Electroweak and Flavor Dynamics at Hadron Colliders–II

Electroweak and Flavor Dynamics at Hadron Colliders±II

b y Estia Eichtena and Kenneth Lane

a Fermi National Accelerator Laboratory, P.O. Box 500 Batavia, IL 60510

b Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215 ABSTRACT II. SIGNATURES OF TOPCOLOR-ASSISTED

This is the second of two reports cataloging the principal sig- TECHNICOLOR

pp pp natures of electroweak and ¯avor dynamics at and collid- The development of topcolor-assisted technicolor is still at an ers. Here, we complete our overview of technicolor with a dis- early stage and, so, its phenomenology is not fully formed. Nev- cussion of signatures speci®c to topcolor-assisted technicolor. ertheless, in addition to the color-singlet and nonsinglet techni- We also review signatures of ¯avor dynamics associated with hadrons already discussed, there are three TC2 signatures that

quark and lepton substructure. These occur in excess produc- are likely to be present in any surviving model; see Refs. [1, 2, E tion rates for dijets and dileptons with high T and high invari- 3, 4, 5]:

ant mass. An important feature of these processes is that they

exhibit fairly central angular and rapidity distributions. The isotriplet of color-singlet ªtop-pionsº t arising from

(2) U (1) spontaneous breakdown of the top quark's SU chiral symmetry;

I. INTRODUCTION

The color-octet of vector bosons 8 , called ªcoloronsº, as-

This and the preceding report summarize the major signals for (3) sociated with breakdown of the top quark's strong SU dynamical electroweak and ¯avor symmetry breaking in exper- interaction to ordinary color;

iments at the Tevatron Collider and the Large Hadron Collider.

0 Z

In the preceding report (referred to below as I), we reviewed The vector boson associated with breakdown of the top (1) the technicolor and extended technicolor scenarios of dynamical quark's strong U interaction to ordinary weak hyper- electroweak and ¯avor symmetry breaking. We also discussed charge. signals for color-singlet and nonsinglet technipions, resonantly

produced via technirho and techni-omega vector mesons. In this The three top-pions are nearly degenerate. They couple to the

m =F m

t t report, we complete this discussion with a summary of the main top quark with strength t ,where is the part of the top-

quark mass induced by topcolorÐexpected to be within a few

signatures of tocolor-assisted technicolor: top-pions t and the

F ' 70 GeV t

GeV of its total massÐand t [3] is the decay

V Z

color-octet 8 and singlet of broken topcolor gauge symme- 1 tries. These are presented in section 2. This arbitrary division constant. If the top-pion is lighter than the top quark, then

has been necessitated by the length requirements of submissions

2 2 2

) (m M

: (t ! ) '

to the Snowmass '96 proceedings. In section 3 we motivate and b (1)

32m F t

discuss the main ªlow-energyº signatures of quark and lepton t E

substructure: excess productionof high- T jets and high invari-

+0:13 +0:13

(t ! W b)=0:87

It is known that B (stat.)

0:11 0:30

ant mass dileptons. Cross sections are presented for a simple

1 M 150 GeV 2

(syst.)[6]. At the level, then, .Atthe form of the contact interaction induced by substructure. We re- t

level, the lower bound is 100 GeV, but such a small branching

emphasize that the shapes of angular distributions are an impor-

! W b (pp ! tt) ratio for t would require at the Teva-

tant test for new physics as the origin of such excesses. We also

+0:63

:75 pb

tron about 4 times the standard QCD value of 4 [7].

0:68

stress the need to study the effect of other forms for the contact

! b The t decay mode can be sought in high-luminosity interactions. At the end of this report, we have provided a table t

which summarizes for the Tevatron and LHC the main processes runs at the Tevatron and with moderate luminosity at the LHC.

If ,then through ± mixing. It is also pos- t

and sample cross sections that we discussed in these two reports. t

! ts b s sible, though unlikely, that through ± mixing.

These reports are not intended to constitute a complete sur- T

M >m ! tb ! tt cc t

If ,then and or ,de-

t t

vey of electroweak and ¯avor dynamics signatures accessible at t

2m hadron colliders. We have limited our discussion to processes pending on whether the top-pion is heavier or lighter than t . with the largest production cross sections and most promising The main hope for discovering top-pions heavier than the top

signal-to-background ratios. Even for the processes we list, we quark seems to rest on the isotriplet of top-rho vector mesons,

M 2m t

.Itishardtoestimate ; it may lie near or closer to t

have not provided detailed cross sections for signals and back- t

= O (1 TeV) grounds. Signal rates depend on masses and model parame- t . They are produced in hadron collisions just as

ters; they and their backgrounds also depend strongly on de- the corresponding color-singlet technirhos (Eq. (3.1) of I). The

conventional expectation is that they decay as ,

t t tector capabilities. Experimenters in the detector collaborations t will have to carry out these studies. 1As far as we know, the rest of the discussion in this and the next paragraph has not appeared in print before. It certainly deserves more thought than has

[email protected] gone into it here. One possible starting place is the paper by Hill, Kennedy,

y [email protected] Onogi and Yu in Ref. [2].

