Contents

Electroweak Symmetry Breaking and New Physics at the TeV Scale 153

1 Introduction 153

2 Weakly-Coupled Higgs Bosons 156

3 Low Energy Supersymmetry: Implications of Models 163

4 Low Energy Supersymmetry: Phenomenology 166

5 Strongly Coupled ESB Sector: Model-

Independent Approaches 170

6 Strongly Coupled ESB Sector: Implications of Models 172

7 New Gauge Bosons 173

8 New particles and Interactions 176

9 Anomalous Gauge Boson Couplings 179

10 Top Quarks as a Window to Electroweak

Symmetry Breaking 182

11 Virtual E�ects of New Physics 184

12 Experimental Issues at Hadron Colliders 186

13 Experimental Issues at e+e� Linear Colliders 187

14 Conclusions 189

References 190

152

Electroweak Symmetry Breaking and New Physics at the TeV Scale

Tim Barklow

Stanford Linear Accelerator Center, Stanford, CA 94309

Sally Dawson

Brookhaven National Laboratory, Upton, NY 11973

Howard E. Haber

University of California, Santa Cruz, CA 95064

James Siegrist

Lawrence Berkeley Laboratory, Berkeley, CA 94720

Working Group Members

H. Aihara, Lawrence Berkeley Laboratory S.P. Martin, University of Michigan

H. Baer, Florida State University H. Murayama, Lawrence Berkeley Laboratory

U. Baur, SUNY, Bu�alo J. Ng, TRIUMF, Vancouver BC

R.S. Chivukula, Boston University S.J. Parke, Fermilab

M. Cveti�c, University of Pennsylvania M.E. Peskin, Stanford Linear Accelerator Center

A. Djouadi, University of Montreal H. Pois, University of California, Davis

M. Drees, University of Wisconsin T.G. Rizzo, Stanford Linear Accelerator Center

S. Errede, University of Illinois R. Rosenfeld, Boston University

S. Godfrey, Carleton University E.H. Simmons, Boston University

M. Golden, Harvard University A. Stange, Brookhaven National Laboratory

J.F. Gunion, University of California, Davis T. Takeuchi, Fermilab

T. Han, University of California, Davis X. Tata, University of Hawaii

J.L. Hewett, Stanford Linear Accelerator Center J. Terning, Boston University

C.T. Hill, Fermilab S. Thomas, Stanford Linear Accelerator Center

D. London, University of Montreal S. Willenbrock, University of Illinois

T.W. Markiewicz,Stanford Linear Accelerator Center D. Zeppenfeld, University of Wisconsin

1 Introduction

The development of the Standard Model of particlephysics is a remarkable success story. Its many facetshave been tested at present day accelerators; no signif-icant unambiguous deviations have yet been found. Insome cases, the model has been veri�ed at an accuracyof better than one part in a thousand. This state of af-fairs presents our �eld with a challenge. Where do we gofrom here? What is our vision for future developmentsin particle physics? Are particle physicists' recent suc-cesses a signal of the �eld's impending demise, or do reallong-term prospects exist for further progress? We assertthat the long-term health and intellectual vitality of par-ticle physics depends crucially on the development of anew generation of particle colliders that push the energy

frontier by an order of magnitude beyond present capa-bilities. In this report, we address the scienti�c issuesunderlying this assertion.

Despite the success of the Standard Model as a de-scription of the properties of elementary particles, it isclear that the Standard Model is not a fundamental the-ory. Apart from any new physics phenomena that mightlie beyond the Standard Model, one knows that the Stan-dard Model neglects gravity. A more complete theory ofelementary particle interactions (including gravity) con-tains the Planck scale (MP ' 1019 GeV) as its basicenergy scale. The Standard Model at best is a good low-energy approximation to this more fundamental theoryof particle interactions, valid in a limited domain of \low-energies" of order 100 GeV and below. In order to extend

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the Standard Model to higher energies, one must addressthree basic questions.

1. What is the complete description of the e�ective the-

ory of fundamental particles at and below the elec-

troweak scale?

In the Standard Model with one physical Higgsscalar, the scale of electroweak symmetry breaking ischaracterized by v = 246 GeV, the magnitude of theHiggs vacuum expectation value. More complicatedmodels of particle physics can be easily constructed whichclosely approximate the Standard Model at present dayenergies, but have a much richer spectrum in the massrange above 100 GeV and below a few TeV (henceforthreferred to as the TeV scale). If one wishes to extrapolatephysics from the electroweak scale and eventually deducethe nature of physics near the Planck scale, one mustknow the complete structure of the particle theory at theelectroweak scale. The Standard Model possesses threegenerations of quarks and leptons (and no right-handedneutrinos) and an SU(3)�SU(2)�U(1) gauge group. Isthat all? Might there be additional particles that popu-late the TeV scale? Some possibilities include:

(a) an extended electroweak gauge group (e.g., ex-tra U(1) factors, left-right (LR) symmetry as inSU(2)L�SU(2)R�U(1) models, etc.);

(b) new fermions (e.g., a fourth generation, mirrorfermions, vector-like fermions, massive neutrinos,etc.);

(c) new bosons (CP-odd neutral and charged scalars inmodels with extended Higgs sectors, Goldstone orpseudo-Goldstone bosons, other exotic scalars, lep-toquarks, vector resonances, etc.).

Clearly, in order to extrapolate our particle theories tohigh energy with any con�dence, one must know the com-plete TeV-scale spectrum.

2. What is the mechanism for electroweak symmetry

breaking?

The Standard Model posits that electroweak symme-try breaking (ESB) is the result of the dynamics of anelementary complex doublet of scalar �elds. The neu-tral component of the scalar doublet acquires a vacuumexpectation value and triggers ESB; the resulting parti-cle spectrum contains three massive gauge bosons andthe photon, massive quarks and charged leptons (andmassless neutrinos) and a physical Higgs scalar. How-ever, if one attempts to embed the Standard Model ina fundamental theory with a high energy scale (MP ),then the masses of elementary scalars naturally assumevalues of order the high energy scale. This is due tothe quadratic sensitivity of squared scalar masses to thehigh-energy scale of the underlying fundamental theory.

In contrast, theoretical considerations (e.g. unitarity) re-quire the mass of the Standard Model Higgs boson to beof order the electroweak scale. To accomplish this, onehas three choices:

(a) \Unnaturally" adjust the parameters of the high-energy theory (a �ne tuning of 34 orders of mag-nitude in the scalar squared mass parameter is re-quired) to produce the required light elementaryscalar �eld.

(b) Invoke supersymmetry to cancel quadratic sensitiv-ity of the scalar squared masses toMP . Electroweaksymmetry breaking is triggered by the dynamics ofa weakly-coupled Higgs sector.

(c) Elementary Higgs scalars do not exist. A Higgs-likescalar state (if it exists) would reveal its compositenature at the TeV scale, where new physics beyondthe Standard Model enters. Electroweak symme-try breaking is triggered by non-perturbative strongforces.

In order to implement (b), one must �rst note thatsupersymmetry is not an exact symmetry of nature (oth-erwise, all known particles would have equal-mass su-persymmetric partners). If supersymmetry is to explainwhy the Higgs boson mass is of order the electroweakscale, then supersymmetry-breaking e�ects which splitthe masses of particles and their super-partners must beroughly of the same order as the electroweak scale. Thus,if supersymmetry is connected with the origin of ESB,one expects to discover a new spectrum of particles andinteractions at the TeV scale or below. In addition, suchmodels of \low-energy" supersymmetry are compatiblewith the existence of weakly-coupled elementary scalarswith masses of order the ESB scale. No direct exper-imental evidence for the supersymmetric particle spec-trum presently exists. But there is tantalizing indirectevidence. Starting from the known values of the SU(3),SU(2), and U(1) gauge couplings at mZ and extrapo-lating to high energies, one �nds that the three gaugecouplings meet at a single point if one includes the ef-fects of supersymmetric particles (with masses at or be-low 1 TeV) in the running of the couplings. Uni�cationof couplings then takes place at around 1016 GeV, only afew orders of magnitude below MP . The three gaugecouplings do not meet at a single point if only Stan-dard Model particles contribute to the running of thecouplings. This could be a hint for low-energy super-symmetry, and suggests that the theory of fundamentalparticles remains weakly coupled and perturbative all theway up to energies near MP .

New physics is also invoked to explain the origin ofelectroweak symmetry breaking in choice (c). For ex-ample, in technicolor models (which make use of themechanism analogous to the one that is responsible forchiral symmetry breaking in QCD), electroweak symme-try breaking occurs when pairs of technifermions con-

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dense in the vacuum. One then identi�es a new scale,�ESB ' 4�v � O(1 TeV), where new physics beyondthe Standard Model must enter. Other approaches, suchas e�ective Lagrangian descriptions of the strongly in-teracting Higgs sector, preon models, top-mode conden-sate models, composite Higgs models, etc., also fall intothis category. Unfortunately, due to the presence of non-perturbative strong forces, it is often di�cult to makereliable detailed computations in such models. More-over, phenomenological di�culties inherent in the sim-plest examples often require additional structure (e.g., anextended technicolor sector is needed in technicolor mod-els to generate fermion masses). Unfortunately, a com-pletely phenomenologically viable fundamental model ofstrongly-coupled ESB has not yet been constructed.

There is one important theoretical lesson that oneshould draw from the above remarks. Namely, the na-

ture of ESB dynamics must be revealed at or below the

1 TeV energy scale. This is not a matter of conjec-ture. The relevant scale is implicitly built into the Stan-dard Model through v � 2mW =g. If one wishes to takethe most conservative approach, one would say that thestudy of the TeV scale must reveal the Higgs boson,but with no guarantees of anything beyond. However,if one takes the naturalness argument seriously, it fol-lows that the study of the TeV scale must reveal a newsector of physics beyond the Standard Model responsi-ble for ESB dynamics|either a super-particle spectrumor a new strongly-interacting sector of fermions, scalars,and/or vector resonances.

3. What is the origin of the Standard Model parame-

ters?

I.I. Rabi asked the famous question concerning theunexpected discovery of the muon: \Who ordered that?!"In the context of the Standard Model, we ponder thegeneralizations of Rabi's question:(a) Why are there three generations? [Or { what is the

origin of avor?](b) Where do the quark and lepton masses come from?

[Or { what is the origin of the fermion mass matri-ces?]

(c) What is the origin of CP-violation? [Or { is thephase in the Cabibbo-Kobayashi-Maskawa (CKM)mass matrix the only source of CP-violation? andwhy is �QCD , which would give rise to CP-violationfrom the strong interactions, so small?]

Note that although the minimal supersymmetric exten-sion of the Standard Model addresses the origin of elec-troweak symmetry breaking, it provides little insight intoany of the above questions. In fact, one would simply addyet another question:(d) What is the origin of the (soft)-supersymmetry-

breaking parameters that characterize the model oflow-energy supersymmetry?

