 Consequences in a supersymmetric scenario P. Janot As described in Section 4.4, a unique feature of a /i+/x~ collider operating at yfs = m^ is the possibility of performing precision measurements from energy scans of the Higgs resonance(s)

58 with unrivalled accuracy. Such an accuracy could be obtained only for mh ^ 10 GeV/c2 above the Z mass (as indicated by LEP), so as not to be overwhelmed by too large a background from Z decays, and below 140 GeV/c2 (as predicted by supersymmetry), so as to ensure a sizeable bb branching fraction. For illustration, the production cross-section of a Standard Model Higgs boson via /J,+fJ,~ —> h —• bb is displayed in Fig. 35a as a function of m^ for y^s = m^ and in Fig. 35b as a function of the centre-of-mass energy for mh = 110 GeV/c2.

~~120 - (a) 100 - j ! L . \ h—»bb dominant~~

~~80- •f ! i |~~

~~\ 60 - \j 1 \ 40 - ;.. .\ ••• { !~~

~~20 - vL h-»\VW* takes ovei!~~

~~0 - i1' ' • • i • ' • • i • iT7|?^' i i i i i ! i j i i , i 100 110 120 130 140 150 160 170 180 109.99 110 110.01 110.02 2 £CM (GeV) mh (GeV/c )~~

Fig. 35: Production cross-section of the Standard Model Higgs boson via n+ft —* h —* bb (a) as a function of mi, for i/s = mh, and (b) as a function of the centre-of-mass energy for mh = 110 GeV/c2, computed at tree-level (top curve), with ISR included (middle curve) and with a relative centre-of-mass energy spread of 3 x 10~s (bottom curve).

The total decay width of a 110 GeV/c2 Standard Model Higgs boson is about 3 MeV. As a consequence, a centre-of-mass energy spread much larger than 3 MeV would entirely wash out the resonance, as shown in Fig. 36a where the effect of the energy spread on the peak production cross-section is displayed for mh = 110 GeV/c2. In all that follows, the relative centre-of-mass energy spread is therefore assumed to amount to 3 x 10~5. (This is pessimistic with respect to the usual assumption that the beam energy spread is 3 x 10~5, by a factor -\/2.) With the strategy presented in Section 4.4, the following accuracy (Table 11) can be achieved on the mass mh, the + width Fh of the Higgs boson, and the peak production cross-section h —• bb).

~~Table 11: Precision reached for the measurements performed in a scan of the Higgs boson resonance. Here, C is the integrated luminosity collected at the top of the resonance, expressed in pb"1.~~

~~Observable Accuracy •^peak ±10 pb / y/C mh ±0.1 MeV/c2 rh ±0.5 MeV~~

~~59 - 50 a (a) -se c ti /i = 40 o : V \ 30~~

~~\ 20~~

~~0 ,—,—,—i—.—i—i—.—.—i— -3 -2 2 log,0(A£/£) mh (GeV/c )~~

Fig. 36: Peak production cross-section of the Standard Model Higgs boson for mh = 110 GeV/c2, as a function of (a) the relative centre-of-mass energy spread and (b) the b-quark pole mass. In (b), the top curve is the total /Lt+\x~ —> h cross-section assuming a negligible beam-energy spread, the middle curve is the n+fx~ —» h —• bb cross-section with a negligible beam-energy spread, and the bottom curve is the n+pT —> h —* bb with a relative centre-of-mass energy spread of 3 x 10~s included. A zoom of the latter is displayed in the top-right insertion.

Whilst the first two measurements are systematic-error limited, the latter is limited only by statistics up to integrated luminosities of the order of 10 fb"1 or so. Indeed, the precise calibration of the centre-of-mass energy and of its relative spread discussed in Section 4.3 enables a prediction of the total cross-section to < 0.5%. In addition, the peak cross-section turns out not to depend on theoretical details in the total decay width, such as those related to the knowledge of the b-quark pole mass (Fh oc mb2). This property is due to delicate cancellation effects between the width and the beam-energy spread, chosen such that rh/mh ~ AE/E. This cancellation is illustrated in Fig. 36b, where the peak cross-section is displayed as a function of the b-quark pole mass. In the absence of beam-energy spread (top curve), the total peak cross-section a(/u+ji~ —> h) is found to decrease when m^ increases, as expected from the larger decay width: 4-7TS h) = mt — mi This behaviour is alleviated in o"(/i+/x —> h —> bb) since the bb branching fraction grows with mb (middle curve). Finally, a narrower resonance is damped more than a broader resonance by the spread of the beam energy, which completes the flattening of the cross-section dependence on mb- It can be seen that a variation of ±10% in m^ corresponds to a variation of less than 0.5% in the peak cross-section. The current uncertainty on the b-quark pole mass is of the order of 1-2%. Several questions have to be answered at this level: 1. Do these measurements bring any additional information beyond that obtained from measurements made at earlier colliders, i.e. the LHC, and an e+e~ LC? 2. Does this outstanding accuracy allow stringent tests of the Standard Model to be performed? 3. Is it of any use for the understanding of the underlying theory?

60 To do so, it is first assumed in the rest of this section that, by the starting time of the First Precision Muon Collider (FPMC), LHC will have completed its running at full luminosity, and an LC will have collected large integrated luminosity at low energy (e.g. 500 fb-1 at y/s = 300 GeV). For an FPMC to make sense, a light Higgs boson will have to have been discovered, e.g. at LHC through h —> 77 or at an LC through e+e~ —• hZ with h —• bb, and the precision of the existing measurements is expected to be as shown in Table 12 in the Standard Model. (Branching fractions other than h —• bb can also be measured at a linear collider, but with a limited statistical accuracy, and are essentially irrelevant for what follows.)

~~Table 12: Precision reached for the measurements performed for a light Standard Model Higgs boson discovered at LHC and studied at an LC.~~

Observable Accuracy Done at ±7 fb = ±20% h) • BR(h -» 77) (dominated by theoretical uncertainties LHC in the production cross-section) mh ±100 MeV/c^ LHC and an LC ±2.5% <7(e+e- -> hZ) • BR(h -> bb) (dominated by theoretical uncertainties LC in the b-quark pole mass) t+t~ ±1% LC

For the sake of defmiteness, it is now assumed that Nature is supersymmetric and is described by the Minimal Supersymmetric extension of the Standard Model (MSSM). In this model, and at tree level, the Higgs sector, i.e. the masses, the production cross-sections and the branching fractions of the three neutral and two charged Higgs bosons, h, H, A and H*, are determined by only two parameters, mx and tan /?. Shown in Fig. 37a is the x2 °f the measurements performed at LHC and an LC for the lighter CP-even Higgs boson h (Table 12), when compared to the Standard Model predictions, in this (IBA, tan/?) plane. The x2 is dominated by the cr(gg —» h —y 77) measurement at LHC and the cr(e+e~ —• hZ) • BR(h —> bb) measurement at an LC, both limited by systematic uncertainties in the theoretical prediction: The former is limited by the knowledge of the gluon structure functions, and the latter by the precision in the b-quark pole mass. (The statistical uncertainties would be of the order of 5% and 0.3%, respectively.) An indirect discovery of a supersymmetric Higgs sector with these measurements would therefore occur only in regions already covered by other possible direct discoveries, either with hA production at an LC for tan/? T+T~ at LHC 2 for tan/3 > 20 and mA ^ 500 GeV/c . The potential of the FPMC is shown in Fig. 37b with a moderate integrated luminosity of 200 pb"1 (corresponding to a year of data-taking with C = 2 x 1031 cm~2s~1), and in Fig. 37c with a total integrated luminosity of 10 fb"1 (corresponding to five years of data-taking with an optimistic instantaneous luminosity C = 2 x 1032cm~2 s"1). The coverage of the (IUA, tan/3) plane is already much improved to A masses of 600- 800 GeV/c2 with 200 pb"1, and gets totally covered up to 2 TeV/c2 with 10 fb"1. The x2 is entirely dominated by the fi+n~ —> h —• bb cross-section measurement, the statistical accuracy of which is 3.5% at low and 0.5% at high luminosity. A precision of 100 MeV/c2 on mh (as achieved at LHC and an LC) translates to a systematic uncertainty of only 0.25% on the cross- section prediction. The 'moderate' accuracy (20%) of the total decay width can never compete.

~~61 ' I ' "I1 200 400 600 1000 1200 1400 1600 1800 2000 200 400 600 800 1000 1200 1400 1600 1800 2000 2 2 m. (GeV/c ) mA (GeV/c )~~

~~200 400 600 1000 1200 1400 1600 1800 2000 m. (GeV/c2)~~

Fig. 37: Expected x2 values for the light Higgs boson measurements compared with the Standard Model prediction, (a) after LHC and an LC, (b) with 0.2 fb"1 at the FPMC, and (c) with 10 fb"1 at the FPMC. The darkest grey shaded area holds for x2 values in excess of 25 (more than 5tr discrepancy with the Standard Model), followed by a 4-5

To summarize, the measurement of the [i+pT —»• h peak cross-section would have a unprecedented impact for stringent tests of the Standard Model. On the other hand, the outstanding measurement of the decay width (±0.5 MeV/c2) would not be precise enough to add any information, while an accuracy better than 100 MeV/c2 on the Higgs boson mass is of no use for that purpose. (These statements would have to be revised if consistency tests of the MSSM had to be performed instead.) These graphs therefore answer the first two questions. While LHC and an LC fail in providing powerful tests of the Standard Model in the situation where only one Standard-Model-like Higgs boson is discovered (and nothing else), the FPMC would give a unique opportunity to provide stringent constraints over a wide range of model parameters. To answer the last question, specific choices have to be made for the underlying theory (here, the MSSM) and for the parameters relevant to the Higgs sector, and an attempt to reconstruct these parameters from a given experiment has to be made. As already mentioned, the two parameters m^ and tan/? are sufficient to describe the Higgs sector of the MSSM at tree level. However, when the radiative corrections due to the large top-quark mass are taken into account, Higgs boson couplings and masses are modified according the properties of the stop sector. For instance, when the two stops are degenerate with mass MSUSY, the square of

~~62 the lighter CP-even Higgs boson is increased by~~

~~2 2 log 8TT sin , )•~~

When the two stops mix, MgySY has to be replaced by the product of the two stop masses, and masses and couplings get further modified by two additional parameters driving the stop mixing: 2 At and fx. (In Fig. 37, a SUSY mass scale of 1 TeV/c was assumed for all supersymmetric particles, i.e. gauginos, sleptons and squarks, thus preventing other s-particles from being discovered either at LHC or at an LC. The maximal stop mixing was chosen, but the basic features of these graphs are unaffected by this particular choice.) For the purpose of this work, the following choices were made. The value of TUA was chosen to be 300 GeV/c2, sufficiently large to be above the kinematic reach of an LC, but sufficiently small to evaluate what the FPMC can do in an 'easy' situation. The value of tan /? was chosen to be 10 so that only the lighter CP-even Higgs boson h is seen at LHC (no A, H —> T+T~). For a similar reason, the scale of all supersymmetric particle masses was set to Mgusy = 1 TeV/c2. (It has to be kept in mind, however, that any additional discovery prior to the FPMC would give even more information on the parameters of the underlying theory.) Finally, At and \x were set to 1 TeV/c2 too, not much of a prejudice, since this choice is essentially irrelevant for what follows. The predictions for the various observables in this case are indicated in Table 13, compared with their Standard Model values, their expected accuracy (including systematics from theory), and their contribution to the x2's °f Fig. 37. The overall x2 is saturated by the measurement of the //+^~ —> h —> bb cross-section. The high sensitivity of this measurement with respect to all the others is due to the following. • It is not, unlike the LHC and LC cross-section measurements, limited by theoretical systematic uncertainties. • The larger coupling of h to the leptons and down-type quarks enters the cross-section with high power: It enlarges the branching fractions into /i+'[T and bb, to which the cross- section is proportional, and it enlarges the total width (Table 13), thus alleviating the reduction of the cross-section due to the beam-energy spread.

Table 13: Prediction for the various observables in the MSSM with the chosen parameters and in the Standard Model, the expected accuracy, and the contribution to the x2- ^n the last two columns of the third row, the two numbers hold for an integrated luminosity of 100 pb"1 and 10 fb"1, respectively.

Observable MSSM value SM value Accuracy XSM mh [MeV/c*] 113256.46 113256.46 0.1 - Th [MeV] 4.88 3.03 0.5 14 a(n+fi- -» h -> bb) [pb] 29.28 18.87 1 /0.1 100 / 1000 cr(e+e- -> hZ) • BR(h -> bb) [pb] 0.162 0.152 0.004 6 cr(e+e- -» hZ) [pb] 0.1954 0.1956 0.0019 0 T(h -> gg) • BR(h -* 77) [eV] 292 482 90 5

Since only the measurements of the width and of the peak cross-section significantly contribute to the discrimination between the MSSM and the Standard Model, and are actually a measure of the same quantity, it cannot be expected that the five MSSM parameters relevant for the Higgs sector be determined simultaneously at an FPMC. The question is whether these measurements can predict TUA with a decent precision, or determine tan/9 instead, or say anything

63 about MsusY) -^-t or /i. Actually, it is reasonable to expect that these measurements are mostly sensitive to m\: When m\ increases, the heavy Higgs bosons decouple and all the predictions of the MSSM get closer and closer to those of the Standard Model. In other words, the difference between the measured cross-section and the prediction of the Standard Model provides a good estimate of mx (see also Fig. 37).

~~2 Fig. 38: lcr and 2~~

Fictitious experiments were performed by smearing the aforementioned MSSM predictions within the quoted errors, in the three following configurations: before the FPMC; with 100 pb""1 taken at the FPMC; and with 10 fb"1 accumulated at the FPMC. A first fit of m-A and tan/? to the 'measurements' was performed with MsusY = A = /i = 1 TeV/c2 (i.e. the input values). The lcr and 2a contours are shown in Fig. 38 for the three situations. The mA prediction capabilities of pre-muon-collider measurements are rather limited: A statistical accuracy not better than ±100 GeV/c2 is achieved on mA, assuming that the MSUSY> 1 At and fi values are known. One order of magnitude is gained with a short 100 pb" run at 2 2 the FPMC (

64 from ±1.1 to ±0.06 and ±0.01, entirely correlated with m\: This is because , when the radiative corrections are known, two parameters (e.g. m^ and m^) suffice to determine unambiguously the Higgs sector properties, and in particular the value of tan/3. If, on the other hand, tan/3 is known from other measurements, we see from Figs. 34a and 34b that not much precision in m& is gained from the LHC and an LC, whereas Figs. 34c and 34d show that there is considerable gain with the muon collider. However, the radiative-correction parameters would be known if, for instance, charginos on the one hand (to determine /J, and m^) and stops on the other (to determine mo and A%, and thus MSUSY) were discovered. As already mentioned, a single relevant measurement cannot predict all five parameters needed to describe the Higgs sector. As a matter of fact, when MSUSY J M and /i are allowed to vary (even restricting the scan within ranges not leading to charge and colour breaking minima), almost any value of tan/3 can be found which accounts for all measurements. Still, a relevant prediction capability for mA, given by the difference between the measured peak cross-section and the Standard Model prediction, is preserved: only values within ±20% of the true T«A value are found to be compatible with all measurements. The results are summarized in Table 14.

Table 14: Summary of the results of the tan/? and THA fits in the various configurations examined in the text: LHC and an LC only, 100 pb"1 and 10 fb"1 at the FPMC, with or without additional discoveries of charginos and stops. The situation where only stops or only charginos would be discovered has not been studied.

~~Other None Charginos discoveries and stops Collider LHC+LC FPMC FPMC LHC+LC FPMC FPMC (100 pbT1) (10 fb-1) (100 pbT1) (10 fb"1) °tan/3 00 oo oo ±1.1 ±0.06 ±0.01~~

~~00 0mA ±20% ±20% ±50% ±3% ±0.5%~~

The accuracy of this prediction of mj^ suffices to envision a scan of the A resonance at a Second Precision Muon Collider (SPMC), with a centre-of mass energy around the predicted value of rriA- In the previous example of parameters (mA = 300 GeV/c2 and tan/? = 10), and as is generally the case for large JTJA values, H and A are almost degenerate in mass (mn — m^ = 700 MeV/c2), with a common total decay width of ~ 600 MeV/c2. The total ji+pT -> H, A -> bb production cross-section is displayed in Fig. 39 as a function of ^/s, for a relative centre-of- mass-energy spread of 3 x 10~5. A wide scan over a ±60 GeV/c2 window with 1 GeV/c2 steps and less than 1 pb"1 per step suffices to discover both H and A in less than a year with the SPMC. Then, a finer scan of the resonances allows the overall line shape to be measured. Six energy points are needed to determine the average mass S = (mn + m,A)/2, the mass difference Am = \mu — m^\, the two peak cross-sections a A and

~~65 100 -~~

~~80 -~~

~~: 60 -~~

~~40 -~~

~~20 -~~

~~0 —,—1—i—,—i—i—,—r-—'—i— 1 1 1 1 ! 1 ! • 296 298 300 302 304~~

~~E,.m(GeV)~~

Fig. 39: Production cross-section of H and A via ^n —> H, A —» bb as a function of the centre-of-mass energy for rriA = 300 GeV/c2 and tan/3 = 10, with a centre-of-mass energy relative spread of 3 x 10"5. The triangles with error bars represent a simulated six-energy-point scan, with 25 pb~' per point.

The coupling of A to bb is proportional to tan (3, and so is that of H to bb when A is heavy. The two decay widths are therefore expected to be approximately equal and increase like tan2 /? (except at low tan-/? values where channels like H —> W+W~, ZZ, hh and A —> Zh have sizeable branching fractions, thus rendering even richer the phenomenology, even giving a possibility of distinguishing H and A). This behaviour is shown in Fig. 40 where the /i+ji~ —> H, A —> bb cross-section is displayed as a function of the centre-of-mass energy for tan/3 = 8,10 and 15. As can also be seen in this figure, the mass difference Am also quickly varies with tan/?. Even more interesting is the observation that the widths and the mass difference are quite insensitive to radiative corrections, and therefore to specific properties of the unknown stop sector. These measurements thus allow for a quasi-parameter-independent determination of tan/3. or a Without knowing anything about MsusY) At, M> precision of ±0.2 can be achieved in tan/3, still largely dominated, however, by these theoretical uncertainties. No real constraint can be obtained on the other parameters of the MSSM, unless sparticles are/have been found. In the latter case, detailed and stringent tests of the MSSM could be performed. The following conclusions can be drawn from this study. • If only a Standard-Model-like Higgs boson is found at LHC or at an e+e~ linear collider, an FPMC operating at ^/s ~ mj,, with a total integrated luminosity between 0.1 and 10 fb"1, would greatly extend the constraints on the Standard Model. Expressed in terms of MSSM parameters, the lower limit on mx would increase from 250 GeV/c2 to about 2 TeV/c2. • If Nature is supersymmetric, the FPMC would predict the A mass with a 20% accuracy, if well below the aforementioned bound. This uncertainty could be reduced to the order of 1% if other sparticles were discovered. • An SPMC operating at y/s ~ TUA with an integrated luminosity of a few 100 pb"1 would thus discover the two heavier neutral Higgs bosons, H and A, and constrain the value of tan/3 to ±0.2.