1006

. Then, the top-pion production rates may be estimated QCD. The may also produce an excess of high invariant mass

t t

C =1 ` ` =2:91 AB

from Eqs. (3.2) and (3.5) of I with and .. It will be interesting to compare limits on contact interac- T The rates are not large, but the distinctive decays of top-pions tions in the Drell-Yan process with those obtained from jet pro-

help suppress standard model backgrounds. duction.

Z qq

Life may not be so simple, however. The t are not completely The topcolor will be produced directly in annhilation

analogous to the -mesons of QCD and technicolor because top- in LHC experiments. Because Z may be strongly coupled to

color is broken near t . Thus, for distance scales between

t so many fermions, including technifermions in the LHC's en-

and 1 GeV , top and bottom quarks do not experience a grow- ergy range, it is likely to be very broad. The development of

t t

ing con®ning force. Instead of t , it is also possible that TC2 models is at such an early stage that the couplings, its

tb bt tt

fall apart into their constituents , and .The t reso-

t width and branching fractions, cannot be predicted with con®-

b nance may be visible as a signi®cant increase in t production, dence. These studies are underway and we hope for progress on

but it won't be in t . these questions in the coming year.

V SU (3)

The 8 colorons of broken topcolor are readily pro-

duced in hadron collisions. They are expected to have a mass of III. SIGNATURES FOR QUARK AND LEPTON

g cot

1/2±1 TeV.Colorons couple with strength S to quarks of

SUBSTRUCTURE

g tan

the two light generations and with strength S to top and

bottom quarks, where tan [5]. Their decay rate is The presence of three generations of quarks and leptons, ap-

parently identical except for mass, strongly suggests that they

S V

2 2 2 2

4 cot + tan 1+ (1 m =M ) = t

V are composed of still more fundamental fermions, often called

t V 8 8 6 ªpreonsº. It is clear that, if preons exist, their strong interaction

(2) q

energy scale must be much greater than the quark and lepton

2 2

= 1 4m =M

where t . Coloronsmay then appear as res-

t V

8 masses. Long ago, 't Hooft ®gured out how interactions at high

bb tt O ( )

onances in and production. For example, the S cross energy could produce essentially massless composite fermions:

qq ! tt section for becomes the answer lies in unbroken chiral symmetries of the preons and

p con®nement by their strong ªprecolorº interactions[12]. There

s^ M i

d^ (qq ! tt)

t 8

S 2 2 2

8 followed a great deal of theoretical effort to construct a realis-

= : 2 + z

t t

dz 9^s

s M + i s^

^ tic model of composite quarks and leptons (see, e.g., Ref. [13])

8 V

8 (3) which, while leading to valuable insights on chiral gauge theo-

! tt

For completeness, the gg rate is ries, fell far short of its main goal.

In the midst of this activity, it was pointed out that the exis-

2 2 2

d^ (gg ! tt) 1+ z

t 2 2 S

9 tence of quark and lepton substructure will be signalled at en-

= (1 + z )[

2 16

dz 6^s 1 z

t ergies well below by the appearance of four-fermion ªcon-

2 2 2

) 1

(1 tactº interactions which differ from those arising in the standard

t t 2 2 2

1 9

+ ]+ (1 z ) :

+ (4)

t t

2 2 8 8

2 2

2 model[9, 10]. These interactions are induced by the exchange of

(1 z ) 1 z t

t preon bound states and precolor-gluons. The main constraint on

(3) SU (2) U (1)

A description of the search and preliminary mass limits for col- their form is that they must be SU invariant

bb orons and other particles decaying to and tt are given in because they are generated by forces operating at or above the

Ref. [8]. electroweak scale. These contact interactions are suppressed by

Colorons have little effect on the standard dijet production 1 , but the coupling parameter of the exchangesÐanalogous 0 rate. The situation may be very different for the Z boson of to the pion-nucleon and rho-pion couplingsÐisnot small. Thus,

3 (1)

the broken strong U interaction. In Ref. [4] a scenario for the strength of these interactions is conventionally taken to be

topcolor was developed in which it is natural that couples . Compared to the standard model, contact interac-

2 2

s= ^ s= ^ EW

strongly to the fermions of the ®rst two generations as well as tion amplitudes are then of relative order S or .