In contrast to the problem of ESB discussed above,the Standard Model does not provide any clues as to theenergy scale responsible for addressing the origin of theStandard Model parameters (or a supersymmetric exten-sion thereof). The relevant energy scale could lie any-where from 1 TeV to MP . For example, in conventionaltheories of low-energy supersymmetry, the origin of theStandard Model and supersymmetric parameters lies ator near the Planck scale. In contrast, theories of extendedtechnicolor typically attempt to solve the avor problemat energy scales below 100 TeV. The latter approach ismore ambitious; perhaps this is one reason why no com-pelling model of this type has been constructed. Never-theless, any model of avor and fermion masses requiresa de�nite framework for electroweak symmetry breaking.Thus, the elucidation of TeV-scale physics will have sig-ni�cant rami�cations for our understanding of physics ateven higher energies.

Other future particle physics experiments may alsoaddress some of these issues. B Factories will thoroughlytest the CKM-parametrization of CP-violation. Any ev-idence for new sources of CP-violation would constitutephysics beyond the Standard Model. The next genera-tion of neutrino mixing and mass experiments will try toverify recent experimental hints for massive neutrinos.If massive neutrinos are con�rmed, then the StandardModel will require an extension. The simplest possi-bility is to include right-handed neutrino states. Ma-jorana mass terms for the right-handed neutrinos areSU(2)�U(1) conserving and therefore constitute a com-pletely new energy scale (MR) characterizing the ex-tended Standard Model. At present,MR is undeterminedand can lie anywhere between the electroweak scale andMP . If MR � mZ , then the e�ect of this new scale willbe simply to add the neutrino mass and mixing param-eters to the list of Standard Model parameters whoseorigin will be di�cult to discern directly from particlephysics experiments in the foreseeable future.

In this sense, the search for electroweak symmetrybreaking presents the unique guarantee|the dynamicsthat generates ESB must be revealed by the next gener-ation of colliders that can directly explore the TeV scale.Thus, it is crucial to explore thoroughly the TeV energy

scale in order to elucidate the dynamics of electroweak

symmetry breaking and the associated fundamental par-

ticle spectrum. This program must be a primary focus of

particle physics research in the long-term future plans of

the �eld.

In this report, we explore the capabilities of the ap-proved future facilities and a variety of hypothetical fu-ture machines, summarized in Table 1. We have alsobegun to study the physics opportunities at more specu-lative future colliders, such as a 60 TeV hadron supercol-lider (which would supersede the LHC) and a multi-TeV�+�� collider, although the overall capabilities of these

155

machines have yet to be addressed in a comprehensivefashion.

Table 1:

Name Typeps Yearly

RLdt

Approved Projects

LEP 2 e+e� � 190 GeV 150 pb�1

Tevatron (Main

Injector) p�p 2 TeV 1 fb�1

LHC pp 14 TeV 10{100 fb�1

Tevatron Upgrades (under consideration)

TeV� p�p 2 TeV 10 fb�1

DiTevatron p�p 4 TeV 20 fb�1

e+e� Linear Collider

JLC, NLC, TESLA e+e� y 0.5{1.5 TeV 50{200 fb�1

(y with e ; ; e�e� options)

In this report, we do not directly address the origin ofthe Standard Model parameters. Nor do we address thepossibility that new and interesting physics beyond theStandard Model might populate the energy interval abovethe TeV scale. We focus directly on TeV-scale physics ac-cessible to the next generation of colliders. Namely, weexamine the requirements for completing the TeV-scaleparticle spectrum, and for unravelling the dynamics ofelectroweak symmetry breaking. Particularly in the lat-ter case, we expect that future colliders will discover newphysics beyond the Standard Model (BSM) associatedwith this dynamics. Ten ESB&BSM subgroups were es-tablished to address these issues. Two additional sub-groups were added to examine experimental issues asso-ciated with the search for ESB&BSM physics at futurehadron and e+e� colliders, respectively. Conveners of thetwelve subgroups prepared executive summaries whichform the basis of this document. More detailed exposi-tions will be published separately in Ref. [1], which willalso contain a more comprehensive list of references.

The subgroups and their conveners are listed below.Three subgroups addressed the case of weakly-coupledESB dynamics:

� Weakly-Coupled Higgs Bosons (J.F. Gunion, A.Stange, and S. Willenbrock)

� Low-Energy Supersymmetry|Implications of Mod-els (M. Drees, S.P. Martin, and H. Pois)

� Low-Energy Supersymmetry Phenomenology (H.Baer, H. Murayama, and X. Tata)

Two subgroups addressed the case of strongly-coupledESB dynamics:

� Strongly-Coupled ESB Sector|Model IndependentStudy (M. Golden and T. Han)

� Strongly-Coupled ESB Sector|Implications of Mod-els (R.S. Chivukula, R. Rosenfeld, E.H. Simmons,and J. Terning)

Two subgroups addressed the question of identifying theinteractions and full spectrum of the TeV-scale particletheory:

� New Gauge Bosons Beyond the W� and Z (M.Cveti�c and S. Godfrey)

� New Particles and Interactions (A. Djouadi, J. Ngand T.G. Rizzo)

Three subgroups addressed the search for ESB&BSMphysics via precision measurements of Standard Modelprocesses:

� Anomalous Gauge Boson Couplings (H. Aihara, U.Baur, D. London and D. Zeppenfeld)

� Top-Quarks as a Window to Electroweak SymmetryBreaking (S.J. Parke, C.T. Hill and M.E. Peskin)

� Virtual E�ects of New Physics (J.L. Hewett, T.Takeuchi, and S. Thomas)

Two subgroups focussed on the interplay of ESB&BSMphysics and detector and machine issues for future col-liders:

� Experimental Issues in the Search for ESB&BSM atFuture Hadron Colliders (S. Errede and J. Siegrist)

� Experimental Issues in the Search for ESB&BSMat Future e+e� Colliders (T. Barklow and T.W.Markiewicz)

2 Weakly-Coupled Higgs Bosons

2.1 The Standard Model and MSSM Higgs Sectors [2]

In the Standard Model (SM), the electroweak symme-try is broken by an elementary weak doublet of scalar�elds, whose neutral component acquires a non-zero vac-uum expectation value. This model predicts the exis-tence of a single CP-even neutral scalar called the Higgsboson, HSM , of unknown mass but with �xed couplingsto other particles proportional to their masses. This isthe minimal model of electroweak symmetry breaking.Detailed studies of the phenomenological pro�le of HSM

are important, since they provide signi�cant benchmarksfor any experimental search for electroweak symmetrybreaking.

The underlying physics responsible for electroweaksymmetry breaking is only weakly constrained bypresent-day experimental data. Thus, in the search forelectroweak symmetry breaking, one must be open tomore complicated possibilities. For example, it is easyto generalize the minimal Higgs model by simply addingadditional scalar doublets. Models of this type possessadditional CP-even neutral scalars, new CP-odd neutralscalars, and charged scalars. One of the simplest exten-sions of the SM Higgs sector is the two-Higgs-doublet

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model (with a CP-invariant scalar potential). The scalarspectrum of this model contains two CP-even neutralscalars, h0 and H0 (with mh0 � mH0 ), one CP-odd neu-tral scalar, A0, and a charged Higgs pair, H�. The im-portance of this model will be clari�ed below.

In Section 1, a theoretical overview was presentedof the possible mechanisms that could be responsible forelectroweak symmetry breaking. The Standard Modelwith its minimal Higgs sector or with an extended Higgssector (as described above) is theoretically unsatisfac-tory, since there is no \natural" way of understandingthe origin of the electroweak symmetry breaking scale.Two generic solutions to this theoretical problem havebeen put forward. In the �rst solution, the StandardModel is extended to include supersymmetric partners.In the second solution, new strongly-interacting forcesare invoked, whose dynamics are responsible for trigger-ing electroweak symmetry breaking. In the former case,the Higgs bosons are elementary weakly-coupled scalars,while in the latter case, any physical scalar state is proba-bly strongly-coupled and composite. The supersymmet-ric approach is treated in Sections 3 and 4, while thestrongly-coupled scalar sector is considered in Sections 5and 6.

The focus of this section is the search for weakly-coupled elementary Higgs bosons. In the StandardModel, the Higgs self-coupling is proportional to thesquare of the Higgs mass. For Higgs masses below(roughly) 700 GeV, HSM is a weakly-coupled scalar. Insupersymmetric models, the Higgs bosons are also ele-mentary and weakly-coupled. Moreover, as reviewed inSection 3, the Higgs sector of the minimal supersymmet-ric extension of the Standard Model (MSSM) consists oftwo scalar doublets (interacting via a CP-conserving po-tential). Thus, the MSSM Higgs spectrum consists ofh0, H0, A0, and H�, introduced above. As a result, thephenomenology of this Higgs sector is particularly impor-tant, since it introduces new kinds of Higgs phenomenathat can be observed in future experiments, while beinga theoretically well-motivated model for the scalar sectorassociated with electroweak symmetry breaking.

This section considers the prospects for the discov-ery of weakly-coupled Higgs bosons at present and fu-ture colliders. Both the SM Higgs boson, HSM , and thescalars of the MSSM Higgs sector are considered. Someaspects of the phenomenology of h0, H0, A0, and H�

do not strongly depend on the fact that they arise ina supersymmetric model. However, the general param-eter space of an arbitrary two-Higgs doublet model isquite large (with four independent mass parameters andat least two other additional dimensionless parameters).In contrast, the two-doublet Higgs sector of the MSSMpossesses numerous relations among Higgs masses andcouplings due to the underlying supersymmetry. In par-ticular, the MSSM tree-level Higgs masses and couplings

are determined in terms of two free parameters: mA0

and tan� � v2=v1 [where v2 (v1) is the vacuum expec-tation value of the Higgs �eld that couples to up-type(down-type) fermions]. One remarkable consequence ofsupersymmetry is that the mass of the lightest CP-evenneutral scalar, h0, is bounded from above by a massvalue of order mZ . However, in obtaining the precise up-per bound, there are important radiative corrections thatcannot be neglected. Through the radiative corrections,the Higgs masses also acquire dependence on the detailsof the MSSM spectrum. The most important piece ofthese corrections depends primarily on the masses of thetop-quark (taken here to be mt = 175 GeV) and its su-persymmetric partners [3]. To be conservative, in thissection the e�ects of the radiative corrections have beenmaximized by assuming that all supersymmetric parti-cle masses (and mass mixing parameters) are of order1 TeV. In this case, the light CP-even Higgs boson massis bounded by mh0 � mmax

h0 ' 120 GeV. The followingproperties of the MSSM Higgs sector are noteworthy. IfmA0 � mZ , then mA0 ' mH0 ' mH� (in addition, iftan � � 1 then mh0 ' mmax

h0 ). Moreover, the couplingsof h0 to fermions and gauge bosons are indistinguishablefrom those of the Standard Model Higgs boson, whilethe couplings H0W+W�, H0ZZ and ZA0h0 are severelysuppressed. Finally, assuming tan � > 1, the couplingsof A0 and H0 to b�b and �+�� (t�t) are enhanced (sup-pressed). In contrast, for the case mA0 <� O(mZ ) andtan � > 1, A0 and h0 exhibit the latter coupling pat-tern to fermions. The couplings h0W+W�, h0ZZ andZA0H0 are severely suppressed, while the H0 couplingsto fermions and gauge bosons are SM-like.