~~66 • The detailed study of these particles, backed up or not by the discovery of other sparticles, would open a new field of precision tests of the MSSM.~~

~~S Noistop mixingi Typical slop mixing (a) (b) c msbsv =' TeV'f i 160 | i 160 -~~

~~120 - 120-~~

~~80- 80- 40- I 40- ft l\ \ n- i j 1 , 1 ]| 1 1 1 1 "i 0- —i—i—j—i—<—i- j , 1 1^ r--T 296 298 300 302 304 296 298 300 302 304~~

~~Ecm (GeV) E (GeV)~~

~~Maximal stop mixing D mSUSY = ' TeV'C~~

~~160- • • -f :~~

~~120-~~

~~80- A \ j 40- -k-i\M \~~

~~o- Ijf 296 298 300 302 304~~

~~EQm (GeV)~~

~~Fig. 40: Total cross-section /J.+\i —• H, A —> bb as a function of~~

4.7 Event generators for muon colliders D. Perret-Gallix Automatic Feynman diagram computation programs as developed in the CPP (Computational Particle Physics) Collaboration9 allow cross-sections to be computed and event generators to be built with little human involvement. These packages (GRACE10, CompHEP11), heavily used at LEP, are general enough to be applicable to n+n~ initial-state processes. Important features like complete tree-level process computation, accounting for fermion mass and full spin correlations are available. 9http://wwwlapp.in2p3.fr/cpp/cpp.html lohttp://www-sc.kek.jp/minami/ uhttp://theory.npi.msu.su/ comphep/

67 Among the many processes studied for the workshop using the GRACE system, the Zbb and JJL+yu~bb final states are presented. Figure 41a shows the bb invariant-mass distributions for £+£~ —> Zbb where £ : e,fi. The Z peak is visible in both distributions, but the neutral Higgs peak (Ho,Ao) is only present for muon initial states, reflecting the Higgs mass dependent coupling. Figure 41b shows that complete calculations can be carried out even for high-multiplicity final- state processes (2 —> 4): p+pT —> /u+/U~bb, where 556 diagrams contribute.

~~! 10"' r io"3 ir 10 Ir Zbb -5 c 10 fh 10 J \ Zbb 10 10 r 10 10 ^~ 10 ft". a) 0 100 200 300 400 500 600 700 800 900 1000 Vs (GeV) bb invoriant Mass~~

~~a> 10~~

~~b) 100 200 300 400 500 600 700 800 900 1000 Vs (GeV) bb invariant Mass~~

+ Fig. 41: bb invariant-mass distribution for (a) £ l~ -> Zbb, t : e,/i, ^/i = 1000 GeV, MHo ^ MAo ~ 300 GeV, + + Mh0 ^ MZo; (b) M M~ —> M M~bb, with, in addition to Fig. 41a settings, -0.985 < cos#M < 0.985.

4.8 Squark production at the H and A resonances S. Kraml, A. Bartl, H. Eberl, W. Majerotto and W. Porod12 The MSSM implies the existence of five physical Higgs bosons: h, H, A, and U.^. For an accurate test of the model the masses and couplings of these particles must be determined with good precision. A muon collider offers unique opportunities due to s-channel production of H and A in a very clean environment [69, 70, 73]. If the masses of H and A differ by few GeV and their widths are sufficiently small, an energy scan will show two separate peaks. For large mA/large tan/3, A and H are nearly degenerate in mass, and the peaks overlap. However, with the excellent energy resolution of a muon collider, the two resonances may still be separated. + If all supersymmetric particles are heavy, /x //~ —> A —> tt, bb, T+T~, Zh and /I+/J~ —> H —> tt, bb, T+T~ , W+W~, ZZ, hh are the dominant processes. If, however, decays into supersymmetric particles are kinematically allowed, fi+fi~ —> A —> tjtj/, bjb^, f^f^7, xtxj > XkXl and M+M~ -> H —> i-ij, bjbj, f+f~, 99, xtxj, XkXl (hj = 1,2; k,l = 1 ..A; i ^ i') can also have large cross-sections. 12Work supported by the 'Fonds zus Forderung der Wissenschaftlichen Forschung' of Austria, project P10843- PHY.

68 As an illustrative example for the importance of the various processes, we show in Fig. 42 the main (1-loop supersymmetric-QCD-corrected) branching ratios of A and H decays [74, 75] as functions of mA for M = 300 GeV, p = 500 GeV, tan/3 = 3, MQ = 400 GeV and At = —400 GeV. For the other soft breaking parameters we have taken MQ : M^ : Mg, : M^ : Mg = 1:8/9: 10/9 : 3/4 : 3/4 and At = Ab = 2AT for simplicity. Moreover, we have used GUT relations for the gaugino masses (M' ~ M/2). For the radiative corrections in the (h,H) system we have used the formulae of Ref. [76]. As can be seen, decays into supersymmetric particles can play an important role. For mA = 300 GeV we have mn = 304 GeV, F(A) ~ 0.1 GeV, and r(H) =J 0.2 GeV, while for mA = 600 GeV we have mH = 602 GeV, F(A) ~ 3 GeV, and T(H) ~ 8 GeV.

~~1. H '••'••'• j 1.~~

~~>-bb { ~\ a '• ti 0.8 \ \^ 0.8 /~~

~~• \ x\ 0.6 • $" 0.6 , W 3, hh I \ • en" 0.4 - | \ ft '• m 0.4~~

Zh X 0.2 - . \ f' " ',---'• 0.2 - ";.ym X+ -'~~M bb _'•'' 'f T>xP • 0. Fr , ', LVti'T-f-i-i-T-i-v-,.-,-.-!....,...,,..., .1 o. 200 400 600 800 1000 1200 200 400 600 800 1000 1200 mAJtGe\f] mAljGeV]

Fig. 42: Branching ratios of A and H decays [at O(aas)} as functions of THA, for M = 300 GeV, /x = 500 GeV, tan/? = 3, Mq = 400 GeV, and At = -400 GeV; MQ : Mo : M5 : Mf, : Mg = 1 : 8/9 : 10/9 : 3/4 : 3/4 and

~~At = Ah = 2AT.~~

The process fJ-+(J,~ —+ A, H —*• bb (tt) has been discussed in Ref. [69]. Pair production of sfermions at yfs ~ mA, mn has been studied in Refs. [77, 78, 79]. Figure 43 shows examples of stop and sbottom pair production at the Higgs resonances with 30% left-polarized JJL+ and fj,~ beams. In Fig. 43a the cross-sections of fJ,+n~ —> tjtj are plotted as a function of y/s for m-ti = 180 GeV, m~t2 = 260 GeV, cos6>| = -0.55, /x = 300 GeV, tan/3 = 3, and mA = 450 GeV (for the other parameters see the figure caption). In this case, mn = 454 GeV, F(A) ~ 7 GeV, and F(H) ~ 5 GeV. As the pseudoscalar A only couples to tit2 combinations, fi+fi~ —* titi yields a single peak at ^/s ~ mn- The Aresonance can be seen in the case of tjtj> (i ^ i') production. The difference of cr(/x+/i~ —• t2ti) and cr(/x+/x~ —• tit2) is due to constructive/destructive interferences of the A and H exchange diagrams andonly occurs for polarized beams. (For 30% right-polarized beams the curves for tit2 and t^ti have to be interchanged in Fig. 43a.) Figure 43b shows the total sbottom production cross-section as a function of yfs for m^ — 157 GeV, m£2 = 188 GeV, cos% = 0.78, /x = 300 GeV, tan/3 = 4, and mA = 380 GeV (forW other parameters see the figure caption). In this example, mn = 383 GeV, F(A) ~ 2 GeV, and F(H) ~ 1 GeV. As can be seen, two distinct peaks occur. In summary, a muon collider is an excellent instrument to measure the masses and couplings of H and A, and to determine the MSSM parameters with very good accuracy.

~~69 450 455 460 375 380 385 390 Vs [GeV] Vs [GeV]~~

+ Fig. 43: (a) Cross-sections of n fj. —> tit, for 30% left-polarized /z* beams, for m-tl = 180 GeV, m-t2 = 260 GeV, cos0{ = -0.55, m6i = 175 GeV, mg2 = 195 GeV, cos<96 = 0.9, tan/3 = 3, and mA = 450 GeV. (b) Total sbottom production cross-section for 30% left-polarized /x* beams, for m^ = 157 GeV, mg2 = 188 GeV, cos 9^ = 0.78, m-tl = 197 GeV, mi2 = 256 GeV, costfj = -0.66, tan/9 = 4, and mA = 380 GeV. In both plots fi = 300 GeV,

~~M = 140 GeV, ML = 160 GeV, Mt = 155 GeV, and AT = 100 GeV.~~

4.9 Chargino production and decay H. Fraas, F. Franke, G. Moortgat-Pick and F. von der Pahlen A muon collider promises to be a remarkable tool to study the properties of charginos in the MSSM. High-precision measurements of the chargino masses can be obtained through threshold production cross-sections, where a muon collider offers an advantage over electron-positron machines by the narrower energy spread and the negligible beamstrahlung [80]. However, for the determination of the chargino mixings and couplings one may also exploit the direct s- channel Higgs production. For chargino masses above the LEP2 bound, it is the resonant production of the heavy neutral scalar Higgs boson H and the pseudoscalar A which dominates the cross-sections. For large mA, the masses of these Higgs bosons only differ by a few GeV. Nevertheless, due to the excellent energy resolution of a muon collider, the resonance peaks may still be separated [81]. The interplay of the Higgs channels with 7, Z and sneutrino-exchange contributing to chargino production offers new opportunities supplementary to e+e~ colliders. Furthermore, suitable beam polarization could help to explore the mixing characteristics of the charginos by suppressing or enhancing different channels. As an example we consider the production of the light chargino /x+/z~ —> X\X\ a* centre- of-mass energies around the Higgs resonances with the subsequent three-body leptonic decay Xi —> xoe~£v Similar to the electron-positron case, one has to take into account the complete spin correlations between chargino production and decay, which turn out to be relevant for the calculation of angular distributions and forward-backward asymmetries AFB [82]. In order to demonstrate the significance of the chargino mixings, we show our results in three scenarios given in Table 15. While the mass of the light charginos is fixed at 180 GeV, they mainly differ by their mixing type, which is predominantly gaugino (scenario A), higgsino (scenario C) or a mixture (scenario B). The Higgs system is given by mA = 400 GeV, tan/? = 3. The values of TA « 1-95 GeV, mH « 404 GeV, TH « 0.72 GeV depend weakly on the parameter // (see formulae e.g. in Ref. [76]).

~~70 Table 15: Parameters, mass eigenvalue and mixing character [84] of the charginos X\ and of the neutralino and the common scalar mass parameter mo-~~

~~M/GeV fi/GeV tan/3 m^i/GeV m^o/GeV mo/GeV A 215 315 -180 + 100 200 B 200 -210 181 +102 200~~

~~C 240 -185 ww w 179 +120 200~~

~~xt Xi (w+| H+) (w-| H-) (7l Z| HJ1I H") A (+.92| -.40) (—.85) +.52) (+.79| -.57| +.15) B (+.85| -.52) (+.63| +.77) (+.87| -.45| -.03| -.20) C (+.58| -.81) (+.29| +.96) (+.83| -.47| +.011 -.32)~~

The total cross-sections ot in the three scenarios for the 'natural' beam polarization of P_ = +28% for the fi~ beam and P+ = -28% for the /*+ beam are given in Fig. 44. The total cross-sections at are independent of the spin correlations and factorize into the chargino production cross-section times the leptonic branching ratio. All cross-sections clearly show the resonance peaks of the Higgs bosons with values up to 40 fb. Since the couplings of the Higgs bosons to charginos are proportional to the off-diagonal terms of the chargino diagonalization matrices (see e.g. Ref. [83]), the Higgs decay into pure gaugino or higgsino states is suppressed. This leads to a larger enhancement of the resonance effect in the mixed scenario B. By comparing the A and H resonance peaks one may infer the phase of the chargino components. In our scenario A with different sign of the Xi components (Table 15), chargino production via A is favoured. The same sign of these components (scenarios B and C) results in a larger H peak. The natural polarization has the advantage of suppressing the sneutrino-exchange channel and therefore minimizing possible destructive interference which may be significant in certain scenarios at e+e~ colliders [84]. An opposite polarization, as shown in Fig. 45 with P_ = —28%, P+ = +28% and in Fig. 46 with P- = -80%, P+ = +80%, however, enhances the non-Higgs channels. One obtains larger cross-sections with, however, smaller effects of the Higgs resonances. Therefore polarization is an important tool to study the interplay between all channels. The lepton angular distributions and the forward-backward asymmetries shown in Figs. 47- 49 may give further important hints for the determination of the chargino mixing properties. Since in the higgsino scenario C sneutrino exchange in production and slepton exchange in decay are suppressed, the forward-backward asymmetry nearly vanishes. In scenarios A and B the gaugino component produces measurable values of about 8%-20%. In general the asymmetries decrease at the Higgs resonances. The asymmetries for natural polarization (Fig. 47) can be enhanced by changing the polarization configuration (Figs. 48 and 49). For muons 80% polarized opposite to the natural polarization the asymmetries become as large as nearly 40% (Fig. 49). In this case, however, the Higgs resonance effects are strongly suppressed. To conclude, a muon collider may significantly help in the determination of chargino mixing properties, especially if different beam polarizations are available.

~~71 394 396 398 400 402 404 406 408 410 394 396 398 400 402 404 406 408 410 V&GeV~~

~~Fig. 44: Natural beam polarization with P- = Fig. 45: Beam polarization P_ = -0.28, P+ = +0.28:~~

~~+0.28, P+ = -0.28: total cross-section <7t for sce- curve notation as in Fig. 44. nario A (thick dotted), for scenario B (solid) and for scenario C (thin dotted).~~

~~0.25~~

~~394 396 398 400 402 404 406 408 410 396 398 400 402 404 406 408 410 Vs/GeV~~

Fig. 46: Beam polarization P_ = -0.80, P+ = +0.80: Fig. 47: Natural beam polarization with P- = curve notation as in Fig. 44. +0.28, P+ = —0.28: forward-backward asymmetry AFB for scenario A (thick dotted), for scenario B (solid) and for scenario C (thin dotted).

~~0.4~~

~~I94 396 398 400 402 404 406 408 410 394 396 398 400 402 404 406 408 410 V&GeV~~

~~Fig. 48: Beam polarization P_ = -0.28, P+ = +0.28: Fig. 49: Beam polarization P- = -0.80, P+ = +0.80: curve notation as in Fig. 47. curve notation as in Fig. 47.~~

72 4.10 Probing CP violation in the Higgs sector of the MSSM A. Pilaftsis and C.E.M. Wagner The MSSM is a very attractive extension of the minimal Standard Model. One of the most appealing features of such a theory is its remarkable perturbative stability from the electroweak to the Planck energy scale. Because of the holomorphic structure of the superpotential and the presence of superpartners, the MSSM must contain two Higgs doublets in order to give tree-level masses to both up and down families and cancel triangle anomalies. Despite the presence of two Higgs doublets in the theory, the Higgs sector of the MSSM is still very predictive: At the tree level, the quartic couplings in the Higgs potential are related to the known electroweak coupling constants gw and g' of the gauge groups 5{/(2)L and U(l)y, respectively. In the existing literature [85, 86, 87, 88], the Higgs-boson mass spectrum of the MSSM has mainly been studied within the restricted framework of an effective CP-invariant Higgs potential. However, recent studies have shown [89, 90] that the tree-level CP invariance of the Higgs potential of the MSSM may be broken sizeably by loop effects induced by CP-violating trilinear couplings of the Higgs fields to the scalar partners of the top and bottom quarks. As a consequence, the high degree of the tree-level mass degeneracy between H and A may be lifted considerably at one loop. Within the context of general two-Higgs doublet models, the latter possibility has been discussed extensively, in connection with observable phenomena of resonant CP violation through HA mixing [91] at future high-energy colliders, such as the Next Linear e+e~ Collider (NLC), the CERN Large Hadron Collider (LHC) and the proposed First Muon Collider (FMC). Because of the reduced CP-conserving background events, the FMC provides a unique chance to explore more efficiently effects due to Higgs-sector CP violation in the MSSM. As we will see, Higgs-sector CP violation in the MSSM may also affect the predictions for the mass of the lightest Higgs boson. The MSSM introduces several new CP-odd phases in the theory that are absent in the Standard Model [92]. Specifically, the new CP-odd phases may come from the following parameters: (i) the parameter fi that describes the bilinear mixing of the two Higgs chiral superfields; (ii) the soft-supersymmetry-breaking gaugino masses m\ for which we assume to have a common phase at the unification point; (iii) the soft bilinear Higgs-mixing mass m^; and (iv) the soft trilinear Yukawa couplings Af of the Higgs particles to the scalar partners of matter fermions. Here, one may slightly deviate from exact universality by assuming the Af of the first and second generation of scalar quarks to be much smaller than that of the third generation, i.e. A[ ~ (0,0,1) A In this way, one may naturally avoid many dangerously large contributions to electron and neutron electric dipole moments (EDMs) [93]. However, not all phases of the four complex parameters mentioned above are physical, i.e. two phases may be removed by suitable redefinitions of the fields. For example, one can rephase one of the Higgs doublets and the gaugino fields A, in a way such that m\ and mf2 become real numbers. Thus, arg(/i) and arg(J4tb) are the only physical CP-violating phases in the MSSM supplemented by universal boundary conditions at high energies. The most general CP-violating Higgs potential of the MSSM is given by the effective Lagrangian

~~(41)~~

Beyond the Born approximation, the quartic couplings receive significant radiative corrections from trilinear Yukawa couplings of the Higgs fields to the scalar partners of the top and bottom quarks (stop and sbottom particles). Analytic expressions for the quartic couplings are given in

~~73 Ref. [90]. The CP invariance of the Higgs potential in (41) is preserved only if [90]~~

~~Im(m$/Xi4) = 0. (42)~~

Within the most general framework of the MSSM, the equality (42) can be violated, thus leading to large CP violation. An immediate consequence of CP violation in the Higgs potential of the MSSM is the presence of mass-mixing terms between the CP-even and CP-odd Higgs fields [89]. Thus, one is led to a (4 x 4)-dimensional mass matrix for the neutral Higgs bosons. In the weak basis (G, a, i, fa),wher e G is the Goldstone field, the neutral Higgs-boson mass matrix MQ takes on the form 2 _ ( Ml Mis \ f431 0 ~ \ M2 M2 ' *- ' Jvl \ JVISP s j where Ms and Ml describe the CP-conserving transitions between scalar and pseudoscalar T particles, respectively, whilst MpS = (MgP) describes CP-violating scalar-pseudoscalar transitions. The characteristic size of these CP-violating off-diagonal terms in the Higgs-boson mass matrix may be estimated by

~~x L -^- i^i sin20CP |Mpt|\ V ' MsW ' tan ^M|' sin^c M2 J ' where the last bracket summarizes the relative sizes of the different contributions, and~~