= s^

those of the third. The probably is heavier than the colorons, The appearance of 1 and the growth with make contact-

M =13TeV

roughly Z ±. Thus, at subprocess energies well interaction effects the lowest-energy signal of quark and lepton

M Z below Z , the interaction of with all quarks is described substructure. They are sought in jet production at hadron and

by a contact interaction, just what is expected for quarks with lepton colliders, Drell-Yan production of high invariant mass

+ + +

e !

substructure at a scale of a few TeV. This leads to an excess of lepton pairs, Bhabha scattering, e and [14], E

jets at high T and invariant mass[9, 10]. An excess in the jet- atomic parity violation[15], and polarized Mùller scattering[16].

E = 1600 GeV

T spectrum consistent with has been reported Here, we concentrate on jet production and the Drell-Yan pro- by the CDF Collaboration[11]. It remains to be seen whether cess at hadron colliders. it is due to topcolor or any other new physics. As with quark The contact interaction most used so far to parameterize lim-

substructure, the angular and rapidity distributions of the high- its on the substructure scale is the product of two left-handed

E Z

T jets induced by should be more central than predicted by electroweak isoscalar quark and lepton currents. Collider exper-

2 iments can probe values of in the 2±5 TeV range (Tevatron) to

We thank John Terning for inspiring this discussion of t decays.

3This interaction differentiates between top and bottom quarks, helping the the 15±20 TeV range (LHC; see Refs. [10, 17]). If is to be this former develop a large mass while keeping the latter light. low, the contact interaction must be ¯avor-symmetric, at least

1007

i i

S =2 g =2 T Q sin = sin 2 g = Q tan

i i W W i W

for quarks in the ®rst two generations, to avoid large and 3 , ,

L R

l l

B =2

+ sin = sin 2 g =2 g = tan z (^s)=

and, possibly, d neutral current interactions. We write

W W

, W and

L R

s=(^s M ) `

it as ^ . The angular distribution of the relative to the

4 incoming quark is an important probe of the contact interac-

L = J J where

LL L

2 tion's chiral structure. Measuring this distribution is easy in a

pp 3

3 collider such as the Tevatron since the hard quark almost al-

X X

J = q q + F ` ` :

aiL ` iL iL

aiL (5) ways follows the proton direction. If the scale is high so that

=1 a=1 i parton collisions revealing the contact interaction are hard, the

quark direction can also be determined with reasonable con®-

= 1 a; b =1;2;3 i; j =1;2;3

Here, ; labels color; labels

qq dence in a pp collider. At the LHC, the quark in a collision

the generations, and the quark and lepton ®elds are isodoublets, p

s=s 1=20

with ^ is harder than the antiquark, and its direc-

q =(u ;d ) ` =( ;e ) F

ai ai i i i ` ai and The real factor is inserted

to allow for different quark and lepton couplings, but it is ex- tion is given by the boost rapidity of the dilepton system, at least

O (1 TeV )

1 75% of the time. The charges of muons can be well- (1)

pected to be O . The factor of in the overall strength of the 2 interaction avoids double-counting interactions and amplitudes. measured even at very high luminosity in the detectors being de- The color-averaged jet subprocess cross sections, modi®ed for signed for the LHC. These two ingredients are needed to insure

0 a good determination of the angular distribution [17].

the interaction , are given in leading order in S by (these LL formulas correct errors in Ref. [10]) It is important to study the effects of contact interactions with

chiral, ¯avor and color structures different from the one in Eq. 5.

d^ (q q ! q q ) d^ (q q ! q q )

i i i i i i i i

^ Such interactions can give rise to larger (or smaller) cross sec-

= = A (^s; t; u^);

dz dz 2^s

tions for the same because they have more terms or because

d^ (q q ! q q )

i i i

i they interfere more ef®ciently with the standard model. Thus, it

= A (^u; t; s^);

dz 2^s

will be possible to probe even higher values of for other struc-

d^ (q q ! q q )

i j j

i tures. Other forms can also give rise to ®nal states. Search-

= A (^s; t; u^);

2^s

dz ing for contact interactions in these modes is more challenging

` `

d^ (q q ! q q )

j i j

i than in , but it is very useful for untangling ¯avor and chi-

= A (t; s;^ u^);

2^s

dz ral structures [17]. Events are selected which contain a single

p E

d^ (q q ! q q ) ^ (q q ! q q ) T T

d high- charged lepton, large missing , and little jet activ-

i j i j i j i j

= = A (t; u^; s^)