We now outline the capabilities of present and pro-posed future colliders to search for the SM Higgs bosonand the MSSM Higgs bosons [2]. The SM Higgs discov-ery limits for the most useful discovery modes are sum-marized in Table 2. The corresponding MSSM Higgsdiscovery limits are summarized in Table 3. For b-taggedmodes, a tagging e�ciency of 30% and purity of 1% areassumed. Since the MSSM Higgs discovery limits arerather complex, additional information is provided hereto assist the reader in interpreting the results presentedin Table 3. The MSSM Higgs sector is most convenientlyparametrized in terms of mA0 and tan �. All values ofmA0 � 1000 GeV and 1 � tan � � 60 have been sur-veyed (as preferred in the MSSM). There is also somedependence of the discovery limits on the radiative cor-rections, the main e�ect of which is to increase the massof h0 above its tree-level value. The discovery regions ofTable 3 have been obtained assuming that the e�ects ofthe radiative corrections are maximal, as noted above.

A few examples are now given to clarify the meaningof the discovery regions presented in Table 3. At LEP 2atps = 176 GeV and 500 pb�1 integrated luminosity,

either h0 or A0 (or both) can be discovered via e+e� !157

Table 2: Standard Model Higgs boson discovery modes. All masses are speci�ed in GeV.

Machine (ps;RL dt) Mode Discovery Region

LEP 1 e+e� ! Z�HSM mHSM<� 65

LEP 2, (176 GeV, 500 pb�1) e+e� ! ZHSM mHSM<� 80

LEP 2, (190 GeV, 500 pb�1) e+e� ! ZHSM mHSM<� 95

Tevatron, (2 TeV, 5 fb�1) p�p!WHSM ; HSM ! b�b mHSM<� 60� 80

TeV�, (2 TeV, 30 fb�1) p�p!WHSM ; HSM ! b�b mHSM<� 95

p�p!WHSM ; HSM ! �+�� 110 <� mHSM<� 120

DiTeV, (4 TeV, 30 fb�1) p�p!WHSM ; HSM ! b�b mHSM<� 95

p�p! ZZ ! 4` mHSM � 200

LHC, (14 TeV, 100 fb�1) pp! HSM ! ZZ(�) ! 4` 120 <� mHSM<� 700

pp! HSM ! 80 <� mHSM<� 150

pp! t�tHSM ;WHSM ; HSM ! 80 <� mHSM<� 120� 130

pp! t�tHSM ; HSM ! b�b mHSM<� 100� 110

NLC, (500 GeV, 50 fb�1) e+e� ! ZHSM mHSM<� 350

WW ! HSM mHSM<� 300

e+e� ! t�tHSM mHSM<� 120

NLC, (1 TeV, 200 fb�1) e+e� ! ZHSM mHSM<� 800

WW ! HSM mHSM<� 700

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Table 3: MSSM Higgs boson discovery modes. All masses are speci�ed in GeV. The ordered pair (mA0 , tan�) �xes

the MSSM Higgs sector masses and couplings. The parameter regime mA0 � 1000 GeV and 1 � tan� � 60 is

surveyed. If a range of tan � values is speci�ed below, then the �rst (second) number in the range corresponds to theappropriate minimal (maximal) value of mA0 . See text for further clari�cations.

Machine(ps;RL dt) Mode (mA0 ; tan�) Discovery Region

LEP 1 e+e� ! Z�h0; h0A0 (<� 25; >� 1) or (<� 45; >� 2)

LEP 2 (176 GeV, 500 pb�1) e+e� ! Zh0; h0A0 (<� 80; >� 1) or (<� 150; <� 4{1)

LEP 2 (190 GeV, 500 pb�1) e+e� ! Zh0; h0A0 (<� 85; >� 1) or (>� 85; <� 5{1.5)

TeV� (2 TeV, 30 fb�1) p�p!Wh0; h0 ! b�b; 2b-tag (>� 130{150;� 1)

DiTeV (4 TeV, 30 fb�1) p�p!Wh0; h0 ! b�b; 2b-tag (>� 130{150;� 1)

LHC (14 TeV, 100 fb�1) pp!Wh0; t�th0; h0! b�b; 2; 3b-tag (>� 130{150;� 1)

pp! t�t; t! H+b; 1b-tag (<� 130;� 1)

pp! H0; H0 ! ZZ(�) ! 4` (<� 350; <� 10{2)

pp! h0;Wh0; t�th0; h0 ! (>� 180;� 1)

pp! b�bA0;H0; A0;H0 ! �+�� (>� 100; >� 5{50)

pp! b�bA0;H0; A0;H0 ! �+�� (>� 100; >� 5{50)

pp! b�bh0; h0 ! b�b; 3b-tag (<� 125; >� 5{10)

pp! b�bH0; H0 ! b�b; 3b-tag (>� 125; >� 10{60)

pp! b�bA0; A0 ! b�b; 3b-tag (<� 125; >� 5{10) or (>� 125; >� 10{60)

NLC (500 GeV, 50 fb�1) e+e� ! Zh0 visible unless (<� 90; >� 7)

WW ! h0 visible unless (<� 80; >� 12)

e+e� ! h0A0 (<� 120;� 1)

e+e� ! ZH0;WW ! H0 (<� 140;� 1)

e+e� ! H0A0 (<� 220;� 1), unless (<� 90; >� 7)

e+e� ! H+H� (<� 230;� 1)

NLC (1 TeV, 200 fb�1) e+e� ! H0A0 (<� 450;� 1), unless (<� 90; >� 7)

e+e� ! H+H� (<� 450;� 1)

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Zh0; h0A0 if mA0 <� 80 GeV and tan � >� 1. A seconddiscovery region also exists, beginning at tan � <� 4 (atmA0 = 80 GeV) and ending at mA0 <� 150 GeV (attan � = 1). If

ps is increased to 190 GeV, both discovery

regions become larger; in particular, the latter region nowbegins at tan � <� 5 (at mA0 = 85 GeV) and ends attan � <� 1:5 for the maximal value of mA0 considered.At the NLC-500, h0 can be detected via e+e� ! Zh0

unless tan � >� 7 and mA0 <� 90 GeV. A similar discoveryregion exception appears for WW ! h0. The reasonsuch restrictions arise is that in the indicated region ofparameter space, H0 is SM-like in its couplings, whilethe h0ZZ and h0W+W� couplings are very suppressed.The ZH0A0 coupling is likewise suppressed in the sameparameter regime, which explains the other two discoveryregion exceptions listed in Table 3.

2.2 A Tour of Higgs Search Techniques at Future

Colliders

The goal of the Higgs search at present and future collid-ers is to examine the full mass range of the SM Higgs bo-son, and the full parameter space of the MSSM Higgs sec-tor. The LHC can cover the entire range of SM Higgs bo-son masses from the upper limit of LEP 2 (mHSM = 80{95 GeV, depending on machine energy) to a Higgs massof 700 GeV (and beyond). The most di�cult region forhigh luminosity hadron colliders is the intermediate-massrange mHSM = 80{130 GeV. The LHC detectors are be-ing designed with the capability of fully covering the in-termediate Higgs mass region. The TeV� and DiTevatronmay also have some discovery potential in this mass re-gion. In contrast, the intermediate mass Higgs search atthe NLC (which makes use of the same search techniquesemployed at LEP 2) is straightforward. At design lumi-nosity, the NLC discovery reach is limited only by thecenter-of-mass energy of the machine.

In the search for the Higgs bosons of the MSSM, twoobjectives are:

� the discovery of h0 and

� the discovery of the non-minimal Higgs states (H0,A0, and H�).

Two theoretical results play a key role in the MSSMHiggs search. First, the mass of h0 is bounded bymmaxh0 ' 120 GeV, as noted above. Second, if the proper-

ties of h0 deviate signi�cantly from the SM Higgs boson,then mA0 <� O(mZ ) and the H

0 and H� masses must liein the intermediate Higgs mass region. As a result, exper-iments that are sensitive to the intermediate Higgs massregion have the potential for detecting at least one of theMSSM Higgs bosons over the entire MSSM Higgs pa-rameter space (parametrized by tan � and mA0 , as notedabove). LEP 2 does not have su�cient energy to coverthe entire MSSM Higgs parameter space, since mmax

h0 lies

above the LEP 2 Higgs mass reach. The TeV�, DiTe-vatron and LHC all possess the capability of detectingHiggs bosons in the intermediate mass range, and conse-quently can probe regions of the MSSM Higgs parameterspace not accessible to LEP 2. As of this writing, no setof experiments at any future hadron collider consideredin this report can guarantee the discovery (or exclusion)of at least one MSSM Higgs boson for all values of mA0

and tan � not excluded by the LEP 2 search. However,it may be possible to close this gap in the MSSM param-eter space if su�ciently reliable b quark identi�cation inhadron collider events is possible. On the other hand, be-cause of the relative simplicity of the NLC Higgs search inthe intermediate mass region, the NLC is certain to dis-cover at least one MSSM Higgs boson (either h0 or H0) ifthe supersymmetric approach is correct. If h0 is discov-ered and proves to be SM-like in its properties, then onemust be in the region of MSSM Higgs parameter spacewhere the non-minimal Higgs states are rather heavy andapproximately degenerate in mass. In this case, the LHCmay not be capable of discovering any Higgs bosons be-yond h0, while H0, A0 and H� can be detected at theNLC only if its center-of-mass energy

ps >� 2mA0 .

Below is a detailed description of the Higgs potentialof present and future colliders. A Higgs boson is deemedobservable if a 5�-excess of events can be detected in agiven search channel.

� LEP 1The current lower bound on the SM Higgs mass is 64.5GeV, and will increase by at most a few GeV. The lowerbounds on the MSSM Higgs masses are mh0 > 44:5 GeV,mA0 > 24:3 GeV (for tan � > 1), and mH� > 45 GeV.

� LEP 2For

ps = 176 GeV, the SM Higgs is accessible via ZHSM

production up to 80 GeV for an integrated luminosityof 500 pb�1 [4]. For

ps = 190 GeV, mHSM values as

high as mZ can be probed with 200 pb�1 of data, us-ing b-tagging in the region mHSM � mZ . The reach forps = 205 GeV is about 105 GeV. In the MSSM, the same

mass reaches apply to h0 if mA0 >� mZ , since in this caseZh0 is produced at about the same rate as ZHSM . IfmA0 <� mZ , then the h0ZZ coupling (which controls theZh0 cross section) becomes suppressed while the ZA0h0

coupling becomes maximal. In the latter parameter re-gion, e+e� ! A0h0 can be detected for all values ofmA0 <�

ps=2� 10 GeV, assuming that tan � > 1. Since

mh0 <� 120 GeV, increasing the LEP 2 energy to roughlyps = 220 GeV while maintaining the luminosity would

be be su�cient to guarantee the detection of at least oneHiggs boson (via Zh0 and/or A0h0 �nal states) over theentire MSSM Higgs parameter space [4,5].

� Tevatron (ps = 2 TeV, L = 1032 cm�2 s�1 with the

Main Injector)The most promising mode for the SM Higgs is WHSM

production, followed by HSM ! b�b [6]. With 5 fb�1

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of integrated luminosity, this mode could potentially ex-plore a Higgs mass region of 60{80 GeV, a region whichwill already have been covered by LEP II via the ZHSM

process.