= arg(i4t/x) + £, (45) where £ is the relative phase between the two Higgs vacuum expectation values. The CP- violating effects can become substantial if \/J,\ and \At\ are larger than the average of the stop masses, denoted as MSUSY- For example, the off-diagonal terms of the neutral Higgs-mass 2 matrix may be of the order of (100 GeV) , if |/z| ~ \At\ ~ 2MSUSY, and Cp ^ 90°. These potentially large mixing effects lead to drastic modifications of the predictions for the neutral Higgs-boson masses and for the couplings of the Higgs states to the gauge bosons. The effect of CP nonconservation on the lightest Higgs boson and on its related couplings to the gauge bosons will only be important for relatively low values of MH+, e.g. MH+ <180 GeV. For large values of MH+, the only difference in the CP-violating case is that the relevant stop mixing parameter entering the definition of M^ is now given by

~~|it | = \At-ti*/tan0\. (46)~~

On the other hand, the contributions from the sbottom sector are limited by constraints that originate from the electron and neutron EDMs. In general, unless cancellations occur between different contributions to the EDMs, the CP-violating quantum effects coming from the sbottom sector are found to be small. At a high-energy [i+fJ.~ collider, the dominant gauge-boson-mediated production mechanisms of the neutral Higgs bosons are (i) the process fi+fx~ —• Z* —> HjZ and (ii) the WW or + ZZ fusion processes, e.g. fi fJ,~ —> i//x^W*W* —> fMPMHj. Furthermore, one may have processes of associated Higgs production, e.g. fi+/J,~~ —> Z* —» HjHj. In these reactions, the couplings involved are WWHj, ZZH; and ZHjHj. Higgs-sector CP violation in the MSSM modifies these

~~74 couplings, i.e.~~

~~(47)~~

4cw (48) where Cw = Mw/Mz and dM = 9^ — 9M. Note that the coupling of the Z boson to two real scalar fields is forbidden due to Bose symmetry. Let us now discuss a representative example, and see what is the effect of Higgs-sector CP violation on the mass of the lightest Higgs boson. We consider an intermediate value for tan£ = 4, and set MSUSY = 0.5 TeV, At = Ab = 1 TeV and p. = 2 TeV. As can then be seen from Fig. 50 for MH+ = 140 GeV, we get regions for which the lightest Higgs-boson mass MHJ is as small as 60-70 GeV and the HiZZ coupling is small enough for the Hi boson to escape

~~-i:*"v; I-1---'... ; tanp = 4 ^^ TeV \ - L4,l = Ubl = 10 - - : —wH+= 140 GeV~~

~~. AfH+ = 200 GeV 1 / •~~

~~-2 . . . 1 . , . 1 . . , I • • .1./.,... i , 20 40 60 80 100 120 [deg] (a)~~

~~, . , . I ...,.., I , _~~

~~0 20 40 60 80 100 120~~

~~and Fig. 50: Numerical estimates of (a) p^zz (b) MHl < MH2 as a function of arg(/U).~~

75 detection at the latest LEP2 run with y/s = 189 GeV. Moreover, the H2 boson is too heavy to be detected through the H2ZZ channel. In addition, either the coupling H1H2Z is too small or H2 is too heavy to allow Higgs detection in the H1H2Z channel [90]. Such an experimentally open window may even persist at the Tevatron machine. However, a muon collider has the potential capability to exclude such windows or confirm their presence. The latter would certainly point towards the existence of large CP violation in the Higgs potential of the MSSM. Owing to the relatively large muon mass, there is also the unique possibility that the neutral Higgs bosons may be copiously produced directly via the s-channel at a n+fj,~~ collider. In this case, the centre-of-mass energy should be tuned to be equal to the Higgs-boson mass under study [94]. The relevant cross-section cr(fj,+n~ —> ff) is proportional to the decay widths of the Higgs particle into muons and into fermions (f), which are in turn proportional to the square of the effective couplings of these fermions to the neutral Higgs particles. The presence of CP violation in the Higgs sector of the MSSM modifies these couplings. Since Higgs particles may mix strongly with one another, the effective Lagrangian induced by such mixing effects is given by

Aflf = ~ 2,^i-i) [ 2M d(Oa - MaOn-ig)d ] <49> The Higgs couplings to leptons may be obtained from those to down quarks, by simply replacing mj by mi. The above couplings are sizeable for third-generation quarks and leptons. As one can readily see from (49), the effect of CP-violating Higgs mixing is to induce a simultaneous coupling of Hj, with i = 1,2,3, to CP-even and CP-odd fermionic bilinears, e.g. to uu and ui'jsu. CP-violating effects induced by radiative corrections to the Higgs-fermion vertices may also be important, particularly for large values of tan/3 [95, 90]. CP violation at muon colliders may be tested by looking at observables of the kind

ff) + vfati - ff) ' + fLfL) - a(/x~M -> fR fefti) ' ( j where f may be top or bottom quarks. The former observable requires polarization of the initial muons. If the facility of polarization is not available at muon colliders, one may still observe CP violation through the second observable and reconstruct the polarization of the final fermions by looking at the angular momentum distribution of their decay products [96]. The magnitudes 2 of these CP-violating observables depend strongly on the expressions 2|(^.ff) (

~~#HlUu = °33/s/3 , 5HlUU = 013 COt 0 , 5|2UU = O32/S0 , 0H2uu = 012 COt 0 ,~~

5Hidd = 023Icp , g^dd = 013 tan0, s|2dd = 022/c/j, #H2dd = O12 tan/?. (52) As can be seen from Fig. 51, CP violation in the heavy H2H3 Higgs system can be large, while CP violation in the Hiff system is small. This may be attributed to the fact that in the limit of large charged Higgs-boson masses MH+, CP violation does not decouple from the H2H3, as the difference in the diagonal entries of the system becomes of the same order as for the off-diagonal ones [90]. In this nearly degenerate Higgs-mixing system, one may also look for resonant CP-violating effects that are induced by the interference of the Higgs states [91].

~~76 . , , , •• .V', r • %~~

\ V #v - 1* =1 -1 S / : 5 10 " / — \lf" / \v. / i|f A/H+=150GeV " !».» MH+ = 300GeV " AfH+ = 400GeV • \ A/H+ = 500GeV \ : 10 • • i i i i • 1 i M ** 1 ... . 1 . . . 1 . 20 40 60 80 100 120 arg (At) = [ deg ] (a)

~~2 2 Fig. 51: Numerical estimates of (a) 2|(ffg2dd) (s£2dd)l/[(lt)-~~

To conclude, muon colliders offer a unique opportunity to probe very systematically the Higgs-boson mass spectrum of the MSSM. In particular, these colliders will help us to unravel the CP nature of the Higgs sector of the MSSM. As has been shown in Refs. [90, 91] and illustrated here by a few examples, CP violation in the MSSM can, in principle, be large, and may be tested in muon colliders.

4.11 Strong electroweak symmetry breaking at muon colliders: pseudo-Nambu- Golstone bosons, very narrow and almost degenerate resonances R. Casalbuoni, A. Deandrea, S. De Curtis, D. Dominici, R. Gatto and J.F. Gunion Models of strong electroweak symmetry breaking (SEWS) [97] avoid the introduction of fundamental scalar fields, but generally predict various resonances, including pseudo-Nambu-Goldstone bosons (PNGBs) and vector particles. Among the PNGBs, the lightest one, P°, is particularly interesting since its mass is in the range 10-200 GeV and its width varies between 0.2 and 11 MeV. Discovery of the P° in the gg —> P° —> 77 mode at the LHC will almost certainly be

77 possible. The e+e colliders, while able to discover the P° via e+e —> 7P0 (as long as is not close to roz) are unlikely to be able to determine the rates for individual final states with sufficient accuracy. The s-channel production at the muon collider is predicted to have a substantial rate for -^/s « mPo. Because the P° has a very narrow width, it is important that the energy resolution of the beam is as low as R = 0.003%. Good measurements of the rates of the P° in the final states will then be possible, together with the determination of the total width and mass. The typical errors for an integrated luminosity of 0.3 fb"1 are shown in Fig. 52 [98].

~~Stat. Error for 0.3 fb -1~~

~~10-1 _~~

~~"cC 10 —2~~

~~o (0~~

~~10 -3~~

~~100 150 20~~

~~mpo (GeV)~~

~~Fig. 52: Statistical errors for the various channel rates of P° obtained with L = 0.3 fb"1. Curve notation: bb (solid); T+T~ (dashes); cc (dot-dash); gg (dot-dot-dash); rjfo* (dots).~~

In many models of SEWS there are narrow vector resonances of relatively low mass. For instance, in the BESS model [99] the existing precision experimental data do not put any practical constraint on the mass of the vectors, and for masses of the order of 250-350 GeV there are regions in the parameter space where the widths are rather small (T/M « 10~3). Since these resonances are produced copiously in the s-channel at lepton colliders, it is important to control the errors coming from the uncertainty on the energy spread, CTE- For instance, for ACTE/VE = 5%) and a mass of 350 GeV, at the NLC (with R at best of the order of 1%) in most of the parameter space the width cannot be measured with a precision better than 20%. The situation would be much better for a muon collider with R = 0.1% [67]. In the degenerate BESS model (D-BESS) [100], one has two triplets of almost degenerate resonances. This is a decoupling model and the limits from electroweak precision data are not very restrictive. The requirement of resolving the two types of states implies bounds on the parameter space. In the case of an NLC up to 350 GeV (again with R = 1%), it turns out to be impossible to separate the two resonances for any allowed value of the parameters, whereas this will be possible for a muon collider at the same energy, and R = 0.1%, as illustrated in Fig. 53.

~~78 oc (pb) (GeV) = 0.07 10000 3~~

~~oE(GeV) = 0.25 1000~~

~~100~~

~~E(GeV) 345 350 355 360 365 370~~

Fig. 53: Born cross-section (CTB = 0) for the production of the almost degenerate Li and R$ resonances of the D-BESS model with masses around 350 GeV, together with the convolution with a Gaussian distribution with energy spread given by

4.12 Z peak, top threshold and W threshold A. Blondel A muon collider running at the Z peak could make important contributions to electroweak precision measurements [101]. Prom a first and brief study, the following could be identified. The measurement of the hadronic to leptonic Z-widths ratio, R^, could lead to a unique precision in as of better than ±0.001. The high degree of accuracy in the beam-energy determination offered by spin precession of the muons would allow very accurate determination of the Z width. Finally, the possibility of longitudinal polarization for both beams, combined with high luminosity, would allow a measurement of ALR with very high precision and reliability, equivalent to a measurement of the weak mixing angle sin2 9^ with a precision of a few parts in 10~5. Ex- perimental difficulties could come from machine-related backgrounds which render delicate the measurement of luminosity and possibly high-precision tracking. High luminosity (100 million Z a year) and beam polarization would make this option highly worthwhile.

4-12.1 Beam polarization As mentioned earlier, muons from pion decay are naturally polarized, with a typical level of 28%. Some of this polarization is expectedly lost in the cooling and acceleration process, so that the muon polarization is anticipated to be at the level of 20%. The polarization can be improved by momentum selection of the muons at the expense of flux, as shown on the dashed curve in Fig. 54. One of the nice features of the muon colliders is that both beams are naturally polarized. If one manages to collide beams of longitudinal polarizations V^+, Vn-, the total cross-section becomes *(?V' Vvr ) = ffu(l - ?W + (?V - *V MLR), (53)

~~79 0.9 - -._~~

~~0.8 '- ''--^~~

~~0.7 '- •-... Peff~~

~~0.6 •••••---.....~~

~~0.5~~

~~0.4 '- --.. P~~

~~0.3 LF4 0.2~~

~~3 2 0.1 10 xAsin ef~~

~~n < T •?••• ""i ' f 1 r v" 0.1 0.2 0..3 0.o.4 . 0.o.5 a0,s6 (0.7 0.8 0.9 1 Luminosity loss factor~~

Fig. 54: Polarization predictions for the Z-factory muon collider. Dashed line labelled 'P': single-beam longitudinal + polarization estimate from Ref. [81]. Dash-dotted line labelled 'Peff': polarization of the n ft~ system for spins pointing in the same direction. Full line labelled 'L.Pgff': polarization figure of merit for polarization asymmetry measurement. Full line labelled Asin20^ff: resulting error on sin2 6^ for a total number of 100 million Z. Below this are the component of the error from event statistics (dashed) and from the polarization normalization (dotted).

~~where~~

~~(54) ' where we have introduced the effective polarization~~

~~(55)~~

The effective polarization is almost twice as large as the single-beam polarization, as shown in Fig. 54. This property allows useful levels of effective polarization to be obtained, even when single-beam polarization is low. The statistical error on ALR. is given by

~~(56)~~

so that the figure of merit for the measurement of the polarization asymmetry is the product CVett2- This quantity is shown in Fig. 54 and can be used to optimize the running strategy. A second nice feature of having two beams polarized is that the comparison between the sum of the cross-sections with opposite helicities and the unpolarized cross-section gives an

80 important cross-check on the beam polarization itself. (One could also compare with the cross- section for like-sign helicities). The quality of the cross-check can be expressed in an equivalent beam-polarization uncertainty by assuming that the polarizations of the two beams have the same absolute value V: 2 a(P,-V)+a(-V,P) = 2au(l + V )> (57) from which one obtains 1 + J>2 Aa ~1^— ' (58) where Aa/a represents the relative precision in the comparison of the polarized and unpolarized cross-sections. Because it is obtained from measured cross-sections, this cross-check applies to the polarization of interacting muons, avoiding difficulties related to the extrapolation from the full beam phase space — the polarization of which would be measured by the asymmetry in decay-electron energy — to the population of muons which is sampled by the other beam at the interaction point. A fraction of the statistics could be devoted to this cross-check. For an exposure yielding 100 million Z without optimization of the beam polarization, 10 million Z could be put aside for this, allowing a cross-check at a level of precision given by Aa/a ~ 3 x 10~4. The resulting error in AhR is AylLR = ALR(AT>efl/Ves)• 2 2 ff The resulting uncertainty on sin 0|f, Asin ^ = 1/7.9A^LR, is shown in Fig. 54, with the decomposition between the statistical error and that from the polarization measurement. With an exposure of one year an experimental error of better than Asin2 9^ ~ 0.4 x 10~4 should be reachable. All of the above assumes quite a bit of flexibility in the spin manipulation. Because of the smaller spin tune, muon spin polarization is much harder to modify at will than that of electrons — and that is already a hard problem! The amplification factor available for electrons in transverse fields is reduced for muons. This has been discussed in Ref. [102]. For spin tunes less than 1, i.e. for beam energies below 90 GeV, the simple-minded spin rotator would be a solenoid. Unfortunately, a spin rotation of 180 degrees for a beam energy of 45.6 GeV requires a solenoid of 477.5 T.m! It is very clear that spin manipulation in the muon collider has to be studied rather carefully and very early in time, so that it is included in the design of the accelerator. In Fig. 55 one can see a(n) (im)possible scenario of spin manipulation, that includes two 477.5 T.m solenoids. Performing spin manipulation at lower energies would probably be more economical. A possible solution would be to foresee that one of the two muon beams undergoes one (or several) turn(s) of a small circular ring along the acceleration path. To give an example, a ring at the energy of 22.6556 GeV would generate a quarter turn of spin. The presence of such a rotation for one of the two signs along the acceleration path would effectively lead to the same effect as the two solenoids displayed in Fig. 55, leading to the configuration of spins displayed in Fig. 56. Whether one of the rings in the acceleration chains can be used for this purpose would need to be studied. One of the best surprises of this study was the realization that spin tune at the Z pole for muons is very close to 0.5. In fact the centre-of-mass energy for which spin tune is exactly 0.5 is 90.6223 GeV, an energy for which the cross-section is more than 80% of that at the maximum. For this energy, if the first collision occurs for a particular configuration of helicities, the configuration will be exactly opposite for the next turn, as shown in Fig. 55. This automat- ically provides the two spin configurations necessary for the measurement of the polarization asymmetry: one on odd turns, the other on even turns. Magic!

~~81 First turn Second turn~~

Fig. 55: A(n) (im)possible scheme assuring longitudinal polarization at the interaction point in a muon collider at a spin tune v = 0.5. This involves two solenoids of 477.5 T.m. The beam lines of the fiT and /J,+ beams have been shown separately. They should be superimposed, so that the two beams collide at the interaction point.

~~First turn~~

Fig. 56: Another scheme assuring longitudinal polarization at the interaction point in a muon collider at a spin tune v — 0.5. This assumes that the polarization of one of the muon beams has been tilted with respect to that of the other beam by an angle of 45° at an earlier stage, for instance by one additional turn in an element of the accelerating chain at 22.6556 GeV. The beam lines of the /x~ and /x+ beams have been shown separately. They should be superimposed, so that the two beams collide at the interaction point.

4.12.2 W and top threshold For broad resonances or pair-production thresholds for which the coupling to muons is not different from that of electrons, the structure that appears in e+e~ or ^+/i~~ collisions is not very different. The advantages of muon colliders in terms of energy calibration and centre-of-mass definition have then to be weighed in view of the luminosity available, although the situation might be helped by the fact that energy spread is not crucial for these broad structures. This is the case for the W-pair threshold. This allows a measurement of the W mass as has been performed by the LEP experiments [103, 104, 105, 106]. The best of them [106] obtained a precision of 330 MeV on the W mass for an exposure of 11 pb"1. Therefore 11 fb-1 would be

82 needed to achieve a precision of 10 MeV. An e+e collider could possibly provide this luminosity, but the energy calibration would possibly be more problematic. The energy calibration for a dedicated /x+/x~ ring at this particular energy would be easy, but then the required luminosity seems harder to get. Before initiating these experiments, it would probably be wise to see what the precision would be in the combination of the final LEP/Tevatron and LHC measurements, which are all expected to reach precisions in the vicinity of 20 MeV. The top threshold studies would lead to conclusions that are more in favour of the muon collider, as studied in Ref. [107] and displayed in Fig. 57. The variation of the top-pair cross- section near threshold depends on the top mass with a derivative of da/dE\ieam = da/dmtop — 0.4 pb/GeV. With an exposure of 10 fb"1, this would lead to an equivalent experimental precision of 15 MeV in the top-quark mass. Of course this has to be contrasted with the fundamental difficulties involved with the interpretation of quark masses. Nevertheless, the muon collider with its sharp energy resolution and definition would open possibilities that would probably be blurred at e+e~ colliders, where the slope is degraded by roughly a factor four by beamstrahlung. This means that 16 times more luminosity is required for the same precision at an e+e~ collider, and the threshold is shifted by about 1-2% of the centre-of-mass energy (i.e. 3-7 GeV). This shift will be very difficult to determine to within < 1%.

~~0.8~~

~~ee: R= 1% 0.6 -~~

~~180 GeV~~

~~0.4 •a I/\SK + Beam~~

~~0.2 ^/lSRJf only~~

~~- 0.0 345 355 365~~

Fig. 57: The top threshold at a muon collider vs an e+e collider. The energy spread of the muon collider is assumed to be 0.1%. The effect of beamstrahlung in the case of the e+e~ collider is assumed to be equivalent to 1%, and to be known and corrected for. Otherwise it would shift the curve by several GeV to the right.