2 ity. Even though the parton c.m. frame cannot be found in this

dz dz 2^s

2 2 2 2 2

^ case, it is still possible to obtain information on the chiral nature

4 u^ +^s 2s^ t +^s

with A (^s; t; u^) = +

j + j j j

S `

of the contact interaction by comparing the ` and ra-

^ ^

9 u^ 3

t tu^

pidity distributions of the high- T leptons. For example, if the

2 2 2

s^ s^ 8 s^ 8

u ! `

angular distribution in the process d between the in-

+ + ; +

2 4

9 u^ 3

d ` (1 + cos ) j j

coming -quark and the outgoing is ,then `

2 2 2

4 u^ u + t

^ is pushed to larger values because the -quark is harder than the

and A (^s; t; u^) = + :

2 (6)

u ` 4

2 -quark and the tends to be produced forward. Correspond-

9 s^

ud ! ` j j

ingly, in ,the ` distribution would be squeezed to

2 For this LL-isoscalar interaction, the interference term (= ) smaller values.

in the hadron cross section is small and the sign of is not very important. Interference terms may be non-negligible in contact interactions with different chiral, ¯avor, and color structures. In IV. CONCLUSIONS AND all cases, the main effect of substructure is to increase the pro- ACKNOWLEDGEMENTS portion of centrally-produced jets. If this can be seen in the jet Many theorists are convinced that low-energy supersymme- angular distribution, it will be important for con®rming the pres- try is intimately connected with electroweak symmetry breaking 4

ence of contact interactions. and that its discovery is just around thecorner[18]. However, the

q q ! i

The modi®ed cross sections for the Drell-Yan process i vast body of experimental evidence favors no particular exten-

+ `

` is sion of the standard model. Therefore, all plausible approaches

+ 2

^ must be considered. Detectors must have the capabilityÐand

d^ (q q ! ` ` ) u^ t

i i

= A (^s) + B (^s) ; i

i experimenters must be preparedÐto discover whatever physics

6^s s^ s^ dz is responsiblefor electroweak and ¯avor symmetry breaking. To (7) this end, we have summarized the principal signatures for tech- where

nicolor, extended technicolorand quark-leptonsubstructure. Ta-

2 2

F s^

i l l i ble 1 lists sample masses for new particles and their production

g z(^s) Q g A (^s) = g z(^s) + Q g

i i i

L L R R

rates at the Tevatron and LHC. We hope that this summary is use-

2 ful to future in-depth studies of strong TeV-scale dynamics.

i l i l

B (^s) = Q g g z(^s) + Q g g z(^s) ;

i i

i (8) We are especially grateful to John Womersley and Robert Har-

L R R L ris for encouragement, advice and thoughtful readings of the 4This is true regardless of the dynamical origin of the contact interaction. manuscript. We are indebted to those members of CDF and Dé

1008 M. Tanabashi and K. Yamawaki, Phys. Lett. 221B, 177 (1989); Table I: Sample cross sections for technicolor signatures at the Mod. Phys. Lett. A4, 1043 (1989); W. A. Bardeen, C. T. Hill and Tevatron and LHC. Cross sections may vary by a factor of 10 M. Lindner, Phys. Rev. D41, 1647 (1990).

for other masses and choices of the parameters. K -factors of [2] C. T. Hill, Phys. Lett. 266B, 419 (1991) ;S. P. Martin, 1.5±2 are expected, but not included. Signal over background

Phys. Rev. D45, 4283 (1992); ibid D46, 2197 (1992);

S=B N =4

rates are quoted as . TC in all calculations; cross sec- Nucl. Phys. B398, 359 (1993); M. Lindner and D. Ross,

N F = F =3=82GeV

tions generally grow with TC . was Nucl. Phys. B370, 30 (1992);R. BÈonisch, Phys. Lett. 268B,

F = 50 GeV

used. T used. Cross section is integrated over 394 (1991);C. T. Hill, D. Kennedy, T. Onogi, H. L. Yu,

M =90110 GeV F = 50 GeV m = 175 GeV

±. T and b b Phys. Rev. D47, 2940 (1993).

were used. The greatly increased LHC cross section is due to the [3] C. T. Hill, Phys. Lett. 345B, 483 (1995). 4 rapid growth of gluons at small-x. Cross sections for a multi-

[4] K. Lane and E. Eichten, Phys. Lett. B352, 382 (1995) ;K. Lane,

scale model with 250 GeV T and 200 GeV intermediate

p Phys. Rev. D54, 2204 (1996).