� TeV� (ps = 2 TeV, L � 1033 cm�2 s�1)

The Higgs mass reach in the WHSM mode, with HSM !b�b, is extended over that of the Tevatron [6,7]. With30 fb�1 of integrated luminosity, a Higgs of mass 95 GeVis potentially accessible, but the peak will not be sep-arable from the WZ, Z ! b�b background. The mode(W;Z)HSM , followed by HSM ! �+�� and W;Z ! jj

(where j stands for a hadronic jet), is potentially viablefor Higgs masses su�ciently far above the Z mass [7].With 30 fb�1 of integrated luminosity, a Higgs in themass range 110� 120 GeV may be detectable. However,the Higgs peak will be di�cult to recognize on the slopeof the much larger Zjj, Z ! �+�� background. Bothof these modes are of particular signi�cance for h0. Fortan � > 1 and mA0 <� 1:5mZ, the enhanced coupling ofthe h0 to b's and � 's makes it unobservable at the LHCvia h0 ! or h0 ! ZZ� ! 4`.

� DiTevatron (ps = 4 TeV, L � 1033 cm�2 s�1)

For the SM Higgs, the \gold-plated" mode, HSM !ZZ ! 4`, requires about 30 fb�1 for the optimal Higgsmass in this mode, mHSM = 200 GeV [6]. The 4` modeis not useful for any of the MSSM Higgs bosons. TheHiggs mass reach in the WHSM , HSM ! b�b mode isonly marginally better than at the TeV�, due to the in-crease in the top-quark backgrounds relative to the signal[6,7]. The mode (W;Z)HSM , with HSM ! �+�� andW;Z ! jj, has less promise than at the TeV� due to therelative increase in the background [7].

� LHC (ps = 14 TeV, L = 1033{1034 cm�2 s�1)

For the SM Higgs boson, the \gold-plated" mode,HSM ! ZZ(�) ! 4`, including the case where one Z bo-son is virtual, covers the range of Higgs masses 130{700GeV and beyond with 100 fb�1 [8,9]. For mHSM > 700GeV, the Higgs is no longer \weakly coupled", and searchstrategies become more complex | see Section 5.

The CMS detector is planning an exceptional electro-magnetic calorimeter (PbWO4 crystal) which will enablethe decay mode HSM ! to cover the Higgs massrange 85{150 GeV with 100 fb�1 of integrated luminos-ity [9]. This range overlaps the reach of LEP II (withps = 190 GeV) and the lower end of the range covered

by the gold-plated mode. The ATLAS detector coversthe range 110-140 GeV with this mode [8]. Both CMSand ATLAS �nd that the modes t�tHSM and WHSM ,with HSM ! , are viable in the mass range 80{120GeV with 100 fb�1 of integrated luminosity [8,9]. Sincebackgrounds are smaller, these modes do not require suchexcellent photon resolutions and jet-photon discrimina-tion as does the inclusive mode. CMS has also studiedthe production of the Higgs in association with two jets,

followed by HSM ! , and concludes that this modecovers the Higgs mass range 70{130 GeV [9].

The modes t�tHSM and WH, with HSM ! b�b, arepotentially useful in the intermediate-mass region [6,7].The reach with 100 fb�1 of integrated luminosity is 100GeV, reduced to 80 GeV with 30 fb�1 [8]. Overall, AT-LAS will cover the Higgs mass region 80{140 GeV with100 fb�1 using a combination of HSM ! ; t�tHSM ,WHSM with HSM ! ; and t�tHSM with HSM ! b�b.

The main search mode for the lightest MSSM Higgsboson is h0 ! , which is viable when mh0 is nearmmaxh0 [8,9,5,10,11]. The processes t�th0 and Wh0, with

h0 ! b�b, can potentially extend h0 detection to the some-what lower mh0 values (corresponding to somewhat lowermA0 ) that would assure that at least one MSSM Higgsboson can be detected over all of the MSSM parame-ter space [6]. Adapting the ATLAS study for the SMHiggs to h0 suggests that the required sensitivity couldbe achieved in the t�th0 mode. Due to the large top-quarkbackground, the Wh0 with h0 ! b�b mode at the LHChas little advantage over this mode at the TeV� or theDiTevatron for the same integrated luminosity.

The other MSSM Higgs bosons are generally moreelusive. There are small regions of parameter space inwhich H0 can be observed decaying to or ZZ(�) [8,9].The possibility exists that the charged Higgs can be dis-covered in top decays [8,9]. For mA0 > 2mZ and largetan �, H0 and A0 can have su�ciently enhanced b quarkcouplings that they would be observed when produced inassociation with b�b and decaying via H0; A0 ! �+��

[8,9,11,6]. For very enhanced couplings of the Higgsbosons to b quarks (which occurs for very large tan �), themodes b�b(h0;H0; A0), with h0;H0; A0 ! b�b, and �tbH+,with H+ ! t�b, are potentially viable [6].

Let us suppose that the modes involving b-tagging(especially t�th0 production with h0 ! b�b) eventuallyprove to be viable. Then, the LHC Higgs search us-ing the b-tagging modes in combination with the 4` and �nal state modes should be capable of discovering atleast one of the MSSM Higgs bosons (or in absence of adiscovery rule out the MSSM) [6]. For much of parame-ter space only the h0 will be detectable. Detection of allthe MSSM Higgs bosons at the LHC is only possible forvery small regions of parameter space at moderate valuesof mA0 .

� e+e� linear collider (ps = 500 GeV to 1 TeV,

L � 5� 1033 cm�2 s�1)At

ps = 500 GeV with an integrated luminosity of

50 fb�1, the SM Higgs boson is observable via the ZHSM

process up to mHSM = 350 GeV [12]. Employing thesame process, a Higgs boson with mHSM = 130 GeV(200 GeV) would be discovered with 1 fb�1 (10 fb�1) ofdata. Other Higgs production mechanisms are also use-ful. With 50 fb�1 of data, the WW -fusion process is ob-servable up to mHSM = 300 GeV [12,13,14]. The t�tHSM

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process is accessible formHSM<� 120 GeV, thereby allow-

ing a direct determination of the t�tHSM Yukawa coupling[13]. The collider mode of operation does not extendthe reach of the machine for the SM Higgs, but does al-low a measurement of the HSM ! partial width upto mHSM = 300 GeV [13].

In the MSSM, for mA0 <� mZ , the h0 and A0 will

be detected in the h0A0 mode, the H0 will be foundvia ZH0 and WW -fusion production, and H+H� pairproduction will be kinematically allowed and easily ob-servable [15,13,14]. At higher values of the parametermA0 , the lightest Higgs boson is accessible in both theZh0 andWW -fusion modes. However, the search for theheavier Higgs boson states is limited by machine energy.The mode H0A0 is observable up to mH0 � mA0 � 220GeV, and H+H� can be detected up to mH� = 230GeV [15,13,14]. The collider mode could potentiallyextend the reach for H0 and A0 up to 400 GeV if tan �is not large [5].

Atps = 1 TeV with an integrated luminosity of

200 fb�1, the SM Higgs boson can be detected via theWW -fusion process up to mHSM = 700 GeV [13,14]. Inthe MSSM, H0A0 and H+H� detection would be ex-tended to mH0 � mA0 � mH� � 450 GeV [5,15,13,14].Measurements of cross sections, branching ratios, andangular distributions of the Higgs events will determinemodel parameters and test the underlying theory of thescalar sector [13].

� In uence of MSSM Higgs decays into supersymmet-ric particle �nal statesFor some MSSM parameter choices, the h0 can decayprimarily to invisible modes, including a pair of thelightest supersymmetric neutralinos or a pair of invisi-bly decaying sneutrinos [6]. The h0 would still be eas-ily discovered at e+e� colliders in the Zh0 mode usingmissing-mass techniques [13]. At hadron colliders, theWh0 and t�th0 modes may be detectable via large miss-ing energy and lepton plus invisible energy signals, butdetermination of mh0 would be di�cult [6]. The H

0, A0,and H� decays can be dominated by chargino and neu-tralino pair �nal states and/or slepton pair �nal states[2,5,10,6]. Such modes can either decrease or increase thechances of detecting these heavier MSSM Higgs bosonsat a hadron collider, depending upon detailed MSSM pa-rameter choices [5,10,6]. At e+e� colliders H0, A0 andH� detection up to the earlier quoted (largely kinemat-ical) limits should in general remain possible.

� Hadron collider beyond the LHCIt could provide increased event rates and more over-lap of discovery modes for the SM Higgs boson. How-ever, its primary impact would be to extend sensitivity tohigh mass signals associated with strongly-coupled elec-troweak symmetry breaking scenarios (see Section 5). Inthe case of the MSSM Higgs bosons, the increased eventrates would signi�cantly extend the overlap of the var-

ious discovery modes, expanding the parameter regionswhere several and perhaps all of the MSSM Higgs bosonscould be observed.

� e+e� collider beyondps = 1 TeV

Such an extension in energy is not required for detect-ing and studying a weakly-coupled SM Higgs bosons,but could be very important for a strongly-coupledelectroweak-symmetry-breaking scenario. Detection ofH0A0 andH+H� production in the MSSM model wouldbe extended to higher masses.

2.3 Precision Measurements of Higgs Properties

Detailed studies of the properties of Higgs bosons canbe carried out at e+e� colliders. The measurements ofcross sections, branching ratios, and angular distribu-tions of Higgs events will determine model parametersand test the underlying theory of the scalar sector. Inthis discussion, h denotes the lightest CP-even neutralHiggs. It may be HSM or h0 (of the MSSM), or perhapsa scalar arising from a completely di�erent model. Oncediscovered, determining the identity of h is precisely whatone hopes to be able to address based on the consider-ations presented here. Below we list some examples ofthe measurements that can be made at

ps = 500 GeV

with an integrated luminosity of 50 fb�1, assuming thatthe Higgs mass is less than 350 GeV and that the pro-cess e+e� ! Zh occurs at approximately the StandardModel rate.

The single event Higgs mass resolution using e+e� !Zh is approximately 4 GeV [14]. The number of Higgsevents provided by an integrated luminosity of 50 fb�1

will then allow the determination of the central valueof the Higgs mass with a statistical accuracy of � 180MeV. Since most Standard Model parameters only havelogarithmic dependence on the Higgs mass, this accu-racy is far greater than what is needed to check the self-consistency of the Standard Model. One could use thismass determination to make accurate predictions for theHiggs production cross sections and branching fractions.

For a SM Higgs boson, signals can be selected withsmall backgrounds and one can easily measure the angu-lar distributions of the Higgs production direction in theprocess e+e� ! Zh and the directions of the outgoingfermions in the Z rest frame [14], and verify the expecta-tions for a CP-even Higgs boson [16]. For a more generalHiggs eigenstate, since only the CP-even part couples attree-level to ZZ, these measurements would still agreewith the CP-even predictions unless the Higgs is primar-ily (or purely) CP-odd, in which case the cross sectionwill be much smaller and the event rate inadequate toeasily verify the mixed-CP or CP-odd distribution forms.Analysis of photon polarization asymmetries in ! h

production rates, and of angular correlations among sec-ondary decay products arising from primary h ! �� or

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h ! t�t �nal state decays in Zh production, can bothprovide much better sensitivity to a CP-odd Higgs com-ponent in many cases [17].