4-12.3 Summary of precision improvement on electroweak observables The improvement in precision on the major electroweak observables is summarized in Ta- ble 4.12.3, and compared with their sensitivity to the physics output. Of course a global improvement of the tests by a factor of typically 5 would have to be backed up by improved calculations at the same degree of precision. A step in this direction has recently been taken by the new calculation of higher orders [108]. In addition, the top-quark mass should by then be known with a precision of 1-2 GeV, allowing the corresponding uncertainties to match the precision that could be obtained at a Z factory. Finally, the (important) error in the calculation of ot(M%) from the e+e~ —* hadrons cross-sections has recently been reduced by use of the QCD prediction with the appropriate systematic error in the energy regions where it is more precise and reliable than existing data [108].

83 Table 16: Summary of the present experimental errors, physics sensitivity and theoretical uncertainties in Standard Model predictions for the main electroweak observables measurable at a muon-collider Z factory. The value of ^M^)'1 is from the new evaluation by Davier and Hocker [109]. The Standard Model value is for m^ = 300 GeV. (*)The W-mass precision given here is what is expected from Tevatron run II, for comparison.

~~Sensitivity to: Winter'98 Possible~~

~~00 Observable value SM mt(GeV) mh(GeV) as a(Mf) ! (mb) Higher accuracy~~

~~(error) 174 ±5 60 1000 ±0.003 128.923(36) 4.7 ±0.3 orders Z factory~~

rz(MeV) 2494.8(2.5) 2493.3 +1.2 +4.2 -5.3 1.7 0.3 0.2 0.6 0.4 T^MeV) 83.91(0.10) 83.93 +0.05 +0.11 -0.14 0.02 - - 0.02 0.03 Rt x 103 20775(27) 20732 -1.5 +15 -13 21 1.5 2 5 6 sin2 Of x 104 2314.9(2.1) 2320.6 -1.6 -8.5 +6.9 0.05 0.9 - 1 0.4 4 Rh x 10 2171(9) 2158 -1.6 -0.4 0 0.05 0.1 0.8 1 5 Mw(MeV) 80375(65) 80314 +31 +103 -97 1 6 - 7 20(*) 4.13 Conclusions A. Blondel A number of distinctive features of the muon colliders at intermediate energies, generically from the Z peak to the higher-mass Higgs states of supersymmetry, have been highlighted. The physics case for lepton colliders in this energy range will depend largely on the findings of the LHC, and the muon collider is no exception to this comment. The first muon colliders would bring in many cases information that is not obtainable otherwise, thanks to their specific features of outstanding energy resolution and calibration. In addition, the coupling to the Higgs would make them unique in studying the Higgs particles' spectrum and couplings, if these particles exist. The studies of thresholds would benefit from the energy resolution and calibration as well, with exact benefits that depend on the particular case envisaged. It can be said that, if Nature is supersymmetric, the precision muon colliders would open a new realm of precision tests of the MSSM. For these reasons, we believe, given that these machines are relatively small and fit nicely with the previously-discussed step 1 (neutrino beams), that their study should proceed actively.

NEXT PAGE(S) I left BLANK 5 STEP 3: HIGH-ENERGY FRONTIER 5.1 Introduction J. Ellis The ultimate motivation for a muon-collider complex, at least at CERN, may be the prospect it offers for exploring the high-energy frontier of particle physics in the multi-TeV range in the period after the LHC [15]. This section of the prospective study focuses on the physics interest of a multi-TeV /u+/x~ collider, primarily on a 4-TeV machine but also with some discussion of a lower-energy machine. These require some advances in accelerator studies beyond those discussed in the previous sections of this report, which are not discussed here. The greatest challenge for a /i+M~ collider at the high-energy frontier may be the neutrino-induced radiation hazard, which is the subject of a separate section of this report. The LHC will be the first machine to probe the energy range up to 1 TeV. For example, it is capable of producing and detecting any Higgs boson weighing & 1 TeV, which is the range favoured by present precision electroweak data [110]. The LHC is also capable of producing new strongly-interacting particles weighing even more than 1 TeV. For example, it can produce and detect squarks and gluinos weighing up to about 2 TeV [111]. However, the LHC has a physics reach limited to only a few hundred GeV for new electroweakly-interacting particles such as charginos and sleptons. We assume that more detailed measurements of new physics in the TeV range will be + made using a linear e e~ collider with Ecm ~ 1 TeV. In addition to Higgs measurements, such a machine should nicely complement [112] the pioneering spectroscopic measurements possible with the LHC [113]. However, complete coverage of electroweakly-interacting particles weighing up to 1 TeV would only be possible with a lepton-lepton collider with Ecm ^ 2 TeV. It remains to be seen whether the LHC will be followed by a higher-energy hadron- hadron collider with ECTn ~ 50 to 100 TeV [15]. Any such machine would presumably require a reduction in the cost per TeV by about an order of magnitude relative to the LHC. Moreover, the luminosity would need to be ^ 1035 cm~2s-1 in order to reap full benefit from a significantly higher Ecm <; 50 TeV, bringing with it new radiation and detector challenges. Also, the political challenge of a machine with a much larger circumference than the LHC might be severe. Since lepton-lepton colliders give access to physics comparable to that of hadron-hadron colliders with Ecm an order of magnitude higher, a multi-TeV lepton-lepton collider becomes an attractive option for exploring the multi-TeV energy range. The natural enemy of such a high-energy lepton-lepton collider is synchrotron radiation, and there are two strategies for combatting it. One is to make a linear collider with electrons, and the other is to make a circular collider with muons. Many technological problems of a multi-TeV e+e~ linear collider are now understood, and CLIC [30] should be regarded as the default option for CERN's future after the LHC. Other sections of this report address technological challenges of fj,+(i~ colliders. The neutrino-induced radiation hazard appears likely to limit severely their Ecm, and is among the topics meriting further study. Although many of the physics goals are common to e+e~ and /x+/x~ colliders, each has some distinctive features that may provide special advantages. In particular, e+e~ colliders offer the options of controllable beam polarization, e±7,77 and e~e~ collisions, all of which offer novel physics analysis tools. On the other hand, fx+fi+ colliders offer the possibility of exploiting flavour non-universal couplings, for example in Higgs physics and in .R-violating supersymmetry, as well as a reduced spread in the Ecm, which can be calibrated very precisely. In this section of the prospective study, we review some of the new physics opportunities opened up by a muon collider at the high-energy frontier, stressing the unique features of flavour non-universality and Ecm precision.

87 Beyond the Higgs studies reviewed in the precision muon collider section of this study, there may be heavier Higgs bosons to explore, such as the H, A of the MSSM. The flavour non-universality and precise Ecm of a muon collider may be needed to study them, including their couplings to super symmetric particles and the possibility of CP violation. Any R- violating supersymmetric couplings are also thought likely to be flavour non-universal, making e+e~ and fj,+/j,~ colliders complementary. One of the intriguing possibilities is the production of a direct- channel sneutrino resonance via p^\i~ —> i>, where the small spread in Ecm may also come into play. In general, this small energy spread will be useful in threshold measurements, for example in the production of sparticle pairs such as charginos: fJ,+p~ —• X+X~ • The small energy spread would also help in the analysis of narrow resonances, as occur in some models of strongly-interacting Higgs sectors and models in which a new space-time dimension opens up at the TeV scale. These physics opportunities are described in more detail in subsequent subsections, and we conclude this section with some general remarks.

5.2 Heavy supersymmetric Higgs bosons 5. Kraml, A. Bartl, H. Eberl, W. Majerotto and W. Porod Detailed aspects of the physics of the heavy supersymmetric Higgs bosons H, A are discussed in the precision muon collider section of this report, assuming that their masses are less than 1 TeV. Similar considerations apply if their masses are above 1 TeV, placing them in the energy range considered in this part of the report. We note that the mass degeneracy between the H, A would be greater in this case. We recall that the important H, A physics topics that could be studied include direct-channel resonance production, decays into sfermions and charginos, and CP violation. These topics all rely in an essential way on the flavour non-universality of the H, A couplings and on the finer energy resolution of the fi+fj,~ collider, as compared to an e+e~ collider with similar centre-of-mass energy. As described in more detail in the precision muon collider section of this report, a high- energy muon collider would also be an excellent instrument to measure the masses and couplings of heavier MSSM Higgs bosons H, A, and thereby to determine the MSSM parameters with great accuracy.

5.3 R-violating supersymmetry S. Lola and S. Raychaudhuri To date, the main working tool for supersymmetry searches has been the MSSM. However, the most general SU(3)C x SU(2)L X U(l)y invariant superpotential with the minimal field content also contains the terms

W = XijkULjEk + X^LiQjDk + A^t^Ac , (59) where L(Q) are the left-handed lepton (quark) superfields and E, D, and U are the corresponding right-handed fields. If both lepton- and baryon-number violating operators were present at the same time in the low-energy Lagrangian, they would lead to unacceptably fast proton decay. To avoid this, a symmetry that forbids these terms, R parity [114], has been invoked. However, it has been shown that there exist symmetries which allow the violation of only a subset of these operators [115]. Such models result in a very rich phenomenology [116]: single superparticle production is allowed and, for couplings >10~6, the lightest supersymmetric particle decays inside the detector. In both cases, the standard missing-energy signature is supplanted by multilepton and/or multijet events. There are three basic categories of new signals: • Production of sparticle pairs and their subsequent decays via i?-violating operators. Such processes are favoured for small /^-violating couplings. However, since the production cross-sections are the standard ones, we will not discuss this possibility further. • For reasonably large i?-violating couplings, one may have single-sparticle production. In this case, the mass reach can be considerably larger than for MSSM processes at the same machine. • Virtual effects from sparticle exchanges provide the optimal signals for a very heavy- sparticle spectrum. For heavy chargino and neutralino masses, the dominant signals at a /J.+fi~ collider arise from sparticle-exchange processes of the type H+li- -> ff , (60) which have been studied in Refs. [117, 118]. In this case, the best signals arise from resonant s-channel processes, similar to the case of e+e~ colliders [119]. For a collider operating in the 13 /J,+/J,~ mode, the only couplings that involve two muons are L1L2E2 and Z^-ks-E^ - The bounds for these couplings appear in Table 17 [120] and scale proportionally to the superparticle masses. For a heavy sparticle spectrum, therefore, the couplings can be quite large. On the other hand, ^-channel exchanges may proceed via all nine LiQjDh operators, as well as the seven L^LjE^ that involve a muon flavour. The bounds on the LQD operators are between 0.09 (0.9) and 0.39 (3.5) for 100 GeV (1 TeV) sparticle masses, whilst the bounds on the LLE couplings are in the range 0.05-0.06 (0.5-0.6).

~~Table 17: Upper limits on couplings for m = 100 (1000) GeV.~~

~~ijk Xjjf. Sources 122 0.05 (0.5) charged-current universality 232 0.06 (0.6) T(r -> ei/P)/T(T~~

The discovery limits for the relevant LLE couplings from the process /x+/x —> /x+/i appear in Fig. 58a [118]. The authors adopt the energy and luminosity parameters given by the Accelerator Physics Study Group at the Fermilab Workshop on the First Muon Collider (FMC), which are y/s = 350, 500 GeV, £ = 10 ftf1, denoted by FMC-350 and FMC-500, respectively. For the high-energy muon collider, denoted here by NMC, these parameters are y/s = 2, 4 TeV, C = 103 fb~\ denoted by NMC-2 and NMC-4, respectively. The sharp dips in the contours correspond to the resonance production of a sneutrino that subsequently decays into /i+/i~ through the same coupling. Figures 58b and 58c describe the non-resonant process fi+n~ —> e+e~. As we can see from the figures, the discovery limits for the relevant couplings are significantly improved at the muon collider. On the other hand, for sparticle spectra accessible at the muon collider, one may also have the following processes:

~~/x+/i~ -H which are similar to reactions that have been studied in the past for e+e~ colliders [121].~~

~~13Remember that, because of SU(2) invariance, the two lepton doublets cannot have the same flavour.~~

~~89 0.01 1 10 0.1 1 10 0.1 10 M_(TeV) M_(TeV) M _(TeV)~~

Fig. 58: Illustrations of the reach at a muon collider in the R-violating coupling XLLE when (a) the differential cross-section for a ii+n~ final state is considered, (b) the differential cross-section for an e+e~ final state is considered, and (c) the total cross-sections for an e+e~ final state are considered. The part of the parameter space above the curves can be excluded at 95% C.L. The oblique straight lines correspond to low-energy bounds on the relevant couplings. The sneutrino width is taken to be 200 MeV, thus it is assumed that the /^-violating decays of the sneutrinos dominate.

Let us focus on resonant single chargino and neutralino production. Whether these processes dominate over di-fermion production depends on (i) the point in supersymmetric parameter space and (ii) the strength of A, as indicated in Table 18. For lower values of M2, a larger number of charginos and neutralinos can be produced in the final state, whilst the phase-space suppressions for the production of the lightest states are small. The situation changes as we pass to larger M2, and this is indicated in the decrease of the width. Depending on the parameters, we have regions where chargino, neutralino or direct fermion production dominates.

~~Table 18: Widths for u decays to charginos, neutralinos and pairs of fermions for sample MSSM parameter values.~~

Here we assume tan/3 = 2, A = 0.1 and 0.4 and m5 = 3000 GeV. p p2 1 1 M2(GeV) /x(GeV) 1 neutr. J- charg. fiviol. Rviol. 1000 -3000 13.604 20.024 0.597 9.549 1000 -1500 13.596 20.024 0.597 9.549 1000 1500 13.603 20.033 0.597 9.549 1000 3000 13.618 20.044 0.597 9.549 2000 -3000 6.910 7.819 0.597 9.549 2000 -1500 6.905 7.824 0.597 9.549 2000 1500 6.920 7.843 0.597 9.549 2000 3000 6.939 7.858 0.597 9.549 3000 -3000 2.136 0.003 0.597 9.549 3000 -1500 2.137 0.016 0.597 9.549 3000 1500 2.159 0.045 0.597 9.549 3000 3000 2.164 0.032 0.597 9.549

~~Once a chargino or a neutralino is produced, it will subsequently decay to an i?-even final state involving several charged leptons with the possibility of explicit ALj ^ 0:~~

~~X (62)~~

~~90 Concerning the chargino decays, we would like to stress that there exist two possibilities. The first is the well-known cascade decay via the lightest neutralino:~~

xr^X? + (W-)*^X? + ff', (63) where ff' are the decay fermions of the (virtual) W boson. However, there exists an alternative possibility. The chargino can decay directly via the operator L^LjE^ (with j being e or r):

xr-*(/i"M+^7'I/MI/i/i")- (64) In this latter case, one of the signals is even more distinct, since in total it involves four leptons in the final state without any missing energy. This is to be contrasted with the cascade decay, which always involves neutrinos in the final state. Which of the two processes will appear depends again on (i) the strength of the R-violating operator (the stronger the operator the larger the decay rate for direct decay of the chargino), and (ii) the relative masses of the chargino and neutralino (if the mass gap between the two states is very small, then the cascade decay is suppressed by phase space). Of course, if many charginos and neutralinos are produced, the cascade decays of the system can be very complicated. In any case, however, exotic signals with explicit ALi ^ 0 can be expected to arise. We conclude that in all the cases that have been studied, there are clear signals for R violation at the proposed signals at the muon collider. Moreover, the .R-violating couplings accessible to such a machine are different from those accessible to an e+e~ collider. We also note that L2QD couplings can also be directly tested by operating the collider in the yup mode.

5.4 .R-violating contributions to tt production S. Raychaudhuri We discuss here the effect on the tt cross-section of .R-violating couplings in supersymmetric models at a high-energy muon collider running at a centre-of-mass energy y/s = 3 TeV. The top quarks undergo three-body decays, and we do not consider here the possibility that the kinematic distributions will tell us much about new physics contributions to the cross-section, but concentrate on the total cross-section. This involves the assumption that the total cross- section can be measured from observables, which is easily done if the top quarks decay only through Standard Model channels. In R-violating supersymmetry, this is mostly the case if the sfermions are heavier than the top quark, and, of course, if the same holds true for all the gauginos. In what follows, we shall freely make this assumption, chiefly because a high-energy muon collider should be thought of as a probe of new physics at a scale of a TeV or more. The present discussions will be relevant, therefore, only if no signs of new physics — or, at least, of supersymmetry — are discovered in the mass range between the limit of present-day experiments (about 350 GeV) and about 1-1.5 TeV. The relevant couplings of the top quark in .R-violating supersymmetry are given by the superpotential W = KikLiQjDk , . (65) where Li and Qj are lepton and quark doublet superfields (containing left-handed fermions), while Dk is a quark singlet superfield (containing a right-handed fermion). On expansion, the relevant terms in the interaction Lagrangian are

Ant = A'23fc p.tdRk + H.c. , (66) which leads to a coupling between muons, top quarks and d-type squarks of flavour k. Obviously, for the process fi+n~ —> tt, this leads to a i-channel squark exchange. The other Standard Model diagrams which contribute to tt production involve 91 • s-channel exchange of photons; • s-channel exchange of Z-bosons; • s-channel exchange of neutral scalars h, H and A, with possible resonances in H and A. These are rendered viable when compared to the case of an e+e~ machine by the fact that the Yukawa couplings of the muon to the scalars are much larger than those to electrons. All the Standard Model contributions involve s-channel particle exchanges, which means that the higher the collision energy, the greater the suppression of the relevant amplitudes. Of course, if the machine energy happens — by design or accident — to be around a heavy scalar resonance, the story is a different one: the resonance (likely to be a narrow one) will dominate the cross-section. However, unless this actually happens, the effects of scalar exchange are small and, for all practical purposes, can be neglected. The cross-section is then the same as it would have been at an e+e~ collider of comparable energy. For a 3 TeV muon collider, it is unlikely that there will be resonances in the scalar propagators, since scalar masses as high as 3 TeV are disallowed on the grounds of perturbative unitarity. Hence, the effect of scalar exchanges on the tt production cross-section would be minimal. Paradoxically, at a high-energy muon collider, it is the smallness of the Standard Model cross-section for tt production which proves to be of great help in the isolation of any R-violating effects. Since the excess contribution comes from a i-channel process, it will not be suppressed by the propagator. Thus, the relative contribution of an R-violating diagram would be enhanced compared to what might happen in, say, a 500 GeV linear e+e~ collider. Formulae for the Standard Model production of tt pairs are readily available in the literature. To these, we add the contributions due to Higgs resonances and the excess contribution due to the i?-violating coupling. These details have been omitted for the sake of brevity. The cross-sections have been incorporated into a simple parton-level Monte Carlo event generator which gives crude, but illustrative results for the relevant cross-sections. As already mentioned, we do not study here the kinematic distributions of the decay products of the top quarks, but concentrate on the total cross-section. Unless, indeed, the distributions due to the excess contribution are very sharply peaked14, the detection efficiency of both Standard Model and excess contributions should be comparable. Hence, if we take ratios, the efficiency should cancel out of the final result. This means that even a parton-level simulation of the process could yield fairly good results. Similar arguments hold in the case of radiative corrections. These have not been incorporated in this analysis, but again, one should expect the bulk of these effects to cancel out of the final result. This is obtained using

~~I A/total _ j\[SM\ SNtl = '"* "« ' , (67)~~

where, generically, iVtt = Lati, L being the integrated luminosity, for which we assume (rather conservatively) the value L = 10 fb""1. We see, therefore, that factors due to efficiency and radiative corrections do not quite cancel, but their effects are weakened nevertheless. In Fig. 59, we present 2a, 5a and 10

~~14This can happen for low values of squark mass, but should not happen for squark masses in the range 1-5 TeV, which we assume.~~

~~92 the values of squark mass in Fig. 59 may be safely ignored. It is hardly necessary to state that with higher integrated luminosity, the discovery limits could be increased quite significantly.~~

~~Fig. 59: Discovery limits at the 2a, 5cr and 10c levels for .R-violating contributions to the tt cross-section.~~

To conclude, therefore, we have shown that the tt cross-section could be a sensitive probe of the i?-violating couplings X'2Zk at a high-energy muon collider. It would be unreasonable to claim this as justification for building such a machine, but it does show, once again, that the range of new physics that can be scanned by a high-energy muon collider is rather promising.