(E )=E = 100%= E states. Jet energy resolution of is as-

[5]C.T.HillandS.Parke,Phys.Rev.D49, 4454 (1994);Also see sumed and cross sections integrated over about resonance

2 K. Lane, Phys. Rev. D52, 1546 (1995);We thank D. Kominis for

cos < j j < 2:0

peak. Jet angles are limited by and j (Teva-

3 corrections to a numerical errors in both papers. 7 tron) or 1.0 (LHC). 6 Cross sections per channel are quoted.

p [6] J. Incandela, Proceedings of the 10th Topical Workshop on

tan = 2=3

S was used, corresponding to a critical top-

8 Proton-Antiproton Collider Physics, Fermilab, edited R. Raja and color couplingstrength. Estimated reaches in dijet and dilep- J. Yoh, p. 256 (1995). ton production are for the indicated luminosities. [7] S. Catani, M. Mangano, P. Nason and L. Trentadue, CERN-

Process TH/96-21, hep-ph/9602208 (1996).

[S ampl eM ass(GeV )]

eV LHC T (pb) (pb)

[8] R. M. Harris, Proceedings of the 10th Topical Workshop on

! W

1 L T

T Proton-Antiproton Collider Physics, Fermilab, edited R. Raja and

[220( ) 100( )] 5 35

1 T

T , J. Yoh, p. 72(1995).

1 T T

T [9] E.J.Eichten,K.LaneandM.E.Peskin,Phys.Rev.Lett.50,811

[220( ) 100( )] 5 25

1 T

T , (1983)

0 2

gg ! ! bb T

5 [10] E. Eichten, I. Hinchliffe, K. Lane and C. Quigg,

300=5000 7000=10

[100] Rev. Mod. Phys. 56, 579 (1984).

gg ! ! tt T

[11] F. Abe, et al., The CDF Collaboration, Phys. Rev Lett 77, 438

[400] 3=3 2000=600

4 (1996).

gg !

T T

0:2 600

[100] [12] G. 't Hooft, in Recent Developments in Gauge Theories, edited by

5 G. 't Hooft, et al. (Plenum, New York, 1980).

! jet jet

T 8

4 5

[250( )] 700=5000 1:5 10 =1:5 10 8

T [13] S. Dimopoulos, S. Raby and L. Susskind, Nucl. Phys. B173,

)] 10=40 2000=6000

[500( 208 (1980);M. E. Peskin, Proceedings of the 1981 Symposium

T 8

6 on Lepton and Photon Interactions at High Energy, edited by

T 8 T 8 T 8

W. P®el, p. 880 (Bonn, 1981) ;I. Bars, Proceedings of the Ren-

[550( ); 250( )] 2 2000

T 8 T 8

6 contres de Moriond, Quarks, Leptons and Supersymmetry, edited

T 8

L LQ

Q by Tranh Than Van, p. 541 (1982).

[550( ); 200( )] 2 1000

T 8

QL 7

[14] For current collider limits on substructure, see Ref. [11] and the

V ! tt

8 Review of Particle Physics, Particle Data Group, Phys. Rev. D54,

8=3 100=600

[500] 1, (1996). 8

reach (in TeV)

1 1

[15] J. Rosner, Phys. Rev. D53, 2724 (1996), and references therein.

[5(TEV ); 20(LH C )] 10 fb 100 fb [16] K. Kumar, E. Hughes, R. Holmes and P. Souder, ªPrecision Low Energy Weak Neutral Current Experimentsº, Princeton Univer- who discussed their work with us and otherwise helped us pre- sity (October 30, 1995), to appear in Modern Physics Letters A. pare our review: Tom Baumann, John Huth, Kaori Maeshima, [17] GEM Technical Design Report, Chapter 2.6, GEM TN-93-262, Wyatt Merritt and Jorge Troconiz. Finally, we thank Dimitris SSCL-SR-1219; submitted to the Superconducting Super Col- Kominis for discussions on topcolor-assisted technicolor and for lider Laboratory, (April 30, 1993);K. Lane, F. Paige, T. Skwar- catching several errors. nicki and J. Womersley, Simulations of Supercollider Physics, Boston University preprint BUHEP-94-31, Brookhaven preprint BNL-61138, hep-ph/9412280 (1994), to appear in Physics Re- V. REFERENCES ports. [1] Y. Nambu, in New Theories in Physics, Proceedings of the [18] See, e.g., P. Ramond, et al., Letter to the Director of Fermilab XI International Symposium on Elementary Particle Physics, and the Co-Spokespersons of the CDF and Dé Collaborations, Kazimierz, Poland, 1988, edited by Z. Adjuk, S. Pokorski (1994). and A. Trautmann (World Scienti®c, Singapore, 1989); Enrico Fermi Institute Report EFI 89-08 (unpublished); V. A. Miransky,

1009