By choosing a decay channel whose reconstruction isindependent of the Higgs mass and decay mode, such ase+e� ! Zh, where Z ! `+`�, one can measure the totalcross section for Higgs production. For an integratedluminosity of 50 fb�1, this can be determined with astatistical accuracy of better than 10% [14]. This is onepossible technique for measuring the hZZ coupling.

A speci�c study [18] has been conducted to considerthe experimental problems of determining the produc-tion cross section � times the branching fractions of adiscovered Higgs boson into all of its possible (Stan-dard Model) �nal states. The resulting expected sta-tistical precisions are strong functions of the mass ofthe Higgs, as the branching fractions change dramati-cally in the mass range 100 GeV< mh < 180 GeV. Fora Standard Model Higgs of mass 120 GeV, it is foundthat statistical precisions of 7%, 14%, 39%, and 48% canbe achieved for � � BR(h ! b�b), � � BR(h ! �+��),� �BR(h! c�c+ gg), and � �BR(h!WW �) respec-tively.

Reasonably precise measurements of certain ��BRcombinations will also be possible at hadron colliders.For example, at the LHC a good determination of �(gg !h)�BR(h! ) should be possible for a SM-like Higgsin the 80 to 150 GeV mass range, and of �(gg ! h) �BR(h! ZZ) for mh > 130 GeV.

3 Low Energy Supersymmetry: Implications of

Models

3.1 Elements of Minimal Low-Energy Supersymmetry

A truly fundamental theory of particles and their interac-tions must account for the large hierarchy of energy scalesinherent in the theory|from the scale of electroweaksymmetry breaking [characterized by (

p2GF )

�1=2 =246 GeV] up to energies as large as the Planck scale(of order 1019 GeV). Supersymmetry (SUSY) provides amechanism for stabilizing the large hierarchy of scales,and thus is a natural framework for addressing suchproblems. The simplest example of such an approachis the minimal supersymmetric extension of the Stan-dard Model (MSSM). The MSSM possesses a new classof particles|supersymmetric partners of the quarks, lep-tons, gauge and Higgs bosons of the Standard Model. Aparticle and its supersymmetric partner would be degen-erate in mass if supersymmetry were an exact symmetryof nature. Since this degeneracy is not realized in nature,supersymmetry must be broken. But, if the breakingis \soft" (with supersymmetry-breaking masses of order1 TeV or less), then the stability of the hierarchy can besuccessfully maintained.

Uni�cation of gauge couplings provides an intriguinghint for an underlying supersymmetric theory of particleinteractions. If one extrapolates the SU(3)�SU(2)�U(1)gauge couplings from their low-energy values measuredat LEP to very large energy scales, one �nds that thethree couplings meet at approximately the same energyscale if the renormalization group equations (RGE's) ofthe MSSM are used [19]. In contrast, if Standard ModelRGE's are used, uni�cation of gauge couplings fails bymore then seven standard deviations! As a result, it ispossible to construct a model of particle interactions suchthat:

� the strong and electroweak forces are uni�ed at verylarge energies (at a scale MX � 2 � 1016 GeV,which is not too far from the Planck scale, MP =1019 GeV);

� the couplings of all particles with non-trivialSU(3)�SU(2)�U(1) quantum numbers are pertur-bative in strength at all energies below the Planckscale; and

� the stability of the large hierarchy between the elec-troweak and grand uni�ed energy scales is guaran-teed by the underlying supersymmetry.

In this approach, the origin of the electroweak scale istied to the scale of supersymmetry breaking. In partic-ular, in the models considered later in this section, elec-troweak symmetry breaking is generated through radia-tive corrections. Brie y stated, the squared Higgs massparameter is positive at the high energy scale,MX . How-ever, due to the one-loop radiative e�ects generated bythe large top quark Higgs Yukawa coupling (i.e., as aconsequence of the large top quark mass), the squaredHiggs mass parameter is driven negative in its evolutionfrom MX down to the low energy electroweak scale [20].These e�ects trigger electroweak symmetry breaking atthe proper mass scale (of order v = 246 GeV) and estab-lish the large hierarchy of scales between MX and mZ .

Although the electroweak symmetry breaking scalehas now been related to the supersymmetry break-ing scale, one has not yet explained where thesupersymmetry-breaking masses come from. As notedabove, these masses must be of order 1 TeV or less in or-der to generate the electroweak symmetry breaking scalewithout an excessive (\unnatural") �ne-tuning of modelparameters. The fundamental origin of supersymmetrybreaking is one of the most important unsolved problemsof supersymmetry theory. Nevertheless, one can take apurely phenomenological approach and parametrize theMSSM in terms of a general set of a priori unknown su-persymmetry breaking parameters. Ultimately, these pa-rameters would be measured in experiment once super-symmetric particles are discovered. A detailed knowledgeof these parameters could provide important clues as totheir origins.

163

A brief synopsis of the parameters of the MSSM isnow presented. The SUSY-conserving part of the MSSMis �xed by the three gauge coupling constants of the Stan-dard Model, the Higgs-fermion Yukawa couplings (de-noted by hU , hD and hE below), and one new supersym-metric Higgs mass parameter �. The particle content ofthe MSSM consists of three families of quarks and leptonsand their scalar partners; the vector gauge bosons andtheir fermionic gaugino partners corresponding to thegauge group SU(3)�SU(2)�U(1); and two SU(2)-doubletHiggs scalars and their fermionic higgsino partners. Theintroduction of a second Higgs doublet is necessary inorder for the gauge anomalies associated with the hig-gsinos to cancel, and to give masses to both \up-type"quarks and \down-type" quarks and charged leptons (thelatter cannot be done with one Higgs scalar without vio-lating SUSY). As a result, the Higgs sector of the MSSMis a two-Higgs doublet model, whose phenomenology wasdiscussed in great detail in Section 2. The colorless gaug-inos and higgsinos with the same electric charge can mix.The resulting mass eigenstates are called charginos andneutralinos, with corresponding electric charges �1 and0, respectively. With the particle content and the Higgs-fermion Yukawa couplings �xed as described above, allSUSY-preserving interactions (which correspond to allthe dimensionless couplings of the model) are determinedby the SU(3)�SU(2)�U(1) gauge invariance and/or bythe supersymmetry.

However, in contrast to the Standard Model, theHiggs-fermion Yukawa couplings do not exhaust all pos-sible scalar{fermion interactions. The MSSM possessesnew scalars|squarks and sleptons|which carry baryonnumber (B) and lepton number (L), respectively. Con-sequently, it is possible to write down additional scalar{fermion interaction terms which violate either B or L(but preserve supersymmetry). In the MSSM, one sim-ply assumes that these terms are not present. This can beimplemented with a discrete symmetry, called R-paritywhich assigns (�1)2S+3(B�L) to particles of spin S [i.e.,+1 to all Standard Model particles and �1 to their super-symmetric partners], and is multiplicatively conserved byall interactions of the model. R-parity conservation guar-antees the existence of a stable lightest supersymmetricparticle (LSP), which is an excellent candidate for darkmatter. Although there are some strong phenomenolog-ical constraints on R-parity violating interactions, it ispossible to construct R-violating models which are notinconsistent with present data. Such models lie outsidethe scope of the MSSM, and will be brie y mentioned atthe end of this section.

The SUSY-breaking part of the MSSM is where mostof the new parameters of the MSSM lie. In addition tobreaking the mass degeneracy between particles and theirsupersymmetric partners, the SUSY-breaking terms arerequired in order to break the SU(2)�U(1) electroweak

gauge symmetry. The Higgs potential, with soft-SUSYbreaking mass terms included, can have a non-trivialminimum. Both neutral Higgs �elds acquire vacuumexpectation values; this introduces an important newparameter, tan � � v2=v1, where vi � hH0

i i. Notethat after electroweak symmetry breaking, the Yukawacoupling matrices are proportional to the correspondingquark and lepton mass matrices. (In the limit whereonly third generation Yukawa couplings are considered,h� =

p2m�=(v cos �), hb =

p2mb=(v cos �), and ht =p

2mt=(v sin �), where v = (v21 + v22)1=2 = 246 GeV.)

Supersymmetric breaking parameters are not com-pletely arbitrary, since they must preserve the stabil-ity of the hierarchy discussed above. Such terms, called\soft", were classi�ed in Ref. [21], and consist of massesfor scalars (but not their fermionic partners), masses forthe gauginos, and trilinear scalar couplings. If there wereno reason for the scalar masses and trilinear couplings tobe diagonal in the same basis as the Yukawa couplings,then there would be a huge number (> 100) of possi-ble new SUSY-breaking parameters. In models basedon supergravity [22], a dramatic simpli�cation occurs.SUSY is presumed to be broken in a \hidden sector"of particles which have only gravitational interactionswith the \visible sector" of quarks, leptons, gauge andHiggs bosons, and their supersymmetric partners. TheSUSY breaking is then transmitted to the visible sectorby gravitational interactions, which results in the soft-SUSY breaking terms of the MSSM, characterized by amass scale MSUSY <� O(1 TeV). Moreover, in the min-imal approach, the soft-SUSY breaking terms are takento be avor independent and can be summarized in termsof a few universal parameters, regardless of the unknownphysics in the hidden sector. The SUSY-breaking scalarinteractions which arise take the form

Lsoft = m20

hjH1j2 + jH2j2

+X

families

(jQLj2 + jURj2 + jDRj2 + jLLj2 + jERj2)i

+ A0(hUQLH2UR + hDQLH1DR + hELLH1ER)

+ B�H1H2 + h:c: (1)

This simple form of the SUSY-breaking Lagrangian,which depends on three new SUSY-breaking parameters:m2

0, A0, and B, holds at a mass scale close to the Planckmass. In addition, three soft-SUSY-breaking Majoranamass terms can be introduced for the fermionic gaug-ino partners of the SU(3)�SU(2)�U(1) gauge bosons,respectively. If one adds the additional assumption ofminimal grand uni�cation at a high energy scale MX ,then one �nds a further reduction of parameters. Boththe gauge couplings and the gaugino masses unify atMX .There may be additional relations among the Yukawacouplings, although these depend on the details of the

164

superheavy particle spectrum and their interactions as-sociated with the grand uni�ed gauge group. The super-symmetry model parameters can then be taken to be:

� the common mass parameter m1=2 for the gauginos,

� a common scalar mass parameter m0,

� a common trilinear scalar coupling parameter A0,

� the ratio of the Higgs vacuum expectation values,tan �, and

� the sign of �.

(The parameters j�j and B can be eliminated in favor oftan � and mZ by minimizing the scalar potential.) Herem1=2, m0, and A0 are all typically of order MSUSY.

To �nd the Lagrangian relevant for physics at theelectroweak scale, one must evolve the parameters of themodel according to their renormalization group equa-tions from MX down to mZ . This splits the gauginomasses and the various scalar masses at low energies.The most striking result of this running is that radiativecorrections due to the large top Yukawa coupling pushthe squared mass of H2 negative at scales far below MX ,resulting in electroweak symmetry breaking [20]. This isa remarkable e�ect, connected with the large top quarkmass, and exhibits the intimate relation between low-energy supersymmetry and electroweak symmetry break-ing. The large top quark mass also has an impact ona number of other MSSM parameters via the e�ects ofthe large top-quark Yukawa coupling in the RGE's. Forexample, one �nds that the squared masses of the topsquarks and left-handed bottom squark are reduced rel-ative to other squark masses, while the mass of the light-est CP-even neutral Higgs boson may be substantiallyincreased above mZ .