5.5 Threshold studies: the case of supersymmetric particles M. Beneke, M. Kramer and S. Lola The reduction in initial-state radiation and beamstrahlung at a \x+pT collider, as compared to an e+e~ collider, together with the possibility of rapid and accurate beam-energy calibration using muon-spin precession and decay, provide novel physics opportunities for accurate measurements at a new-particle threshold. Here we discuss supersymmetric thresholds to exemplify these possibilities. Supersymmetric particle masses are functions of the fundamental parameters of a given supersymmetric model. Their precise knowledge allows us to perform precision tests of supersymmetric models, and to check hypotheses such as gaugino-mass unification in detail. A /i+/i~ collider is particularly well suited for this purpose, because one can take advantage of reduced initial-state radiation and beamstrahlung, and a small beam-energy spread, to exploit the sensitivity of the cross-section to the particle mass near the production threshold. This advantage applies to both a precision muon collider and to a high-energy muon collider. For the sake of illustration, we consider a scenario in which the supersymmetric spectrum is heavy. To illustrate the impact of initial radiation and various beam-energy spreads, the effect of the electromagnetic Coulomb attraction, and of a small but non-vanishing decay width, we have considered pair production of the lightest chargino state with a mass of 1001.28 GeV. The result is shown in Fig. 60. Near threshold, the parametric dependence of the cross-section factorizes schematically as follows:

a ~ normalization (M2, fi, tan(3, m^) x profile (\/s; mXl, F[SUSY param.]). (68) This implies that the threshold cross-section depends on the parameters of the supersymmetric model only through three quantities: the chargino mass, an overall energy-independent normalization, and the chargino width.

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~~'.'/"" '• 0.25 0.5 - .....-•••" ' ^- BS(l£/E-0.003X), ISR~~

~~—v '•" . I ... I . . I . . . I . , , I , . , " A 2002.4 2004 2002.6 2002.7 •Ss (GeVl /G IGeV]~~

Fig. 60: Chargino production cross-section near threshold. The second figure is a zoom-in on the extreme threshold region of the first figure. We denote by ISR initial-state radiation and by BS the (Gaussian) beam-energy spread. Beamstrahlung is not included.

The threshold profile depends on the chargino mass and its width. In order to display the gain due to the excellent energy resolution, we have chosen a point in the super symmetric parameter space where the chargino decays only to the lightest neutralino and the decay into an on-shell W is strongly phase-space suppressed. In this case the width is small: FX1 = 4.7 MeV, 6 or rxi/mXl ~ 5 x 10~ . If the chargino width is small enough, the charginos live long enough to form Xi^Xf bound states completely analogous to positronium. Their binding energy is of order m a 5 E/ xi ~ em/4 ~ 10~ - If TXl/mXl is not much larger, a resonance-like structure emerges in the threshold region. Its experimental detection would, however, require an energy resolution AE/E below 1(T5. In the figures, we show the threshold cross-section before application of initial-state radiation (ISR) and beam-energy spread (BS) (solid lines) and after including both effects. For the BS, we chose a conservative value, 0.15%, and a more optimistic value, 0.003%. Although even the smaller BS is not sufficient to resolve the resonance peak, the improvement in the sensitivity to the chargino mass, as evidenced by the slope of the cross-section in the threshold region, is clearly seen as the BS decreases. For comparison, we show in the first figure the cross-section as it would be measured at an e+e~ collider with a projected beam-energy spread of 0.5%. Relative to the e+e~ collider curve, the slope of the cross-section in the threshold region increases by a factor of 3 for a muon collider with AE/E = 0.158%. For small AE/E = 00.003% one gains another factor of about 8. These factors translate into corresponding gains in the precision of the mass measurement. A fi+fJ,~~ collider could be used to map out a large part of the supersymmetric particle spectrum. Squark production would be particularly interesting, because squarks are produced in a P-wave state. This leads to a slower rise of the cross-section near threshold, with a loss of precision in the mass measurement as a consequence. On the other hand, if the squark is sufficiently short-lived for resonances to exist, their spectrum is determined by the strong 3 coupling and hence £/msquark ~ 10~ , a value large enough to be resolved relatively easily with a H+H~ collider.

94 5.6 Implications of precision measurements G.F. Giudice, R. Rattazzi and A. Strumia An important task of a future muon collider will be to make detailed measurements of possible new particles discovered at the LHC. This experimental programme can be very rich with new information on the fundamental underlying theory. In this respect, we can draw a close analogy with the essential role played by LEP in investigating the Standard Model, after the discovery of the gauge bosons W and Z, and the top quark. The muon collider offers an excellent environment to perform such studies, because of the small initial-state radiation, the high attainable beam-energy resolution, and the flexibility in the choice of the centre-of-mass energy. As discussed in the previous subsection, it is indeed possible to reach a precision of more than 0.01% in the measurements of new particle masses. Such precise measurements can give us very important physics information, as we will illustrate here in the case of supersymmetric theories. Supersymmetric theories provide a well-motivated extension of the Standard Model and introduce many new particles with masses below the TeV region. The new-particle masses cannot be uniquely predicted because of the present ignorance of the fundamental supersymmetry- breaking mechanism. There are two broad classes of models where certain mass predictions can be made: theories with gravity-mediated supersymmetry breaking embedded in GUTs, or theories with gauge mediation. Recent theoretical developments have allowed us to compute the mass spectrum within a few per cent, as a function of the unknown parameters of each class of models. Only measurements with comparable precision can conclusively distinguish various models and guide us towards the fundamental theory of elementary-particle interactions. As an illustrative example, let us consider the correlations between different supersymmetric particle masses. In Fig. 61 from Ref. [122], we show the predictions for the gluino-squark and weak gaugino-slepton mass ratios, for different choices of the fundamental parameters of the theory. In the case of gauge mediation, these mass ratios depend on two free parameters: the value of the messenger mass scale (which is chosen to vary between 100 TeV and 1015 GeV) and the messenger index 77 (varied between 1/3 and 3). In the case of gravity mediation we assume SU(5) GUT relations and vary the ratio of gaugino and squark masses at the unification scale. As is apparent from Fig. 61, combined measurements of different supersymmetric particle masses can determine the fundamental parameters and discriminate between the two scenarios. Precise measurements of particle-production cross-sections can also give us indirect evidence of new heavy particles, through their effects in radiative corrections. We are very familiar with this phenomenon in the case of LEP, and we give here a important example in the context of supersymmetric theory, valid for the muOn collider. Suppose that one part of the supersymmetric particles is too heavy to be directly produced at a collider experiment, while the other part is below the production threshold. This situation is not unusual in supersymmetric models where the new coloured particles receive large QCD contributions to their masses. At the relevant collider energies, we can consider an effective theory where the heavy particles are integrated out. In this theory, supersymmetry is broken explicitly. Therefore, the equality between the couplings of the fermion-fermion-gauge-boson vertex and the fermion-scalar-gaugino vertex, which is only guaranteed by supersymmetry, is now violated. The experimental comparison between the gauge boson and gaugino production cross-sections can isolate this non-decoupling effect caused by the heavy supersymmetric particles. In particular, the slepton production cross-section receives corrections of the order of

~~11231 ACT; ~ 4% In — , (69) 1 m v~~

95 where M and m are the heavy and light supersymmetric masses, respectively. An experiment sensitive to such corrections can give indirect evidence for the existence of particles too heavy to be directly produced.

~~1.4 I .? HX)TeV - -O - Gauge-mediated models 1.2- Unified super-gravity Non-minimal GUT model GeV 1 -~~

~~•2 0.8 -~~

~~0.6-~~

~~0.4-~~

~~0.2 T 0.4 0.6 0.8 1.2~~

~~mass ratio M3//~~

Fig. 61: Correlations between gluino/squark and wino/slepton masses (Ms/mj^, M2/ML, as predicted by unified supergravity (continuous line) and gauge-mediated models (dashed lines) for different values of the messenger scale and of the messenger index r\. We have employed a${M-i) — 0.118. The supergravity and gauge-mediation predictions with MM = 1015 GeV are also shown for as(Mz) = 0.125 (lower lines). In the shaded area it is possible to observe the clean signature of LSP decay. The dotted line refers to a non-minimal unification model.

5.7 Strongly-interacting Higgs sector R. Casalbuoni, A. Deandrea, S. De Curtis, D. Dominici, R. Gatto and J.F. Gunion Models of dynamical symmetry breaking of electroweak interactions [97] rely on general features such as the existence of strong interactions at the TeV scale implying, as the energy increases, an enhancement of the WW scattering amplitudes (to be referred to as continuum in the following) and the presence of resonances at the strong scale. This physics is pretty much the same at e+e~ and ^+/x~ colliders, except that n+(J,~ colliders may allow for higher energy and better energy resolution. In particular, a fi+(J<~ collider with y/s « 2-4 TeV would allow us to explore the full spectrum of the resonances of the strong electroweak symmetry breaking (SEWS) models. Generally speaking, there are two ways of exploring this physics: one is through fusion processes, that is WW scattering, and the other through annihilation at lepton colliders, or Drell-Yan type processes at hadron colliders [124]. The fusion channel is particularly convenient for the study of the continuum and of the scalar resonances, while vector resonances are far better seen in the annihilation channel. The continuum and scalar resonance production have been studied at the LHC [125], at an e+e~ collider with y/s = 1.5 TeV and integrated luminosity L = 200 fb"1 [126], and at a M+M~ collider with y/s = 4 TeV and with the same integrated luminosity [127]. The main results are that at the LHC the scalar resonances would be visible in the ZZ and in the W+W~ channels, whereas the continuum should be detectable in the double-charged channels W±W±. At an e+e~ collider the situation will be similar, but with a much better signal/background ratio. In particular, 1 TeV scalars will be visible in the ZZ and in the WW channels, whereas the continuum will be detectable through ZZ. This pattern allows a probe of the SEWS dynamics. At the ^'\T collider the situation will be pretty much the same, except for a very high statistical significance in all channels, see Fig. 62. This allows us to discriminate among the various models by isolating the polarization components TT, TL and LL of the cross-section.

96 As far as the vector resonances are concerned (as described, for instance, by the BESS model [99]), the fusion channel becomes important only for masses around 2 TeV. However, the unitarity requirement from WW scattering puts a bound of about 2-2.5 TeV on the vector resonance masses [128]. At lower masses the production is largely dominated by the Drell-Yan or annihilation processes. It turns out that vector resonances of the techni-p type are detectable at the LHC up to masses of order 1.5 TeV [129]. At lepton colliders fusion and annihilation processes can be discriminated, but vector resonances are better detected from the annihilation. As an example consider the vector resonance with My = 2 TeV with a width of 0.2 TeV, shown in Fig. 62. The statistical significance of its production in /i+/i~ —* i>u~W+W~ is about 36, whereas the statistical significance evaluated at the peak for /i+/i~ —> V —> W+W~ is about 400 (the peak cross-section is roughly 500 fb).

~~o o • • • • 1 • • • • i 2 _ CVJ 10 u -» ZZ X (b)-l \ = 1 TeV > 10 1 _ ^^ TeV TH =*= s. 10'0 _ X Total Bckgn TJ 10 -1 .... i . . . . i 0.5 1 1.5 2 2.5 Mzz (TeV)~~

~~Fig. 62: Number of events in the fusion processes for a collider with -/s = 4 TeV and L = 200 fb * versus Mvv for SEWS models from Ref. [127].~~

The annihilation processes are distributed among the final states, WW and ff. In most of the SEWS models, heavy vector resonances have WW as the main decay mode. Correspondingly, in most of the parameter space, heavy vector resonances are relatively wide. However there are regions where the ratio F/My is of the order of 10 ~3. For vector resonances with masses up to 2-2.5 TeV the physics potentials of e+e~ and /x+/x~ colliders at the same energy and luminosity are equal, except for the case of narrow widths. In fact, when the width is of the order of the energy spread of the beam, the parameters of the resonance cannot be measured with good precision [67]. Specifically, the energy spread CTE is related to the beam energy E by the relation aE = 0.007 R(%) E(GeV), where R is the energy resolution of the collider. The typical R value for an e+e~ collider is bigger than 1%, whereas for a (J,+fi~ collider at high energy it is about

97 0.1% or better. An example of a narrow resonance with My = 1 TeV, as seen at an e+e collider and at the ji+'\i~ collider by convoluting the Born cross-section with a Gaussian of width <7E, is given in Fig. 63.

~~OTOT(WW) pb 990 1000 1010 40 • • | i 40 • Mv(GeV) = 1000 • HGeV) = 3 30 - R = 0 - 30 Pr R = 0.1% 20 - n - 20 R=l% / \ 10 - - 10~~

~~/:Bckgnd ^~~

~~l 990 1000 1010 Ecm(GeV)~~

Fig. 63: Total cross-section £+£ —> V —» WW obtained by convoluting the Born cross-section with a Gaussian with spread erg. Also we show the Born cross-section (R = 0), and the background from the Standard Model.

In the degenerate BESS model [100], the main decay modes are into ff, and thus the widths are generally small. Degenerate BESS is a model which has decoupling, and for this reason the existing precision data do not put stringent limits on its parameter space. The model has two almost degenerate spin-1 isotriplets. The smallness of the widths and the almost degeneracy of the resonances makes the /^+/x~ collider the ideal machine for accurate tests, which would be very hard at an e+e~ collider [67]. Just to exemplify this point, in the model it is possible to have two vectors of masses around 2 TeV separated by 14 GeV with widths of 1.4 GeV and 0.2 GeV, respectively. The energy spread at the NLC would be about 14 GeV, making impossible to separate the two resonances, whereas at the /i+//~ collider, with an energy resolution R = 0.1% one could easily see the two-peak structure (though in order to measure with reasonable accuracy the widths one should lower the energy resolution at the expense of the luminosity). This will not be a problem since the peak cross-sections are of the order of tens of pb's. In conclusion, one can hope to see spin-1 resonances at the LHC for masses up to 1.5 TeV, + or at an e e~ collider depending on its energy and their masses. A /JL+/J,~ collider could offer the unique possibility of studying them in detail.

5.8 Physics from extra dimensions G.F. Giudice, R. Rattazzi and J. Wells Recently considerable interest has been raised by the possibility that quantum-gravity effects appear at energy scales much lower than the Planck mass ^f — 1.2 x 1019 GeV [130]-[153]. In particular, this is the case in scenarios [130] in which gravity can propagate into extra dimensions, while ordinary matter is confined to a 3 + 1-dimensional space. The observed smallness of Newton's constant is a consequence of the large compactified volume of the extra dimensions, and the problem of the hierarchy between the Fermi and Planck scale is addressed in a totally new way. This has the exciting implication that future high-energy collider experiments can directly probe the physics of quantum gravity. Above the TeV energy scale, completely new

98 phenomena could emerge, such as resonant production of the Regge recurrences of string theory or as excitations of Kaluza-Klein modes of ordinary particles. However, because of our basic ignorance about the underlying quantum-gravity theory, it is not completely clear what the distinguishing experimental signatures would be, and whether any of these signatures would depend only on the conceptual theoretical hypothesis and not on the specific model realization. It is possible, nevertheless, to identify some specific experimental signatures, which provide a rather model-independent test of the idea that gravity propagates in extra dimensions. Let us consider an effective theory, valid below the quantum-gravity scale M& (of the order of the TeV), containing the Standard Model particles and the Kaluza-Klein excitations of the graviton. Production at high-energy colliders of low-energy gravitons (E < MD) is an infrared effect that can be reliably computed in the effective Lagrangian approach, with limited assumptions and with no reference to the model-dependent ultraviolet behaviour of the theory. For experimental purposes, the Kaluza-Klein gravitons behave like massive, non-interactive, stable particles; their collider signature is imbalanced in final-state momenta and missing mass. They have an almost continuous distribution in mass, because the lowest Kaluza-Klein mode mass is negligible with respect to the typical experimental energy resolution. Note that this is a peculiarity of the graviton signal with respect to other new-physics processes. For instance, supersymmetry with conserved R parity also can yield an excess of missing-energy events, but these correspond to a fixed invisible-particle mass. Here we concentrate on the graviton-production process /x+yu~ —* 7G, but similar considerations hold for Ai+/X~ ~* ZG. The inclusive differential cross-section, where the contributions of the different Kaluza-Klein modes have been summed up, is

~~,2 A/<2 / r- \ , Gx-V - 7G) = 3^^ {—) - /(*7,cos0), (70)~~

~~/(x'y) = 2(g(l -tf)x [(2"x)2(1 ~x+x2)" %V(1"x) ~yv] • (71)~~

Here x7 = 2Ey/y/s, E1 is the photon energy, 9 is the angle between the photon and beam directions, and 6 is the number of extra dimensions. Although we are considering a two-body process, the differential cross-section depends on two kinematic variables, because of the continuous distribution in the graviton mass m = \/s(l — x7). Note that, for 6 > 2, the factor 2 1 (1 — z)^/ )" in (71) tilts the photon-energy spectrum towards small values of £?7. The origin of this effect is the much wider graviton phase space available at large values of m. The Standard Model background comes predominantly from the process ju+/x~ —> ^uv. The peak contribution from /x+/i~ —* 7Z can be eliminated by excluding the photon-energy region around Ey = (s — M|)/(2v/i). On the other hand, the remaining continuous distribution in Ery from /J.+H~ —> ^vv represents a significant background. Other background contributions, e.g. from fi+fj,~ —*• ry(/J-+fJ,~) or /x+yu~ —» 7(7), are not important in the region of large photon transverse energy we will consider below.

In Fig. 64 we show the total cross-section for .&r,7 = .E7sin0 > 1000 GeV, Ey < 1950 in the case of a muon collider with s/s = 4 TeV. The signal is plotted as a function of the fundamental mass scale Mo for different values of the number of extra dimensions 5.

~~99 10* I ' ' ' ' I • ' ' • I • • ' ' I ' ' ' ' I • • • •_ H*li' Vs = 4 TeV~~

~~5.0 7.5 10.0 12.5 15.0 17.5 20.0 MD [TeV]~~

Fig. 64: Total M+A£" ~~* 7 + nothing cross-section at a 4-TeV centre-of-mass energy muon collider. The signal from graviton production is presented as solid lines for various numbers of extra dimensions (5 = 2,3,4,5). The Standard Model background for unpolarized beams is given by the dash-dotted line. The signal and background are computed with the requirement E-y < 1950 GeV for y/s = 4 TeV, in order to eliminate the ^Z —> 71/1/ contribution to the background

~~To extract the range of MD that can be probed at a future muon collider with yfs = 2 TeV and an integrated luminosity C = 100 fb"1, we require~~

^signal -•* (72) c The results for the corresponding maximum values of MD are given in Table 19 and compared with the sensitivity that can be reached by a muon collider with yfs = 1 TeV and £ = 200 fb"1. Note that the sensitivity range of MD for colliders with different centre-of-mass energies can be obtained simply by rescaling Fig. 64, since the variable MD always appears in the cross-section in the combination

Table 19: Upper bounds on the MD sensitivity that can be reached by studying the final state 7+ $ at a muon collider with yfs = 1 TeV, integrated luminosity C = 200 fb"1, with yfs = 2 TeV, C = 100 ftr1 and with , £= 100 fb"1. MD sensitivity MD sensitivity MD sensitivity s upper bound upper bound upper bound yfs = 1 TeV yfs = 2 TeV yfs = 4 TeV 2 4.1 TeV 6.5 TeV 10.6 TeV 3 3.1 5.2 8.6 4 2.5 4.3 7.3 5 2.0 3.7 6.5

The ability to observe the signal is limited by the background which, with our cut on E-f, comes primarily from processes involving virtual W exchange. Therefore, with the use of polarized beams, the background can be significantly reduced without affecting the signal, which is parity-invariant. Moreover, a peculiarity of the muon collider is the possibility of very precise beam-energy resolution, due to small initial-state radiation and bremsstrahlung. This is useful in the search for graviton emission, since it allows precise measurements of the rapid rise of the cross-section with yfs. Such measurements give direct information on the number of extra dimensions 5 and on the onset of quantum gravity.

100 Table 20: Upper bounds on the MD sensitivity that can be reached by studying the final-state jet + fir at the LHC with \/s = 14 TeV and integrated luminosity C = 100 fb"1 or 10 ft*"1. The bounds have been obtained by 1 1 requiring 2.6 fb (for C = 100 fb' ) or 3.7 fb (for C = 10 fb" ) with the acceptance cuts |»jjet| < 3 and Er,jet > 1 TeV. We also give an estimate of the minimum value of MD for which the effective-theory calculation can be trusted. MD sensitivity MD sensitivity MD perturbativity 5 upper bound upper bound lower bound C = 100 fb-1 C = 10 fb-1 (TeV) (TeV) (TeV) 2 8.5 7.9 3.8 3 6.8 6.3 4.3 4 5.8 5.5 4.8 5 5.0 4.6 5.4

A search for graviton production can also be performed at the LHC, studying the process pp —> jet + ET- The expected sensitivity range of MD is shown in Table 20. In hadron colliders the elementary scattering processes occur at different centre-of-mass energies. Therefore it is not straightforward to assess the applicability of the effective-theory approach. In Table 20 we have given an estimate of the minimum value of MD for which our approximation is valid, using the criterion described in Ref. [150]. For certain values of MD, the LHC could discover new physics phenomena which cannot be predicted perturbatively. In this case, a future muon collider will be essential to disentangle the many possible contributions to related signals, and to measure the energy and angular dependence of the graviton-induced cross-sections. We conclude with two important remarks. First of all, we have to be aware that other effects inherent in the fundamental theory, and therefore not computable with an effective La- grangian approach, can give various experimental signals. These effects could be more easily detectable than the effects we are studying. Therefore the discovery modes could be different from what is discussed here. However, these will be model-dependent effects, and little can be said about them with sufficient generality at present. The specific experimental processes discussed here can provide a handle to disentangle unexpected signals and test a precise hypothesis. Moreover, if no deviation from the Standard Model is observed, they define in a quantitative way the strategy to obtain lower bounds on the new-physics energy scale. The second remark concerns the value of the ultraviolet validity cut-off of the effective theory. In practice, this is an important issue, because this cut-off determines the maximum energy to which we can extrapolate our predictions and, analogously, the minimum value of MD that can be reliably studied at a collider experiment. This energy cut-off is expected to be of order MD- In reality it is reasonable to believe that the fundamental theory that regularizes quantum gravity sets in well before the latter becomes strongly interacting. In the context of string theory, the belief is that the string scale is smaller than MD, and therefore the energy range in which our effective theory applies is more limited, although large enough to be used for collider predictions, as we have illustrated here. It is also possible that the fundamental theory of gravity introduces new phenomena at scales equal to or less than MD, but does not significantly corrupt the graviton-emission signals up to larger energy scales.

5.9 General remarks J. Ellis Table 21 summarizes the main impressions we have gathered from this prospective study of the physics opportunities for a /x+/i~ collider at the high-energy frontier. A selection of possible physics topics is listed, and their principal features accessible to different high-energy colliders

101 are noted. The first accelerator column recalls the relevant capabilities of the LHC, to the extent that they have been investigated. This serves to baseline the further opportunities provided by the high-energy e+e~ and fJ,+fi~ colliders which are reviewed in the last two columns, for which we assume Ecm = 4 TeV.

Table 21: Accessibilities to various possible new physics phenomena with the LHC, a 4-TeV e+e collider and a 4- TeV n+n~ collider. The crosses X denote inaccessible features of models, the symbols Y denote accessible features. We indicate by F (E) the topics where flavour non-universality (energy resolution) is a particular advantage for a H+IJ.~ collider, and by 7 (P) topics where 77 collisions (polarization) confer advantage on an e+e~ collider. Physics topic LHC e+e n+n Supersymmetry Heavy Higgses H, A X? ?:7 Y: F,E Sfermions q I I: F Charginos X? Y: P Y: F,E R violation q decays \iij- F,E SUSY breaking some more detail: F,E Strong Higgs sector Continuum < 1.5 TeV <2TeV <2TeV Resonances scalar, vector vector, scalar vector (E), scalar (F) Extra dimensions Missing energy large ET Y Y: E? Resonances q*,9* l\Z*,e* l\Z*,f: E

In the case of supersymmetry, the LHC has unique physics reach beyond 2 TeV for squarks and gluinos, but the £+£~ colliders outclass it in studies of sleptons and charginos. Flavour non- universality would provide the /x+/x~ collider with unique opportunities to study the couplings of the heavier MSSM Higgs bosons to sfermions and charginos. The precise knowledge of the + + m tne Ecm would permit studies of fi /J," —> X X~ threshold region with unparallelled detail and accuracy, including measurements of Fx±. There may even be the possibility of observing 'charginonium' if the beam-energy spread and Fx± are small enough. The LHC is already known to be able to make some detailed supersymmetric spectroscopic measurements, and either £+£~ collider would be able to complement them, enabling any candidate model of supersymmetry breaking to be identified and over-constrained. The /x+/x~ collider with its greater energy precision would restrict the phase space of allowed models considerably more than an e+e~ collider. If R parity is violated in a supersymmetric model, sparticles could still be discovered at the LHC. A (A+/J,~ collider would provide measurements of i?-violating couplings that are complementary to those possible with an e+e~ collider, in view of their likely flavour non-universal structure. If there is an i?-violating LLE coupling, the £+£~ colliders could produce a direct- channel sneutrino resonance £+£~ —> v via different couplings, and hence are complementary. The decay width and branching ratios of such a v resonance would provide many interesting measurements. These would be considerably more precise at a ^\x~ collider, because of its reduced spread in Ecm. In the case of a strongly-interacting Higgs sector, the LHC could explore vector-boson continuum physics up to an invariant mass myv ~ 1.5 TeV. A 4-TeV £+£~ collider could extend these measurements up to myv ~ 2 TeV, which would be essential for disentangling models. Some of these predict resonance structures, which could again be explored more easily at a y.+ \i~~ collider, though the degree of advantage would depend on their natural widths. Finally, we have also made a tentative exploration of the extent to which the different colliders can explore the physics opportunities that would appear if a new space-time dimension opens up at the TeV scale. A generic prediction of such models would be missing-energy events

102 due to the production of higher-dimensional gravitons, G, e.g. g + g —> g + G at the LHC or £+£" -» 7 + G at an £+£~ collider. The LHC has the ability to produce events with very large missing Er, but distinguishing the G signal from other mechanisms would require more study. The G signal could in principle be distinguished almost equally well at e+e~ and n+n~ colliders, + though the more precise Ecm of a /x /x~ collider might confer some advantage. This would be more apparent in the production of Kaluza-Klein resonant states, which are expected in some models. The LHC would have a unique physics reach for g + g or q + q —»• g* and q + g —> q*, + whereas £ £~ colliders could produce 7*, Z*, £* or W* states. The reduced spread in Ecm of the fi+fj.~ collider would again confer considerable advantage in the study of 7* and Z* resonances. These examples serve to emphasize the unique physics interest of a /J,+fi~ collider at the high-energy frontier. They emphasize the need to establish the possible upper limit on its Ecm imposed by the neutrino-induced radiation hazard, in order to see whether a fj,+fj,~ collider could + be competitive in Ecm with a high-energy e e~ collider such as CLIC. In view of the interest attached to the precision of Ecm, it is desirable to explore in more detail the possible choices in beam-energy spread and luminosity for a high-energy fi+(J,~ collider, extending the studies already undertaken for the precision muon collider. We believe that this prospective study provides sufficient motivation to study in more detail the feasibility and characteristics of a /x+'\iT collider at the high-energy frontier.

NEXT PAGE(S) left BLANK 1UO I •—•—— 6 RADIOLOGICAL HAZARD DUE TO NEUTRINOS FROM A MUON COL- LIDER C. Johnson, G. Rolandi and M. Silari 6.1 Introduction This chapter is intended to provide a first estimate of the radiological hazard posed by the neutrino radiation generated by decays of high-energy muons circulating in a future muon collider installed at CERN. Owing to their extremely low interaction cross-section, only recently has the possibility of radiological consequences induced by neutrinos been raised. Cossairt and co-workers have presented a method for conservatively estimating the dose equivalent due to neutrinos over a wide energy range, from the MeV domain (solar neutrinos) to TeV (muon colliders) [154]. These are the only data currently available in the open literature (at least to the best of our knowledge). Four processes are considered, of increasing importance with increasing neutrino energy, namely scattering from atomic electrons, scattering from nuclei and scattering from nucleons, with the neutrino beam either unshielded or shielded. The latter case, which becomes important for Ev > 0.5 GeV, is the most common situation encountered with particle accelerators. The fluence to dose-equivalent conversion coefficients as a function of neutrino energy, taken from Ref. [154], are listed in Table A.I of the Appendix, for both the unshielded and the shielded case. Column 3 actually includes contributions from all processes, the first two being important only at low energies, and therefore coincides with the total value of the conversion coefficient. Dose-equivalent rates due to solar and atmospheric neutrinos and to neutrinos from present-day accelerators are insignificant. Expected dose-equivalent rates for the neutrino beams planned for future long- and short-baseline neutrino experiments, namely the CERN/Gran Sasso beam and the NuMI project at Fermilab, are also negligible [154]—[156], as shown in Table 22. However, the neutrino flux generated in a muon collider is much higher. The radiological hazard is in actual fact much larger (up to three orders of magnitude at TeV energies) if the neutrino beam is shielded than if it is left unshielded, because of the secondary radiation (mainly hadrons, electrons and muons) produced in the shielding material (in practice, earth, if the collider is installed underground). The secondaries with the longest range are the muons. The maximum energy of these secondary muons obviously cannot exceed the energy of the collider. The collider must obviously be shielded and the shield must be thick enough to absorb the full muon beam circulating in the ring in case of a beam loss. It follows that the shield must be thicker than the maximum range of all secondaries, i.e. the neutrino radiation emerging from the shield is in equilibrium with its secondary radiation. The data to be used for the present assessment are therefore those of column 3 in Table A.I.

~~Table 22: Expected annual dose equivalent from natural and accelerator neutrino sources (short- and long-baseline neutrino experiments) [154]-[156].~~

Annual dose equivalent (/uSv) y Solar neutrinos (Eu ~ 1-10 MeV) io- y Atmospheric neutrinos (Ev ~ 100 MeV - 2 GeV) 2 xl0- Neutrino experiments [Eu ~ 10-100 GeV): Fermilab (NuMI) SBL, 1 km distance 10 LBL, 730 km distance 8.5 xlO~6 CERN/Gran Sasso SBL 10 Gran Sasso 5 xlO~5

105 6.2 Neutrino fluence expected from a muon collider Let us assume that bunches of iV° = 2 x 1012 muons are produced at a repetition period F = 15 Hz. The average rate of neutrino production is therefore TV = 2N°F = 6 x 1013 s"1 . The time structure of the neutrino rate is bunched since the muon lifetime in the laboratory frame is typically shorter than the repetition period of muon production: 2 2 rM = 2.2 x 1(T s (E0/l TeV) versus 1/F = 6 x 10~ s , where EQ is the energy of the muon beam. The average radius R of the machine is determined by the beam energy and the magnetic field: R = 420 m (8 T/B) (EQ/1 TeV) . The divergence of the neutrino beam (the opening half-angle) induced by the decay (expressed in radians) is the inverse of the relativistic factor:

At a distance of 10 km this divergence produces a spot size of 2 m (1 TeV/Eo). The neutrino fluence rate is mainly concentrated in the plane of the machine. At a distance L from the centre of the machine the average fluence rate is 2 5 2 2 $„ = 7v7/(27rL ) = 10 cm" s-^lO km/L) {E0/l TeV) . (73) A straight section of length I will concentrate the fluence by a factor: 7 l/R = 500 (B/8 T) (1/20 m) Therefore an inter-magnet gap of 0.5 m will increase the neutrino fluence by one order of magnitude and a comparatively short straight section of a few tens of metres (e.g. for injection) by three orders of magnitude. On the other hand, at the interaction point (along the associated straight sections within and near to the detector) the beam divergence is given by where e is the beam emittance and a and /? are the local Twiss parameters. The low (3 and/or large a values reduce the fluence by an order of magnitude. Further away from the interaction point, but still within the interaction-point lattice insertion, dipole fields must be introduced to avoid hot spots in regions of locally low beam divergence. For the present purpose we will assume that elsewhere, on average, a straight section in the regular collider lattice will enhance the neutrino fluence by a factor of 10. The spectrum of the neutrinos from muon decay in the muon reference system can be approximated by the expression

~~2 &EV m This is a good approximation for the muon neutrinos and a decent approximation for the electron antineutrinos. The spectrum in the laboratory system, averaged over all production angles, is~~

which is the expression we will use below. Note that at TeV energies the transverse broadening of the hadronic and leptonic showers is comparable to the overall neutrino-radiation opening angle, and this partly justifies averaging the neutrino-energy spectrum over all production angles. A correct integration of the neutrino spectrum will be included in any detailed design.

~~106 6.3 Shielding The collider has to be installed underground to shield the muon beam in the event of a beam loss. The energy loss of a muon is~~

~~dE/dx = 0.6 TeV/km (p/3 g cm"3) , (75) which means that a 5 TeV muon beam is dumped in less than 10 km of earth and a 10 TeV beam in less than 20 km.~~

~~On the other hand, the interaction cross-section av of neutrinos is extremely small, of the 35 2 order of 10~ cm {Evj\ TeV). The attenuation length is then~~

6 3 A = A/{pNAav) = l/{Nau) = 0.5 x 10 km(l TeV/£,,)(3 g cnT /p) , (76) in which A and p are the atomic number and the density of the medium, N& is the Avogadro number and N is the number of atoms per unit volume. From expression (76) one sees that the attenuation length is very long, i.e. the neutrino fluence is not attenuated at all while traversing the shield. Neglecting local effects, i.e. approximating the Earth as a sphere, it can be easily shown that, for a machine situated at a depth d, the exit point of the neutrino beam is at a distance L given by

2 L = V2dRt - d PS y/2dRt = 36 km ^d/100 m , (77) in which Rt — 6400 km is the radius of the Earth. For the purpose of muon shielding, it would be sufficient that a 5 TeV collider be placed at a depth of 10 to 20 m, but we shall see below that this is not sufficient for the neutrino radiation.

6.4 Neutrino dose equivalent Starting from the above assumptions we can estimate the radiological hazard which can be posed by the neutrinos generated by decays of high-energy muons in the collider. The dose-equivalent rate is obtained by folding the neutrino spectrum dN^/dE^ with the conversion coefficients

~~C(EV) of Table A.I, column 3:~~

~~(78) Jo~~

2 l l where dNv/dEv is given by expression (74). If Ev is in GeV, dNv/dEv in cm s GeV and 2 1 C(EV) in [iSv cm , H is in /xSv s" . In the neutrino-energy range from 0.5 GeV to 10 TeV, the fluence to dose-equivalent conversion coefficients can be fitted by the expression

~~loSl0C{Ev) = 2]ogw{Ev)-lb. (79)~~

Let us consider a collider placed at two different 'reasonable' depths, d = 100 m and d = 200 m, and at a more problematic depth, d = 500 m. From expression (77) it follows that the exit point of the neutrino beam is at distances L = 36 km, L = 51 km and L = 80.5 km, respectively. The integral neutrino fluence rate $o emerging from the earth is calculated from expression (73) and is given in Table 23 for a few representative values of the collider energy EQ. The divergence of the neutrino beam induced by the decay (from 100 /zrad for a collider energy of 1 TeV to 10 ^rad at 10 TeV) is such that, even at the shortest of the above distances from the source, the beam is large enough (at 36 km the spot radius is 3.6 m and 0.36 m, respectively, at 1 TeV and 10 TeV) that a whole body exposure to the radiation should be considered. The annual dose equivalent expected for operation of the collider for 180 days/year

107 operation (1.56 x 107 s) is given in Table 24 and in Figs. 65-67. Estimates are given for neutrino radiation emitted from a bending section and from a straight section, assuming an enhancement factor of 10, as discussed above. The dose scales with EQ.

~~Table 23: Integral neutrino fiuence rate $o at L = 36 km, L = 51 km and L — 80.5 km.~~

2 Collider energy $o (cm"~' s~ L) (TeV) L == 36 km L = 51 km L = 80.5 km 3 3 3 1 8 X 10 3.8 X 10 1.6 X 10 4 3 2 1.6 X 10 7.7 X 10 3.1 X 103 4 4 3 5 4 X 10 1.9 X 10 7.8 X 10 4 4 4 10 8 X 10 3.8 X 10 1.6 X 10

~~10° 1 ' I ' ' ' • I ' • • • I ' ' ' ' I~~

~~10° >~~

~~3 a" v v mo star: arc diamond: straight section (arc x 10)~~

~~. •"• ,[.,.. I .,..[.,.. I ,,,, I ,,,. 101 0 2 4 6 8 10 12 Collider energy (TeV)~~

~~Fig. 65: Dose equivalent due to neutrino radiation at 36 km distance (collider at 100 m depth).~~

~~10°~~

~~n5 -~~

~~,3 ^- 3 10~~

~~o •a "3 0 C 101 -~~

~~Fig. 66: Dose equivalent due to neutrino radiation at 51 km distance (collider at 200 m depth).~~

~~108 10° I • • ' ' I I ' • ' ' I • ' ' ' I ' ' ' ' =~~

~~> 10J CO~~

~~c 104 103 qu i w o 102 T3 n0 star: arc a diamond: straight section (arc x 10)~~

~~1OU I , , i , , , , i . , 2 4 6 8 10 12 Collider energy (TeV)~~

~~Fig. 67: Dose equivalent due to neutrino radiation at 80.5 km distance (collider at 500 m depth).~~

Table 24: Estimated annual dose equivalent at 36 km, 51 km and 80.5 km distances from 1, 2, 5 and 10 TeV muon colliders, for operation of 180 days per year. The neutrino fluence from a straight section (SS) is supposed to be 10 times more intense than from a bending section.