3.2 Features of the Superpartner Spectrum

With the masses of all the superpartners determinedonly by the parameters (m1=2, m0, A0, tan�, sign �),the spectrum is highly constrained. With a universalm0, squarks (or sleptons) with the same gauge quantumnumbers will remain degenerate even at low energies, un-less they have large Yukawa couplings. This degeneracyis a success of the model, since it automatically main-tains the suppression of FCNCs in low-energy physics.(This remains true even if one relaxes the usual mini-mal assumptions by introducing a larger gauge group atsome intermediate scale or allowing the gaugino massparameters to be independent.) So the superpartnerspectrum will contain seven distinct groups of degener-ate scalar states (~uL; ~cL); ( ~dL; ~sL); (~uR; ~cR); ( ~dR; ~sR;~bR);(~eL; ~�L; ~�L); (~�e; ~��; ~�� ); (~eR; ~�R; ~�R). If tan � � 1, thenthe bottom and tau Yukawa couplings are non-negligible,so that ~bR, ~�L, ~�R, and ~�� need not be degenerate withtheir colleagues. With the minimal assumptions, one�nds for the physical squark and slepton masses of the

�rst two families approximately

m2~eR = m2

0 + 0:15m21=2 � 0:23m2

Z cos2�; (2)

m2~eL = m2

0 + 0:52m21=2 � 0:27m2

Z cos2�; (3)

m2~� = m2

0 + 0:52m21=2 + 0:50m2

Z cos2�; (4)

m2~q = m2

0 + (4:5 to 6:5)m21=2: (5)

Eq. (5) holds for �rst and second generation squark mass.The range in the coe�cient of m2

1=2 is partly due to theuncertainty in �3; moreover, this coe�cient is smaller forlarger squark masses. Eqs. (2){(5) imply m~q > m~eL >

m~eR . At least one of the top squark mass eigenstates andusually a bottom squark are below the main squark bandimplied by (5), because of radiative e�ects from the topYukawa coupling. This ordering of squark masses shouldlead to enhanced production of third generation squarksat hadron colliders, and to enhanced branching ratios ofgluinos, charginos and neutralinos into third generationquarks.

In the minimal approach, the physical gluino mass isrelated to m1=2 by

M~g = (2:2 to 3:5)m1=2 (6)

Therefore, the squarks whose corresponding Higgs{quarkYukawa couplings are small cannot be much lighter thanthe gluino. When correlations among parameters aretaken into account, one �nds m~q > 0:8M~g. With mt '175 GeV, radiative electroweak breaking requires that j�jbe large compared to the electroweak gaugino masses.The lighter two neutralinos and the lighter chargino willthen be gaugino{like, and the heavier neutralinos andchargino will only rarely be produced in the decays ofsquarks and gluinos. This also implies that the heav-ier Higgs mass eigenstates A; H0 and H� will be quiteheavy and almost degenerate; they will usually also beable to decay into charginos and neutralinos. The light-est Higgs scalar, h0, will have couplings close to thoseof the Standard Model Higgs boson. There is an upperbound on the h0 mass of about 120 GeV in the MSSM.A similar h0 mass bound of about 150 GeV is found ina completely general class of low-energy supersymmetricmodels [23] (assuming all model couplings are perturba-tive up to MX ).

3.3 Beyond the Minimal Planck Scale Assumptions

Many model builders have begun to explore the conse-quences of relaxing the minimal assumptions outlinedabove. For example, the boundary condition of univer-sal scalar masses at MX can be modi�ed by non-trivialstring e�ects, threshold e�ects associated with the granduni�ed model, evolution e�ects between MX and MP ,or additional contributions arising from the e�ects of a

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larger gauge symmetry group which is broken at a scaleabove MX [24]. Generally, small or moderate changesof the boundary conditions at MX will only be impor-tant near the border of the allowed region of parameterspace. For example, if the mass squared of H1 is largerthan that of H2 at the scale MX , tan � of order mt=mb

or larger becomes possible without strong �ne-tuning ofsoft breaking parameters. Non-universal scalar massesmay also reduce j�j, possibly allowing for light higgsinos.

One can even entertain the possibility of large non-universalities among sfermions with the same electroweakquantum numbers. One often �nds the statement in theliterature that near{degeneracy of sfermion masses at thescale MX is required by bounds on FCNC. This state-ment is not entirely correct; the potentially most danger-ous gluino loop contributions will always vanish if quarkand squark mass matrices are aligned [25], i.e., can bediagonalized simultaneously. This is true independent ofthe (di�erences between) squark masses. The same is alsotrue for neutralino loops. In such models only charginoloops contribute to FCNC. Notice that in general thesedo not constrain masses of SU (2) singlet squarks. Themost sensitive bound comes from K0{ �K0 mixing. De-manding that the chargino loop contribution to �mK besmaller than the experimental value of 3:5� 10�15 GeVgives

j�~u~cj � 0:8TeV�1(1 + 6m21=2=m

20)q4:3m2

1=2 + 0:4m20;

(7)

where m20 is the average and �~u~c �m2

0 the di�erence be-tween the squared ~uL and ~cL masses at scale MX . Wesee that �~u~c ' 1 is allowed even for m0 = m1=2 = 100GeV. Highly non{degenerate squarks are therefore al-lowed if quark and squark mass matrices are (approx-imately) aligned. This might make squark hunting athadron colliders di�cult, since the signal from any onesquark state might be too weak to be visible above back-grounds.

One should also consider extensions of the MSSMthat go beyond simple modi�cations of the MSSM bound-ary conditions at the scale MX . The \Next{to{Minimal"Supersymmetric extension of the Standard Model intro-duces a gauge{singlet Higgs chiral supermultiplet in addi-tion to the usual MSSM particles. This variation does notseem to have a major e�ect on the spectrum of the MSSMparticles [26], but it does impact on discovery channelsfor the Higgs and neutralinos. In particular, one mayhave a light Higgs scalar with reduced couplings to the Zboson. One can also contemplate low-energy supersym-metric models in which R-parity conservation is absent.For example, R-parity could be broken spontaneously bya sneutrino vacuum expectation value h~�i 6= 0. One canalso replace R-parity by an alternative discrete symmetry[27] which allows either baryon number or lepton num-

ber violation (but not both!) among the renormalizableinteractions. The phenomenology of R-parity violatingmodels is quite di�erent from that of the MSSM. This ismainly due to the fact that lightest supersymmetric par-ticle is no longer stable, but can decay via an R-parityviolating interaction. No systematic study of R-parity vi-olating models in the context of supergravity and super-uni�ed theories has yet been undertaken.

4 Low Energy Supersymmetry: Phenomenology

If supersymmetry is associated with the origin of theelectroweak symmetry breaking scale, then low-energysupersymmetry must exist at a scale of order 1 TeV orbelow. That is, supersymmetry must be discovered ateither upgrades of existing colliders or at the LHC. Dueto its mass reach, the LHC is the de�nitive machine fordiscovering or excluding low-energy supersymmetry. Sec-tion 4.1 summarizes the supersymmetry mass discoverypotential for hadron colliders. A variety of signatures areexplored. The conventional models of low-energy super-symmetry (which are R-parity conserving) possess a sta-ble lightest supersymmetric particle (LSP) which is elec-trically (and color) neutral and therefore interacts veryweakly in matter. It follows that the LSP behaves likea heavy neutrino which does not interact in collider de-tectors. Its presence would be signaled by excess missingtransverse energy (which could not be attributed to neu-trinos). Many of the supersymmetry searches rely on themissing energy signature as an indication of new physicsbeyond the Standard Model. Multi-leptonic signaturesalso play an important role in supersymmetry searchesat hadron colliders. (Such signals can also be exploitedin the search for R-parity-violating low-energy supersym-metry.)

Suppose that a signal is observed in one of the ex-pected channels. This would not be a con�rmation oflow-energy supersymmetry, unless there is con�rming ev-idence from other expected signatures. This presents aformidable challenge to experimenters at the LHC. Canthey prove that a set of signatures of new physics is low-energy supersymmetry? Can they extract parameters ofthe supersymmetric models with any precision and testthe details of the theory? These are questions that haveonly recently attracted seriously study. It is in this con-text that a future e+e� collider can be invaluable. Asshown in Section 4.2. if the lightest supersymmetric par-ticles were produced at LEP 2 or the NLC, precision mea-surement could begin to map out in detail the parameterspace of the supersymmetric model. In particular, beampolarization at the NLC provides an invaluable tool forstudying the relation between chirality and the propertiesof supersymmetric particles. For example, one can beginto prove that there is a correlation between the left andright-handed electrons and their slepton partners as ex-

166

pected in supersymmetry. The elucidation of the detailsof the light chargino and neutralino spectrum at the NLCcould also play a pivotal role in untangling complex de-cay chains of heavier supersymmetric particles producedat the LHC.

4.1 Supersymmetry at Hadron Colliders

The detection of supersymmetry at a hadron collideris a complex task. It requires the ability to extract sig-nals of new physics out of data samples with potentiallylarge Standard Model backgrounds. Realistic simulationsare required that can accurately model the physics ofQCD jets and the theoretical predictions of low-energysupersymmetry. The physics of low-energy supersymme-try can be treated either in the context of speci�c theo-retical models such as those discussed in Section 3, or ina more phenomenological approach which makes as fewtheoretical assumptions as is practical. Both approacheshave been followed in this section. The minimal super-symmetric model (MSSM) [29] has recently been embed-ded in the event generator program ISAJET [30], so thatall lowest order sparticle production processes and de-cay chains can be adequately simulated. In addition,ISAJET now allows the input of a mixed GUT and weakscale parameter set (m0;m1=2; A0; tan�; sgn(�);mt), forwhich a complete superparticle spectrum is generated us-ing renormalization group equations with radiative elec-troweak symmetry breaking, under the assumption ofgauge coupling uni�cation at MGUT � 2 � 1016 GeV,and universal GUT scale soft supersymmetry breakingterms. In addition, versions of ISAJET past 7.11 includeall lowest order e+e� ! SUSY reactions, so the e�ectof cascade decays can be explored at future e+e� collid-ers [31].

Much e�ort has gone into examining the superpar-ticle mass reach and discovery potential of various pro-posed future colliders, to aid in decision making and pri-oritization for future collider facilities. A summary ofthese results can be found in Table 4. First, we con-sider the case of gluino and squark production, followedby their cascade decays via three-body e�� and e�0 de-cay modes. Kamon et al. [32] have examined the massreach in m~g at the Tevatron and DiTevatron collidersusing the missing transverse energy (E/T ) signature, andfound gluino mass reaches of m~g � 270(450) GeV forthe Tevatron Main injector (DiTevatron), assuming thatm~q � m~g . In addition, Ref. [33] has examined the ~gmass reach via multi-lepton topologies. The LHC reachfor gluinos and squarks has recently been examined inconsiderable detail by ATLAS studies [8]. It is generallyexpected that the lighter of the two top squarks (~t1) issigni�cantly lighter than the other squarks, due to thelarge top quark Yukawa coupling which drives diagonalstop masses to small values and enhances the o�-diagonal

mixing of ~tL and ~tR. In this case, the present squarkmass collider limits do not apply to ~t1. In Ref. [34], it isshown that Tevatron collider experiments with 100 pb�1

of data can explore m~t1 � 80{100 GeV, considerably fur-ther than the best current bounds of � 45 GeV fromLEP.

Next, we examine neutralino and chargino produc-tion. A signi�cant portion of the parameter space of min-imal supergravity models can be explored at the Tevatronand DiTevatron colliders by searching for the clean trilep-ton plus E/T signal from e��1 e�02 ! 3` production [28]. InTable 4, we present the mass reach of the neutralino andchargino searches in terms of an equivalent gluino mass.The latter is obtained under the assumption of uni�edsoft gaugino masses at the GUT scale (although thereis some additional dependence on other supersymmet-ric model parameters). Note that the DiTevatron doesnot signi�cantly increase the mass reach in the 3` chan-nel beyond that of the Tevatron Main Injector, althoughfurther optimization of cuts may be possible. This isin contrast to the mass reach for gluinos and squarks viaE/T searches, which is signi�cantly higher for the DiTeva-tron. The clean trilepton signal has also been examinedin Ref. [28] for the LHC. Note that it is not possible toprobe m~g >�600{700 GeV via 3`+E/T mode at the LHCdue to the turn on of the e�02 ! e�01h or e�02 ! e�01Z de-cay modes which spoil the signal. However, the dileptonspectrum from e�02 ! e�01`� decay can be used at the LHCto measure me�0

2

�me�01

with signi�cant precision. Finally,

if R-violating e�01 decays are present (via baryon or lep-ton number violating interactions), then sparticle massreaches can change signi�cantly to either higher or lowervalues [35].

The search for sleptons at hadron colliders was ad-dressed in Ref. [36]. It was shown that it would be dif-�cult to search at the Tevatron for m~ much beyond 50GeV (and beyond 100 GeV at TeV�), due to low sig-nal rates and irreducible backgrounds. In contrast, atthe LHC sti�er cuts may be made; in this case sleptonmasses up to 250{300 GeV can be detected.

Tevatron signals within the constrained supergravityframework have been discussed in Ref. [37]. Because allsignals are determined by just four parameters, the var-ious SUSY processes are strongly correlated, and mayprovide an experimental probe of GUT scale assump-tions. For example, Ref. [38] argues that in the parame-ter regime where sleptons are much lighter than squarks,the Main Injector discovery limit may reach m~g � 500GeV via the enhanced multi-lepton signals from super-symmetric particle production and their subsequent de-cay chains.

167

Table 4: Discovery reach of various options of future hadron colliders. The numbers are subject to �15% ambiguity. Also, the

clean trilepton signals are sensitive to other model parameters; we show representative ranges from Ref. [28] where j�j is typicallymuch larger than the soft-breaking electroweak gaugino masses. For � > 0, the leptonic decay of e�02 may be strongly suppressed

so that 3` signals may not be observable even if charginos are just above the LEP bound (m~g � 150 GeV).

Tevatron I Tevatron II Main Injector Tevatron� DiTevatron LHCSignal 0.01 fb�1 0.1 fb�1 1 fb�1 10 fb�1 1 fb�1 10 fb�1

1.8 TeV 1.8 TeV 2 TeV 2 TeV 4 TeV 14 TeV

E/T (~q� ~g) ~g(150) ~g(210) ~g(270) ~g(340) ~g(450) ~g(1300)

`�`�(~q � ~g) | ~g(160) ~g(210) ~g(270) ~g(320) ~g(1000)

all ! 3` (~q � ~g) | ~g(150{180) ~g(150{260) ~g(150{430) ~g(150{320)

E/T (~q � ~g) ~g(220) ~g(300) ~g(350) ~g(400) ~g(580) ~g(2000)

`�`�(~q � ~g) | ~g(180{230) ~g(325) ~g(385{405) ~g(460) ~g(1000)

all ! 3` (~q � ~g) | ~g(240{290) ~g(425{440) ~g(550) ~g(550) >�~g(1000)~t1 ! ce�01 | ~t1(80{100) ~t1(120)

~t1 ! be��1 | ~t1(80{100) ~t1(120)

�(~t1~t�1)! | | | | | ~t1(250)~~� | ~(50) ~(50) ~(100) ~(250{300)

4.2 Supersymmetry at e+ e� Colliders

At an e+e� collider, discovery of superparticles is rela-tively easy up to the kinematic limit. There is a vastliterature concerning the discovery reach at LEP 2 [39].Recent works discuss measurement of SUSY parame-ters rather than discoveries alone. For instance with achargino pair production alone, one can put stringentconstraints on the parameter space (M1;M2; �; tan�;m~l)using the cross section, forward-backward asymmetryand branching fractions, where the sensitivity on partic-ular parameters depends on the actual parameter values[40].

Experimentation at linear e+e� colliders would bericher due to the higher energies and beam polarizationwith the following characteristics:

� small beam energy spread (better than 1 %) evenafter including initial state radiation and beam-strahlung e�ects,

� clean environment basically without underlyingevents even with photon induced hadronic processes,and

� high beam polarization of 90% and beyond.

The virtues of polarization are two-fold. First, use ofpolarization can suppress the background substantiallyby as much as two orders of magnitudes, resulting in avery pure signal sample appropriate for precision studies.Second, one basically doubles the number of experimen-tal observables by using both polarization states, whichenables the e�cient measurements of various parameters.

A detector simulation of e+e� ! ~�+~�� based on anALEPH-type detector at

ps = 500 GeV and

RLdt =

20 fb�1 gives a 5 � signal for ~� for m~� below 230 GeV

[41]. A mass di�erence of 25 GeV between slepton andthe LSP is enough for detection even without employingbeam polarization. The case for the chargino search issimilar. It is noteworthy that both purely hadronic andmixed hadronic-leptonic modes can be used for discoveryand study of charginos [42].

We show here the sample results of Monte Carlo anal-ysis with detector simulation [43] based on JLC-I detec-tor [44]. Fig. 1 shows the power of the polarization toobtain a pure sample (>99%) of ~� pair signals with highe�ciency (� > 50%). Since the signature of a sleptonpair is an acoplanar lepton pair, the main background isW+W�, which can be substantially suppressed by em-ploying right-handed electron beam. A kinematic �t tothe end points of lepton energy distribution allows usthe determination of both slepton and LSP masses betterthan 1%. The typical sensitivity of the chargino and neu-tralino mass measurements are shown in Fig. 2. Here themixed hadronic-lepton mode is used, and the measure-ment is based on total dijet energy distribution. Using atechnique to combine information from the tracking de-tector and calorimeters, one achieves mass measurementsof the chargino and LSP at the 3% level. Similar sensitiv-ities are expected for top and bottom squark signals [45].

The determination of superparticle masses allows usto test theoretical assumptions at various levels. For ex-ample, generation independence of slepton masses (uni-versality) can be tested at the 1% level. More experimen-tally challenging is the test of the GUT-relation amonggaugino masses, since the gauginos mix with higgsinosto form chargino and neutralino mass eigenstates. How-ever, one can still test the GUT-relation at a few percentlevel combining slepton and chargino signals, based on

168

Figure 1: Acoplanarity distribution of muon pair for ECM =

350 GeV, m~l= 142 GeV,

RLdt = 20 fb�1, for the signal

(solid) and standard model backgrounds (dashed). Fig. b)shows the dramatic reduction of the backgrounds using the

right-handed electron beam. Taken from Ref. [43].

Figure 2: a) Dijet energy distribution from chargino pair pro-

duction, for the Monte Carlo generated events (points), poly-

nomial �t to the Monte Carlo (solid), contributions from theW -pair background (dashed) and the sum of other standard

model backgrounds (dotted). b) Obtained contour on the

masses of chargino and LSP. Taken from Ref. [43].

Figure 3: Test of the GUT-relation of the gaugino masses.

The contours are obtained by a four-dimensional �t of

(M1;M2; �; tan �) plane, using the LSP and chargino masses,and the production cross sections for selectrons and charginos

with a right-handed electron beam. Taken from Ref. [43].

the measured masses and polarization dependence of thecross sections (see Fig. 3).

4.3 Complementarity

Typically, e+e� colliders have lower center-of-mass ener-gies compared to hadron machines of the same era, buttheir complementary character in superparticle searchesis easily understood. The colored superparticles whichare the main targets of the hadron colliders are sup-posed to be 3{4 times heavier than the colorless ones un-der GUT assumptions. For example, the constraints onthe supersymmetric parameter space from experimentsat LEP (

ps = 90 GeV) and the Tevatron (

ps = 1:8 TeV)

are comparable. This continues to be true for LEP 2 andthe Tevatron with Main Injector, especially in the contextof models with minimal supergravity boundary conditionconstraints [37,38]. The discovery reach of an e+e� lin-ear collider with

ps = 1 TeV will be again comparable

to that at the LHC. But their complementary characterwill be more important after the discoveries of superpar-ticles. Suppose that signals from squarks and gluinosare seen at the LHC. Then it would be a formidabletask to demonstrate that they are superparticles due tothe simultaneous production of many new particles andtheir complicated decay chains. The e+e� collider mightnot reach the energies where squarks could be produced;however, it would study the low-lying spectrum of super-particles (the sleptons, neutralinos and charginos) as de-scribed in the previous section. Analysis of data from thehadron collider with inputs from the e+e� collider could

169

sort out the complex decay chains, revealing the massspectrum and parameters of the heavier superparticles.These results would augment the measurements of theproperties of light superparticles made at the e+e� col-lider, and would provide additional tests of GUT and/orsupergravity predictions and test other model assump-tions.

5 Strongly Coupled ESB Sector: Model-

Independent Approaches

If a Higgs boson or technirho meson or some other di-rect indication of electroweak symmetry breaking is notfound at some future accelerator, one would like to knowwhether it is still possible to learn something about elec-troweak symmetry breaking by studyingWW scattering.In this scenario, whatever is responsible for giving the Wand Z bosons their masses occurs at a high energy scaleand most probably gives rise to a strongly interactingsector where perturbation theory is not applicable. For-tunately, one can still analyze the low energy behaviorof the theory with a generalization of the �� scatteringtheorems derived by Weinberg cast in the form of chiralperturbation theory.

The low energy theorems can easily be generalizedfrom pions to the longitudinal components of the W andZ gauge bosons. These scattering theorems are only validat low energy, that is

ps << (MRes; 4�v), where MRes is

the mass of the lowest lying resonance interacting withthe longitudinal W 's and Z's. The attraction in thisapproach is that it is valid for any mechanism of elec-troweak symmetry breaking. It is also possible to couplethe chiral Lagrangian describing the low energy interac-tions of the gauge bosons with a (color-singlet) vectormeson (the BESS model-equivalence) or with a scalarparticle (a Higgs scalar type of models). This descrip-tion of vector mesons and scalars coupled to longitudinalgauge bosons relies only on the symmetry of the theoryand so is independent of the details of speci�c models.