Annual dose equivalent (fiSv) d - 100 m, L = 36 km d = 200 m, L = 51 km d = 500 m, L = 80.5 km Arc SS Arc SS Arc SS Eo = lTeV 20 200 10 100 4 40 Eo = 2 TeV 160 1,600 80 800 32 320 Eo = 5 TeV 2,500 25,000 1,250 12,500 500 5,000 Eo = 10 TeV 20,000 200,000 10,000 100,000 4,000 40,000

It can be shown that the neutrino radiation produced in the event of a loss of the circulating muon beam has an average energy of 100 MeV (3 g cm~3/p) (Eo/1 TeV), too low to represent any radiological hazard.

6.5 Discussion An assessment of the radiological risk due to neutrinos from a muon collider has been made at Fermilab but it is still unavailable [157]. Some results given in Ref. [158] are in agreement with the present estimate (which is possibly not surprising as the data of Table A.I come from Fermilab). Conversion coefficients for neutrinos in equilibrium with their secondaries, calculated at Fermilab by Mokhov with the Monte Carlo code MARS [159], are still unpublished but were provided by the author as a private communication to G.R. Stevenson. These values, shown in Fig. 10 of Ref. [155], are somewhat higher than those listed in Table A.I for energies up to about 10 GeV, but approximately the same above. As the most important contributions to the dose equivalent come from the highest energies, the difference in using either set of data in this context should be very small. The present estimates are also in substantial agreement with those of B. King for various collider parameters [160], who has also calculated that for a 4 TeV collider the distance at which the neutrino dose from an arc is within the US limit of 1 mSv per year is 34 km [161]. The

109 present estimates are also in agreement with those of Ref. [162] which, for a 3 TeV centre-of-mass (i.e. EQ = 1.5 TeV) collider placed at a depth d = 500 m and a muon current close to the value used in the present paper, predict an off-site annual dose in the plane of a bending dipole of 11 /iSv. The value of ambient dose equivalent caused by ionizing radiation emitted by CERN beyond the boundaries of its site must not exceed 1.5 mSv per year [163]. The radiological impact on the environment of a muon collider built at or nearby CERN will therefore have to comply with this limit. In addition, the effective dose received by any person living or working outside of CERN's boundaries must not exceed 0.3 mSv per year. Since it might not be possible (or feasible) to position the collider in order to avoid straight sections pointing towards villages or single houses, at this stage it is wise to take the latter limit. If the collider is built at a sufficient depth to guarantee a minimum distance of 30 to 40 km from the surface exit points of the neutrino-induced radiation, a problem exists only if the collider centre-of-mass energy exceeds 3 TeV. For higher energies some countermeasure must be adopted. To distribute the radiation and lower the average dose equivalent, Fermilab has proposed to vary the production direction of the neutrino beam by instituting a vertical wave in the collider ring [158]. To limit the number of 'hot spots', King has suggested to decrease the number of straight sections by designing a magnet lattice with combined function magnets, where bending and focusing of the beam is achieved in the same magnet, thus avoiding the straight sections between dipoles and quadrupoles [161]. However, this solution cannot possibly avoid the need for a few long straight sections. In the event that a number of radiation 'hot spots' are unavoidable, one can think to fence off the area where the neutrino beam emerges from the ground. At the location where the neutrinos emerge from the earth, at a distance L given by expression (77), the radial extent of the region traversed by the radiation is (Fig. 68)

in which a « 29L, 6 is the opening half-angle of the neutrinos and is the angle subtended by L with respect to the Earth's centre. The height of the radiation fan above ground is a function of the distance z from the point where the radiation cuts the Earth's surface:

~~h « z tan .~~

~~The relevant geometrical parameters for a muon collider of increasing energy placed at increasing depth are given in Table 25.~~

~~Table 25: Geometrical parameters for a few representative cases of muon colliders of increasing energy installed underground at increasing depth.~~

Eo (TeV) d(m) L (km) (rad) z (km) Mm) d(fivad) a (m) 6(m) 1 100 36 5.6 xl0~a 10 56 106 7.6 1360 2 100 36 5.6 xlO-3 10 56 53 3.8 680 5 200 51 8 xl0~3 10 80 21 2.1 260 10 500 80.5 12.5 xlO-3 10 125 11 1.8 145

~~Another solution which can perhaps be conceived is to transport the collimated neutrino beam from a 'hot spot' in a beam pipe for the last tract (let us say one kilometre) before it~~

110 emerges from the ground. In this way the secondary radiation produced in the upstream material would be absorbed in the earth shield surrounding the pipe. Evacuating the pipe to a modest vacuum of 1 torr would prevent even the small production of secondaries which occurs in air (already a factor 10~3 with respect to the earth shielding). One has of course to make sure that the 'pure' neutrino beam emerging from the Earth's surface does not interact with any other material (such as buildings) before lifting to a sufficient height from the ground.

Fig. 68: Some typical geometrical features of the neutrino radiation from an underground muon collider: 2 2 L = 2Rtd- d ,sin(f> = L/Rt,h ss Z tan, 6 « 1/7,0 « 20L,6« a/ {Rt is the radius of the Earth).

The last, obvious, solution to decrease the neutrino radiation dose is to decrease the muon current in the ring. This would imply changes to the machine parameters requiring substantial R&D work. The use of optical stochastic cooling and/or beam-beam tune-shift compensation [164] are speculative proposals to this end. But the study of parameter sets for muon colliders in the centre-of-mass energy range of 5 TeV and above still offers much scope for invention. It should be recalled that the present estimates only represent a first approach. A more comprehensive evaluation of the problem may require a detailed Monte Carlo calculation by a code treating neutrino transport, which at present is only provided by MARS [159]. In addition to the collider energy, other relevant parameters to be considered are the number, location and length of the straight sections. The enhancement factor of the neutrino fluence due to a straight section is a critical issue which needs to be carefully assessed. Important also is the choice of orientation, positioning and possible tilting of the collider ring, as well as the site selection of the accelerator complex. Disregarding 'exotic' solutions such as installing the collider on top of a mountain (in order that the radiation halo is above ground level) or at a few hundred metres depth in the sea, in the case of CERN the site selection is limited to the French region currently housing the SPS and LEP. The actual orography of the region must be taken into account, as locally there may be significant deviations in the inclination of the ground from the spherical approximation used for the present assessments.

~~NEXT PAGE(S) left BLANK Ill Appendix~~

Table A.I: Fluence to dose-equivalent conversion coefficients for neutrinos. Data are extracted from Fig. 1 of Ref. [154]. In the neutrino energy range from 0.5 GeV to 10 TeV, the fluence to dose-equivalent conversion coefficients C(EV) can be fitted by the expression log10 C(EV) = 21og10(^) - 15.

~~Energy (GeV) Dose equivalent per unit fluence 3V cm2) Unshielded Total (« shielded)~~

2 x lO-4 lo-27 4 5 x lO- 10-26 1 xlO"3 5 x 10~26 2 X lO-3 2 x 10-25 5 X lO-3 3 x 10-24 1 xlO-2 2 x lO-23 2 xlO"2 3 x lO-22 5 xlO"2 2 x 10-21 1 X lO-20 1 x 10-1 8 x 10-20 2x IO-19 2 X 10-1 2.5 x 10~i8 4 x 10-i8 5 x 10-1 8 x 10-17 2.5 x 10-16 1 1.5 x 10-i6 1 x IO-15 2 4 x 10~16 4x IO-15 5 2 x 10-15 2.5 x IO-14 10 4 x IO-15 1 x IO-13 20 8 x IO-15 4x IO-13 50 4 x 10-14 2.5 x IO-12 1 xlO2 1 x IO-13 1 x 10-n 2 x 102 3 x 10-13 4x 10-u 5 x 102 1.5 x IO-12 2.5 x 10-1° 1 x 103 4 x IO-12 1 x 10-9 2 xlO3 1 x lO-11 4 x 10-9 5 x 103 5 x IO-11 2.5 x 10~8 1 x 104 1.5 x 10-1° 1 x lO-7

NEXT PAGE(S) left BLANK 113 References [1] G.I. Budker, Accelerators and colliding beams (in Russian), in Proc. 7th Int. Conf. on High Energy Accel. (Yerevan, 1969), p. 33; extract: AIP Conf. Proc. 352 (1996) 4. [2] G.I. Budker, Int. High Energy Conf. (Kiev, 1970), unpublished; extract: AIP Conf. Proc. 352 (1996) 4. [3] A.N. Skrinsky, Intersecting storage rings at Novosibirsk, Proc. Int. Seminar on Prospects of High-Energy Physics (Morges, Mar. 1971), unpublished; extract: AIP Conf. Proc. 352 (1996) 6. [4] G.I. Budker and A.N. Skrinsky, Electron cooling and new possibilities in elementary particle physics, Sov. Phys. Usp. 21 (1978) 277. [5] A.N. Skrinsky, Acceleration and instrumentation prospects of elementary particle physics, AIP Conf. Proc. 68 (1980) 1056. [6] A.N. Skrinsky and V.V. Parkhomchuk, Methods of cooling beams of charged particles, Sov. J. Part. Nucl. 12 (1981) 223. [7] A.N. Skrinsky, Accelerator and detector prospects of elementary particle physics, Sov. Phys. Usp. 25 (1982) 639, sec. 3n. [8] V.V. Parkhomchuk and A.N. Skrinsky, Ionization cooling: physics and applications, in Proc. 12th Int. Conf. on High Energy Accel., ed. by F.T. Cole and R. Donaldson (Fermilab, 1983), p. 485; http://www-ppd.fnal.gov/muscan/munotes/mc-003.pdf. [9] A.N. Skrinsky, Ionization cooling and muon collider, AIP Conf. Proc. 372 (1996) 133. [10] A.N. Skrinsky, Polarized muons beams for muon collider, Nucl. Phys. B (Proc. Suppl.) 51A (1996) 201. [11] D. Neuffer, Multi-TeV muon colliders, AIP Conf. Proc. 156 (1987) 201; http://www-ppd.fnal.gov/muscan/munotes/mc-006.pdf. [12] D. Cline and D. Neuffer, A muon storage ring for neutrino oscillation experiments, AIP Conf. Proc. 68 (1980) 846; reproduced in AIP Conf. Proc. 352 (1996) 10. [13] D. Neuffer, Colliding muons beams at 90 GeV, Fermilab report FN-319 (July 1979); http://www-ppd.fnal.gov/muscan/munotes/mc-001.pdf. [14] D. Neuffer, Principles and applications of muon cooling, in Proc. 12th Int. Conf. on High Energy Accel., ed. by F.T. Cole and R. Donaldson (Fermilab, 1983), p. 481; Part. Ace. 14 (1983) 75; reproduced in AIP Conf. Proc. 353 (1996) 12. [15] J. Ellis, E. Keil and G. Rolandi, Options for future colliders at CERN, CERN-SL/98-004 (1998). [16] C. Ankenbrandt et al., The Muon Collider Collaboration, Status of muon collider research and development and future plans, draft, can be found on http: //www. cap. bnl. gov/mumu/status jreport. html. [17] D.G. Koshkarev, Proposal for a decay ring to produce intense secondary particles at the SPS, CERN/ISR-DI/74-62.

115 [18] S. Geer, Phys. Rev D57 (1998) 6989. [19] V.M. Lobashev and O.V. Serdyuk, A pion and muon magnetic trap as a source of electron and muon neutrinos, Nucl. Instrum. Methods 136 (1976) 61-71. [20] H. Lengeler, The European spallation source study, Nucl. Instrum. Methods B139 (1998) 82-90; ESS, A next generation neutron source for Europe, Vol. 3, The technical study, ISBN 090-2376-658, November 1996. [21] C. Johnson, http://nicewww.cern.ch/cdj/public/mumutargex 23. [22] R. Bennett, http://muonstoragerings.cern.ch/Welcome.html/Events/131198/Bennett/index.html. [23] N. Mokhov, The MARS code system user's guide, version 13 (95), Fermilab FN-628 (1995). [24] R. Chehab, Positron sources, LAL/RT 92-17 (December 1992). [25] G. Swain, Linac reference design for PILAC, Pilac technical note NO 14, LA-UR-91-717 (20 February, 1991). [26] The MUCOOL Collaboration, Ionization cooling research and development program for a high luminosity muon collider; http: //www. f nal. gov/pro j ects/muon_collider/cool/cool. html. [27] C. Leemann, The CEBAF superconducting accelerator - an overview. CEBAF-PR-86- 003. [28] see for instance: http://preprints.cern.ch/archive/electronic/cern/sl/sl-98-060.pdf; G. Geschonke, E. Keil, A recirculating electron accelerator (ELFE) using the LEP super-conducting cavities, CERN SL/98-060. [29] J.-P. Delahaye, Accumulation schemes, http://muonstoragerings.cern.ch/Welcome.html/Events/Neutrino/Delahaye/index.html. [30] J.-P. Delahaye et al., CLIC, a 0.5 to 5 TeV e+/- compact linear collider, CERN/PS/98- 009(LP); CLIC home page: http://www.cern.ch/CERN/Divisions/PS/CLIC/Welcome.html. [31] C. Ankenbrandt et al., Bunching near transition in the AGS, Phys. Rev. ST Accel. Beams 1 (1998) 030101; http://fnalpubs.fnal.gov/archive/1998/pub/Pub-98-006.pdf. [32] G.W. Foster, Status report on the transmission line magnet; http: //www-ap. f nal. gov/VLHC/vlhcpubs/pubsl-100/5/mag_stat .html. [33] K.R. Symon et al., Fixed-field alternating-gradient particle accelerators, Phys. Rev. 103 (1956) 6. [34] A.A. Mikhailichenko and M.S. Zoloterev, Phys. Rev. Lett. 71 (1993) 4146. [35] B. Autin, A.M. Sessler, D.H. Whittum, Plasma compensation effects with relativistic electron beams, Proc. 1990 IEEE Conference, New York, Eds. F. Bennett and J. Kopta, Conference series 89CH2669-0, LBL 26930, CERN PRE 89-025.

116 [36] R. Garoby, M. Vretenar, Proposal for a 2 GeV linac injector for the CERN PS, PS/RF/Note 96-27. [37] G. Bollen, D. Boussard, R. Cappi, R. Garoby, H. Haseroth, C.E. Hill, P. Knaus, A.M. Lom- bardi, M. Martini, P.N. Ostroumov, J.M. Tessier, M. Vretenar, Report of the study group on a superconducting proton linac as a PS injector; http://nicewww.cern.ch/ vretenar/Spl.htm. [38] D.B. Montgomery, Solenoid magnet design, Wiley-Interscience, New York, 1969. [39] G. Aubert, Physica Scripta T35 (1991) 168-71. [40] G. Aubert et al., 1994-1997 Technical Report of Grenoble High Magnetic Field Laboratory, MPI-FKF - CNRS, 25 avenue des Martyrs BP 166 - 38042 Grenoble cedex 9, France. [41] The neutrino group of the prospective study on n+^~ colliders, Physics opportunities at a CERN-based neutrino factory, CERN-SPSC/98-30, Memorandum SPSC/M 617 (1998).

[42] A. Bueno, M. Campanelli and A. Rubbia, A medium baseline search for v^ <-> ve oscillations at a v beam from muon decays, hep-ph/9809252, preprint CERN-EP/98-140. [43] A. de Riijula, B. Gavela and P. Hernandez, Neutrino oscillation physics with a neutrino factory, preprint CERN-TH/98-321, FTUAM-98-19 (1998). [44] A. Bueno, M. Campanelli and A. Rubbia, Long baseline neutrino oscillation disappearance search using a v beam from muon decays, ETHZ preprint hep-ph/9808485 (1998). [45] Y. Fukuda et al., Phys. Lett. B433(1998) 9, hep-ex/9805006, Phys. Rev. Lett. 81 (1998) 1562; T. Kagita, in Proc. XVIIIth International Conference on Neutrino Physics and Astrophysics, Takayama, Japan (June 1998). [46] L. Wolfenstein, Phys. Rev. D17 (1978) 2369; D20 (1979) 2634; S.P. Mikheyev and A. Yu Smirnov, Sov. J. Nucl. Phys. 42 (1986) 913. [47] B. Pontecorvo, Sov. Phys. JETP 26 (1968) 984. [48] E. Abies et al., MINOS Collaboration, Fermilab Proposal P-875 (1995). [49] G. Aquistapace et al., CERN 98-02, INFN/AE-98/05 (May 1998). [50] A. De Rujula, M.B. Gavela and P. Hernandez, hep-ph/9811390, to appear in Nucl. Phys. B. [51] M. Messier, Atmospheric neutrinos at SuperKamiokande, talk at APS-DPF meeting, Los Angeles, January 1999. [52] See for example F. Boehm and P. Vogel, Physics of Massive Neutrinos, Cambridge Uni- versity Press, 1997. [53] R. Barbieri et al., hep-ph/9807235, LBNL-42020, UCB-PTH-98/44, SNS-PH/98-15, IFUP-TH/98-25. [54] G.L. Fogli et al., hep-ph/9808205, Phys. Rev. D59 (1999). [55] A. Bueno, M. Campanelli and A. Rubbia, hep-ph/9809252. [56] G. Baldini et al., NICE Proposal, LNGS-LOI 98/13 (1998).

117 [57] V. Barger et al., Phys. Rev. D22 (1980) 2718; H.W. Zaglauer and K.H. Schwarzer, Z. Phys. C40 (1988) 273. [58] O. Yasuda, hep-ph/9809205, TMUP-HEL-9810. [59] N. Cabibbo, Phys. Lett. B72 (1978) 33. [60] J. Arafune, M. Koike and J. Sato, Phys. Rev. D56 (1997) 3093, hep-ph/9703351; M. Tan- imoto, Phys. Lett B345 (1998) 373, hep-ph/9806375; H. Minakata and H. Nunokawa, Phys. Lett. B413 (1997) 369; Phys. Rev. D57 (1998) 4403. [61] T.K. Kuo and J. Pantalone, Phys. Lett. 198 B (1987) 406; S.M. Bilenky, C. Giunti and W. Grimus, hep-ph/9712537, Phys. Rev. D58 (1998). [62] For a recent review, see F. Wilczcek in NEUTRINO 98, Takayama (Japan), June 1998, hep-ph/9809509, IASSNS-HEP-98-79. [63] D. Ayres et al., MINOS proposal, NUMI-L-63, February 9, 1995. [64] P. Cennini et al., ICARUS II. A second generation proton decay experiment and neutrino observatory at the Gran Sasso Laboratory, Experimental proposal LNGS 94/99-1 and 94/99-11 (1994) [65] W. Molzon, Physics with low energy muons at the front end of the muon collider, in Proc. Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, FNAL, USA, 6-9 November 1997, Eds. S. Geer and R. Raja (AIP Conf. Proc 435, 1998); and references cited therein. [66] R. Barbieri, L. Hall and A. Strumia, Nucl. Phys. B445 (1995) 445; J. Hisano, T. Moroi, K. Tobe and M. Yamaguchi, Phys. Lett. B392 (1997) 341. [67] R. Casalbuoni, talk given at this workshop, http://www.fi.infn.it/pub/rootcl.ps, andR. Casalbuoni, A. Deandrea, S. De Curtis, D. Dominici, R. Gatto and J.F. Gunion, UCD-99-5, DFF-333/2/99, UGUA-DPT-1999- 03-1029, March 1999. [68] R. Raja and A. Tollestrup, Calibrating the energy of a 50 x 50 GeV muon collider using g-2 spin precession, Phys. Rev. D58 (1998) 13005; httphttp://xxx.lanl.gov/ps/hep-ex/9801004. [69] V. Barger, M.S. Berger, J.F. Gunion and T. Han, Phys. Rev. Lett. 75 (1995) 1462; Phys. Rep. 286 (1997) 1. [70] J.F. Gunion, hep-ph/9802258, in Proc. Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, FNAL, USA, 6-9 November 1997, Eds. S. Geer and R. Raja (AIP Conf. Proc 435, 1998). [71] T. Sjostrand, PYTHIA 6.120, pre-release. [72] G.J. Gounaris and F.M. Renard, PM/98-34, THES-TP 98/08, and references therein. [73] V. Barger, hep-ph/9803480, Proc. 4th International Conference on Physics Potential and Development of jz+/z~ Colliders (MUMU 97), San Francisco, CA, 10-12 Dec. 1997, Ed. D.B. Cline (AIP Conf. Proc. 441).

118 [74] J.F. Gunion, H.E. Haber, G. Kane and S. Dawson, The Higgs Hunter's Guide, Addison- Wesley, 1990; A. Bartl, H. Eberl, K. Hidaka, T. Kon, W. Majerotto and Y. Yamada, Phys. Lett. B389 (1996) 538; A. Djouadi, J. Kalinowski, P. Ohmann and P.M. Zerwas, Z. Phys. C74 (1997) 93. [75] J.A. Coarasa, R.A. Jimenez and J. Sola, Phys. Lett. B389 (1996) 312; A. Bartl, H. Eberl, K. Hidaka, T. Kon, W. Majerotto and Y. Yamada, Phys. Lett. B402 (1997) 303. [76] J. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B262 (1991) 477. [77] A. Bartl, H. Eberl, S. Kraml, W. Majerotto, and W. Porod, hep-ph/9712412, in Proc. Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, FNAL, USA, 6-9 November 1997, Eds. S. Geer and R. Raja (AIP Conf. Proc 435, 1998). [78] A. Bartl, H. Eberl, S. Kraml, W. Majerotto, and W. Porod, Phys. Rev. D58 (1998) 115002. [79] S. Kraml, PhD Thesis, T.U. Vienna (1999) hep-ph/9903257. [80] V. Barger, M.S. Berger and T. Han, hep-ph/9801410. [81] V. Barger, M.S. Berger, J. Gunion and T. Han, Phys. Rep. 286 (1997) 1. [82] G. Moortgat-Pick, H. Fraas, A. Bartl and W. Majerotto, hep-ph/9804306, to be published in Eur. Phys. J. C (1998), DOI 10.1007/sl00529800956. [83] J. Gunion and H. Haber, Nucl. Phys. B272 (1986) 1; ibid. B278 (1986) 449. [84] A. Bartl, H. Fraas and W. Majerotto, Z. Phys. C30 (1986) 441; A. Bartl, H. Fraas, W. Majerotto and B. Mosslacher, Z. Phys. C55 (1992) 257. [85] M.S. Berger, Phys. Rev. D41 (1990) 225; Y. Okada, M. Yamaguchi and T. Yanagida, Prog. Theor. Phys. 85 (1991) 1; Phys. Lett. B262 (1991) 54; H.E. Haber and R. Hempfling, Phys. Rev. Lett. 66 (1991) 1815; J. Ellis, G. Ridolfi and F. Zwirner, Phys. Lett. B257 (1991) 83; R. Barbieri, M. Frigeni and F. Caravaglios, Phys. Lett. B258 (1991) 167; P.H. Chankowski, Warsaw preprint 1991, IFT-7-91 (unpublished); J.R. Espinosa and M. Quiros, Phys. Lett. B266 (1991) 389; J.L. Lopez and D.V. Nanopoulos, Phys. Lett. B266 (1991) 397; M. Carena, K. Sasaki and C.E.M. Wagner, Nucl. Phys. B381 (1992) 66; P.H. Chankowski, S. Pokorski and J. Rosiek, Phys. Lett. B281 (1992) 100; Nucl. Phys. B423 (1994) 437; D.M. Pierce, A. Papadopoulos and S.B. Johnson, Phys. Rev. Lett. 68 (1992) 3678; A. Brignole, Phys. Lett. B281 (1992) 284; V. Barger, M.S. Berger and P. Ohmann, Phys. Rev. D49 (1994) 4908; G.L. Kane, C. Kolda, L. Roszkowksi and J.D. Wells, Phys. Rev. D49 (1994) 6173; R. Hempfling and A.H. Hoang, Phys. Lett. B331 (1994) 99; P. Langacker and N. Polonsky, Phys. Rev. D50 (1994) 2199. [86] H.E. Haber and R. Hempfling, Phys. Rev. D48 (1993) 4280. [87] M. Carena, J.R. Espinosa, M. Quiros and C.E.M. Wagner, Phys. Lett. B355 (1995) 209; M. Carena, M. Quiros and C.E.M. Wagner, Nucl. Phys. B461 (1996) 407. [88] H.E. Haber, R. Hempfling and A. Hoang, Z. Phys. C57 (1997) 539; S. Heinemeyer, W. Hollik and G. Weiglein, Phys. Rev. D58 (1998) 091701; Phys. Lett. B440 (1998) 96; R.-J. Zhang, Phys. Lett. B447 (1999) 89. [89] A. Pilaftsis, Phys. Rev. D58 (1998) 096010; Phys. Lett. B435 (1998) 88.

119 [90] A. Pilaftsis and C.E.M. Wagner, hep-ph/9902371. [91] A. Pilaftsis, Phys. Rev. Lett. 77 (1996) 4996; A. Pilaftsis, Nucl. Phys. B504 (1997) 61; S.-Y. Choi and M. Drees, Phys. Rev. Lett. 81 (1998) 5509. [92] J. Ellis, S. Ferrara and D.V. Nanopoulos, Phys. Lett. B114 (1982) 231; W. Buchmiiller and D. Wyler, Phys. Lett. B121 (1983) 321; J. Polchinski and M. Wise, Phys. Lett. B125 (1983) 393; F. del Aguila, M. Gavela, J. Grifols and A. Mendez, Phys. Lett. B126 (1983) 71; D.V. Nanopoulos and M. Srednicki, Phys. Lett. B128 (1983) 61; M. Dugan, B. Grinstein and L. Hall, Nucl. Phys. B255 (1985) 413; Y. Kizukuri and N. Oshimo, Phys. Rev. D46 (1992) 3025; T. Falk, K.A. Olive and M. Srednicki, Phys. Lett. B354 (1995) 99; T. Ibrahim and P. Nath, Phys. Lett. B418 (1998) 98; T. Falk and K.A. Olive, hep-ph/9806236; M. Brhlik, G.J. Good and G.L. Kane, hep-ph/9810457. [93] D. Chang, W.Y. Keung and A. Pilaftsis, Phys. Rev. Lett. 82 (1999) 900. [94] V. Barger, M.S. Berger, J.F. Gunion and T. Han, Phys. Rept. 286 (1997) 1. [95] J.A. Coarasa, R.A. Jimenez, and J. Sola, Phys. Lett. B389 (1996) 312; R.A. Jimenez and J. Sola, Phys. Lett. B389 (1996) 53; M. Carena, S. Mrenna and C.E.M. Wagner, hep-ph/9808312; K.S. Babu, C. Kolda, J. March-Russell and F. Wilczek, Phys. Rev. D59 (1999) 016004; K.S. Babu and C. Kolda, hep-ph/9811308. [96] B. Grzadkowski and J.F. Gunion, Phys. Lett. B350 (1995) 218. [97] S. Weinberg, Phys. Rev. 13 (1976) 974; Phys. Rev. 19 (1979) 1277; L. Susskind, Phys. Rev. 20 (1979) 2619. [98] R. Casalbuoni, A. Deandrea, S. De Curtis, D. Dominici, R. Gatto and J.F. Gunion, hep- ph/9809523. [99] R. Casalbuoni, S. De Curtis, D. Dominici and R. Gatto, Phys. Lett. B155 (1985) 95; Nucl. Phys. B282 (1987) 235. [100] R. Casalbuoni, A. Deandrea, S. De Curtis, D. Dominici, F. Feruglio, R. Gatto and M. Grazzini, Phys. Lett. B349 (1995) 533; R. Casalbuoni, D. Dominici, P. Chiappetta, A. Deandrea, S. De Curtis, R. Gatto, Phys.Rev. D56 (1997) 2812. [101] A. Blondel, in Proc. Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, FNAL, USA, 6-9 November 1997, Eds. S. Geer and R. Raja (AIP Conf. Proc 435, 1998); and references cited therein. [102] B. Norum and R. Rossmanith, Nucl. Phys. B (proc. suppl.) 51A (1996) 191. [103] OPAL Collaboration, Phys. Lett. B389 (1996) 416. [104] L3 Collaboration, Phys. Lett. B398 (1997) 223. [105] DELPHI Collaboration, Phys. Lett. B397 (1997) 158. [106] ALEPH Collaboration, Phys. Lett. B401 (1997) 347. [107] A. Hoang, talk at Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, Fermilab, 6-9 Nov. 1997, hep-ph/9801273, hep-ph/9801275; V. Barger, M. Berger, J. Gunion, T. Han, hep-ph/9702334; M. Berger, talk at Workshop on Particle Theory and Phenomenology: Physics of the Top Quark, Iowa State, May 1995, hep-ph/9508209.

120 [108] G. Degrassi, P. Gambino, A. Sirlin, hep-ph/9611363 (1996). [109] M. Davier and A. Hocker, Improved determination of a(M|) and the anomalous magnetic moment of the muon, hep-ph/9711308. [110] LEP Electroweak Working Group home page: http://www.cern.ch/LEPEWWG/Welcome.html. [Ill] S. Abdullin and F. Charles, hep-ph/9811402. [112] E. Accomando et al., ECFA/DESY LC Physics Working Group, Phys. Rept. 299 (1998) 1. [113] I. Hinchliffe, F.E. Paige, M.D. Shapiro, J. Soderqvist, W. Yao, Phys. Rev. D55 (1997) 5520. [114] P. Fayet, Phys. Lett. 69B (1977) 489. [115] L. Ibanez and G.G. Ross, Nucl. Phys. B368 (1992) 3; S. Lola and G.G. Ross, Phys. Lett. B314 (1993) 336; J. Ellis, S. Lola and G.G. Ross, Nucl. Phys. B526 (1998) 115. [116] For some of the earlier references, see: F. Zwirner, Phys. Lett. B132 (1983) 103; L. Hall and M. Suzuki, Nucl. Phys. B231 (1984) 419; J. Ellis et al., Phys. Lett. B150 (1985) 142; S. Dawson, Nucl. Phys. B261 (1985) 297; R. Barbieri and A. Masiero, Nucl. Phys. B267 (1986) 679. [117] J.L. Feng, J.F. Gunion and T. Han, Phys. Rev. D58 (1998) 071701. [118] D. Choudhury and S. Raychaudhuri, CERN-TH-98-222, hep-ph/9807373. [119] J. Kalinowski, R. Ruckl, H. Spiesberger and P.M. Zerwas, Phys. Lett. B406 (1997) 314. [120] For reviews, see for example: H. Dreiner, Perspectives on Supersymmetry, Ed. G.L. Kane (World Scientific, Singapore); G. Bhattacharyya, hep-ph/9709395, presented at Workshop on Physics Beyond the Standard Model, Tegernsee, Germany, 8-14 June 1997. [121] H. Dreiner and S. Lola, EE500 Workshop, Hamburg, September 1991, DESY 92-123, Part B, 707; Workshop for e+e~ collisions at TEV energies, DESY-96-123D. [122] A. Strumia, Phys. Lett. B409 (1997) 213. [123] H.-C. Cheng, J.L. Feng, and N. Polonsky, Phys. Rev. D56 (1997) 6875; Phys. Rev. D57 (1998) 152; M.M. Nojiri, D.M. Pierce, and Y. Yamada, Phys. Rev. D57 (1998) 1539. [124] R. Casalbuoni, talk given at this workshop: http://www.fi.infn.it/pub/sem.ps. [125] J. Bagger, V. Barger, K. Cheung, J. Gunion, T. Han, G.A. Ladinsky, R. Rosenfeld, C- P. Yuan, Phys. Rev. D52 (1995) 3878. [126] V. Barger, K. Cheung, T. Han, R.J.N. Phillips, Phys. Rev. D52 (1995) 3815. [127] V. Barger, M.S. Berger, J.F. Gunion, T. Han, Phys. Rev. D55 (1997) 142. [128] R. Casalbuoni, S. De Curtis, D. Dominici, A. Deandrea, R. Gatto, J.F. Gunion, hep- ph/9801243, in Proc. Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, FNAL, USA, 6-9 November 1997, Eds. S. Geer and R. Raja (AIP Conf. Proc 435, 1998).

121 [129] R. Casalbuoni, P. Chiappetta, S. De Curtis, F. Feruglio, R. Gatto, B. Mele, J. Terron, Phys. Lett. B249 (1990) 130. [130] N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Lett. B429 (1998) 263; preprint hep-ph/9807344. [131] J. Lykken, Phys. Rev. D54 (1996) 3693. [132] E. Witten, Nucl. Phys. B471 (1996) 135. [133] P. Horava and E. Witten, Nucl. Phys. B460 (1996) 506; Nucl. Phys. B475 (1996) 94. [134] I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Lett. B436 (1998) 257. [135] G. Shiu and S.-H.H. Tye, preprint hep-th/9805157; Z. Kakushadze and S.-H.H. Tye, preprint hep-th/9809147. [136] A. Pomarol and M. Quiros, preprint hep-ph/9806263. [137] K.R. Dienes, E. Dudas, T. Gherghetta, and A. Riotto, preprint hep-ph/9809406. [138] K. Benakli, preprint hep-ph/9809582. [139] I. Antoniadis, S. Dimopoulos, A. Pomarol, and M. Quiros, preprint hep-ph/9810410. [140] D. Ghilencea and G.G. Ross, preprint hep-ph/9809217. [141] L. Randall and R. Sundrum, preprint hep-th/9810155. [142] C.P. Burgess, L.E. Ibariez, and F. Quevedo, preprint hep-ph/9810535. [143] R. Sundrum, preprint hep-ph/9807348. [144] N. Arkani-Hamed, S. Dimopoulos, and J. March-Russell, preprint hep-th/9809124. [145] K. Benakli and S. Davidson, preprint hep-ph/9810280. [146] I. Antoniadis, Phys. Lett. B246 (1990) 377; I. Antoniadis, C. Munoz, and M. Quiros, Nucl. Phys. B397 (1993) 515. [147] K.R. Dienes, E. Dudas, and T. Gherghetta, Phys. Lett. B436 (1998) 55; preprint hep- ph/9806292. [148] I. Antoniadis, K. Benakli, and M. Quiros, Phys. Lett. B331 (1994) 313. [149] R. Sundrum, preprint hep-ph/9805471. [150] G.F. Giudice, R. Rattazzi, and J.D. Wells, preprint hep-ph/9811291. [151] E.A. Mirabelli, M. Perelstein, and M.E. Peskin, preprint hep-ph/9811337. [152] T. Han, J.D. Lykken, and R.-J. Zhang, preprint hep-ph/9811350. [153] J.L. Hewett, preprint hep-ph/9811356.

~~122 This work was motivated by the hypothesis that astrophysical neutrinos might have biological effects:~~

[154] J.D. Cossairt, N.L. Grossman and E.T. Marshall, Health Phys. 73 (1997) 894-898. [155] G.R. Stevenson and H.H. Vincke, Initial estimates of radiological parameters of environ- mental interest for the CERN/INFN Gran-Sasso neutrino project, CERN Internal Report TIS-RP/IR/98-13 (1998). [156] T. Rancati, Deep inelastic scattering e dose da neutrini, Scuola di Specializzazione in Fisica Sanitaria, Universita di Milano, A.A. 1997/98. [157] N.V. Mokhov and A. Van Ginneken, Muon collider neutrino radiation, to be published. [158] C.J. Johnstone and N.V. Mokhov, Shielding the muon collider interaction region, Fermilab Internal Note. [159] O.E. Krivosheev and N.V. Mokhov, New MARS and its applications, Proc. Third Work- shop on Simulating Accelerator Radiation Environments (SARE3), KEK, Tsukuba, Japan, 7-9 May 1997, KEK Proc. 97-5 (1997) 12-20. [160] B. J. King, Discussion on muon collider parameters at centre of mass energies from 0.1 TeV to 100 TeV, Proc. 6th European Particle Accelerator Conference, Stockholm, Sweden, 22- 26 June 1998 (in press, see Bruce King's Web page at http://pubweb.bnl.gov/people/bking/). [161] B.J. King, A characterisation of the neutrino-induced radiation hazard at TeV-scale muon colliders, to be published (see Bruce King's Web page at http://pubweb.bnl.gov/people/bking/). [162] C.M. Ankenbrandt et al., Status of muon collider research and development and future plans (draft), BNL-65-623, Fermilab-PUB-98/179, LBNL-41935 (1998). [163] CERN Radiation Safety Manual, Safety Code F (1996). [164] A. Skrinsky, Towards ultimate luminosity polarized muon colliders (problems and prospects), Proc. Workshop on the Physics Potential and Development of /i+/i~ colliders, AIP Conf. Proc. 441 (1997) pp. 249-264.

~~123 List of CERN Reports published in 1999~~

CERN 99-01 CERN. Geneva Russenschuck, S. [ed] Proceedings, ROXIE: Routine for the optimization of magnet X-sections, inverse field calculation and coil end design, CERN, 16-18 March 1999 CERN, 12 April 1999.-258 p

~~CERN 99-02 CERN. Geneva Autin, B; Blondel, A; Ellis, J [eds] Prospective study of muon storage rings at CERN CERN, 30 April 1999. - 144 p~~

~~CERN 99-02 ISSN 0007-8328 ISBN 92-9083-143-0~~