Lastly, we discuss a model with a \hidden" symmetrybreaking sector, one in which the electroweak symmetrybreaking sector has a large number of particles. Thetheory can be strongly interacting and the total W andZ cross sections in this model are large: most of the crosssection is for the production of particles other than theW or Z. In such a model, discovering the electroweaksymmetry breaking sector depends on the observationthe other particles and the ability to associate them withsymmetry breaking.

5.1 Strongly Coupled ESB Sector at the LHC

In what follows, we assume the LHC runs at 14 TeV witha luminosity of 1034 cm�2 sec�1 (an annual integratedluminosity 100 fb�1).

Vector Resonance Signal

A vector meson with a mass up to m� = 2:5 TeV canbe found at the LHC through the W�Z channel [46].One would need to run the LHC for about 2 years tocollect about 10 leptonic events, after kinematical cutsto e�ectively suppress the backgrounds.

Complementarity of Vector Resonant and Non-resonant

WW Scattering:

Ref. [47] considered a vector-dominance model forthree sets of mass-width parameters: (m�;��) =(1.78,0.33), (2.52,0.92), and (4.0,0.98). Their criterionfor a signi�cant signal (S) with a background (B) is�" � S=

pB � 5; �# � S=

pS + B � 3; S � B. The

complementarity here implies that one observes eithera low mass (I; J)=(1,1) resonance via the W�Z chan-nel, or signi�cant enhancement via the W�W� channelwith I = 2. From Table 5, one sees that the worst caseamong those parameter choices is at m� = 2:52 TeV,where an integrated luminosity of at least 105 fb�1|slightly more than the LHC annual luminosity|is re-quired for the W�W� channel to meet their discoverycriterion. ATLAS collaboration [8] carried out a MonteCarlo study for W+W+ channel including detector sim-ulations, obtaining qualitatively similar results.

Table 5: Minimum luminosity to satisfy observability crite-

rion for W�Z and W�W� channels at the LHC. Each en-try contains LMIN in fb�1, the number of signal/background

events per 100 fb�1.

m� (TeV) 1.78 2.52 4.0

44 fb�1 325 fb�1 NoW�Z 38/20 5.8/3.4 Signal

142 fb�1 105 fb�1 77 fb�1

W�W� 12.7/6.0 15.9/5.8 22.4/8.9

All-Channel Comparison for WW Scattering

Ref. [48] compared all-channel WW scattering atps = 40 TeV and 16 TeV, and new analysis at 14 TeV

is in progress. In particular, the signal for a 1 TeV Higgsboson may be observable through the leptonic channelsH ! WW ! l�l� and ZZ ! l�l���, to add to the cleanbut low rate ZZ ! 4l mode.

ATLAS collaboration [8] also studied a 1 TeV Higgsboson signal via the decay mode H ! WW ! l�jj andZZ ! l�ljj. It was found that after identifying one Win the leptonic mode and one W in the di-jet mode withMjj � mW , with a tagged forward jet and a veto onall other central jets, the WW ! `�jj channel gives aviable signal with statistical signi�cance above 6.8�.

170

5.2 Strongly Coupled ESB Sector at the NLC

Our standard NLC has an energyps =1.5 TeV and an

integrated luminosity of 190 fb�1 per year.

Vector Resonance Signal

At the NLC a vector resonance would be probed moste�ectively via e+e� ! W+

LW�L . This can be generi-

cally described [49] by an Omn�es function with a complexform factor FT . An in�nitely massive vector resonance isequivalent to the case where the W+

LW�L scattering am-

plitude is described by the Low Energy Theorem (LET).Fig. 4 shows the results in Ref. [50] for a technirho-

like vector resonance in the e+e� !W+W� process. Inone year at the NLC, technirhos of arbitrarily large masscan be distinguished from the weakly-interacting SM. Anintegrated luminosity of 225 fb�1 (1.2 years at design lu-minosity) would yield 7:1�, 5:3�, and 5:0� signals for a4 TeV technirho, a 6 TeV technirho, and LET, respec-tively. As was the case for the LHC of Table 5, theseresults assume statistical errors only. The systematic er-rors for the e+e� ! W+W� results will be small com-pared to the statistical error, since the analysis consistsof a background-free maximum likelihood �t of angulardistributions.

0.9–0.2

–0.1

0

0.1

0.2

1.1 1.2 1.3

SM with Light Higgs

Mρ = 6 TeV

4 TeV3TeV

LET

1.41.0Re(FT) 7820A210-94

Im (

FT)

Figure 4: Con�dence level contours for Re(FT ) and Im(FT )

at c.m. energy 1.5 TeV and L = 190 fb�1. The contour

about the light Higgs value of FT = (1; 0) is 95% C.L. and

the contour about m� = 4 TeV point is 68% C.L..

The processes of e+e� ! W+W� and e+e� ! f �f 0

via the vector resonance have also been studied in thecontext of the BESS model and variables such as the to-tal cross sections, forward-backward and left-right asym-metries are used to constrain the virtual V e�ects. Forps � m�, the NLC will be very sensitive to the BESS

model parameters [51].

WW Fusion Processes

WW fusion processes open more channels to studythe strongly coupled ESB sector beyond a vector reso-nance. Ref. [52] demonstrates that the signal for a 1TeV Higgs boson should be observable at a 12� level,for

ps =1.5 TeV and 200 fb�1. Furthermore, the ra-

tio R � �(W+W� ! W+W�)=�(W+W� ! ZZ) mayprovide hints that help to distinguish di�erent stronglycoupled ESB sector models, such as a scalar resonance(R > 1), a vector resonance (R � 1), or a Low EnergyTheorem amplitude (R < 1).

Due to the relatively clean environment in e+e� col-lisions, cross sections for background processes may bemeasured rather well for both the normalization as wellas the shape of the distribution, so that statistically sig-ni�cant deviation from the SM background may be eas-ily identi�ed as new physics signal. One example is the\Hidden Sector" [53], which may be impossible to observein hadronic collision environment but possibly feasible ine+e� collisions.

Searches at Colliders

The heavy Higgs boson and other strong scatteringsignals in longitudinal gauge boson channels can be in-vestigated at the NLC at

ps = 1:5 TeV operating in

the collider mode [54]. The processes consideredhere involve two gauge boson �nal states ! ZZ, ! W+W , and four gauge boson �nal states !W+W�W+W�, W+W�ZZ [55]. The four gauge boson�nal state processes seem to be more promising in search-ing for strongly coupled ESB dynamics as compared withthe two gauge boson �nal states, although all the aboveprocesses are plagued by large backgrounds consisting oftransversely produced gauge bosons [54]. This issue hasbeen addressed recently in Refs. [56,57]. For example,Ref. [56] �nds that with luminosity of 200 fb�1, a 1.5TeV e+e� collider operating as a collider can suc-cessfully observe a heavy Higgs boson with mass up to700 GeV. To obtain a reach in the Higgs boson massup to 1 TeV, a 2 TeV e+e� collider is required with lu-minosity of 200 fb�1. The results were obtained takinginto account the back-scattered photon luminosity spec-trum. It is also found that a 2 TeV linear collider in the mode is roughly equivalent to a 1.5 TeV e+e� col-lider in searching for heavy Higgs boson physics (roughlyscales as

ps � 0:8

psee). The viability of this signal

still requires that the decays of the W and Z bosons beincorporated, and detector simulations be performed todetermine a realistic acceptance.

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6 Strongly Coupled ESB Sector: Implications of

Models

6.1 Ingredients of Techni-models

In theories of dynamical electroweak symmetry break-ing (ESB), such as technicolor [58], ESB is due to chiralsymmetry breaking in an asymptotically-free, strongly-interacting, gauge theory with massless fermions. Thesetheories attempt to understand electroweak symmetrybreaking without introducing any scalar particles such asa Higgs boson. Instead, the symmetry breaking is mod-eled after that which occurs in QCD when the SU (3)ccolor gauge group becomes strong. In QCD, the break-ing of the chiral symmetry gives rise to pions. In thesimplest technicolor theory one introduces a left-handedweak-doublet of \technifermions", and the correspondingright-handed weak-singlets, which transform as the fun-damental [N ] representation of a strong SU (N )TC tech-nicolor gauge group. The global chiral symmetry of thetechnicolor interactions is then SU (2)L�SU (2)R . Whenthe technicolor interactions become strong, the chiralsymmetry is broken to the diagonal subgroup, SU (2)V ,producing three Nambu-Goldstone bosons, which thenyield the correct W and Z masses.

However, the symmetry breaking sector must alsocouple to the ordinary fermions, allowing them to ac-quire mass. In models of a strong ESB sector there musteither be additional avor-dependent gauge interactions,the so-called \extended" technicolor (ETC) interactions,or Yukawa couplings to scalars which communicate thebreaking of the chiral symmetry of the technifermionsto the ordinary fermions. The most popular type ofstrong ESB model that attempts to explain the massesof all observed fermions contains an entire family of tech-nifermions with Standard Model gauge couplings.

Since these models contain more than one doubletof technifermions, they have a global symmetry grouplarger than SU (2)L SU (2)R. Therefore chiral sym-metry breaking produces additional (pseudo-)Nambu-Goldstone bosons (PNGBs). Furthermore, the modelstypically possess a larger variety of resonances than theone-doublet model. There will be heavy (� 1{2 TeV)vector meson resonance with the quantum numbers ofthe �; ! etc. The phenomenology of color-neutral reso-nances with the quantum numbers of the � is discussedin Section 5. In the case of color-neutral PNGBs the phe-nomenology is much like that of the extra scalars in \two-Higgs" doublet models. Therefore we will focus on thecolored resonances and PNGBs occuring in most techni-color models. These models have a possibly unique signa-ture: resonances associated with the electroweak symme-try breaking sector which are strongly produced. Hadroncolliders will be especially important for searching forsignatures of such colored particles associated with ESB.

6.2 Theoretical Challenges for Technicolor Model

Building

Models incorporating ETC interactions ran into troublewith avor changing neutral currents (FCNC's) early on.Assuming technicolor behaved like a scaled-up version ofQCD it was found that it is impossible to generate a largeenough mass for the s quark (much less the c quark) whileavoiding FCNC's. One possible solution is to make theTC gauge coupling run slower than in QCD (i.e. make it`walk'). This makes the technifermion condensate muchlarger than scaling from QCD suggests, so that for a�xed quark or lepton mass, the necessary mass scale forETC gauge bosons is increased, suppressing FCNC's. Asecond solution is to build a Glashow-Illiopoulos-Maiani(GIM) symmetry into the ETC theory (sometimes calledTechni-GIM).

A further problem for ETC models is producing alarge isospin splitting for the t and b quark masses with-out causing large isospin splitting in theW and Z masses.Isospin splitting in the gauge sector, as described by theradiative correction parameter T is tightly constrainedby experiment.a

A current challenge for TC models is that mod-els with QCD-like dynamics tend to produce large pos-itive contributions to the electroweak radiative correc-tion parameter S, while experiments tend to prefer smallS. Since the discrepancy grows with the number oftechnicolors and the number of technidoublets, one wayto evade the problem is to limit the number of tech-nifermions contributing to ESB. Alternatively one caninvoke mechanisms yielding a negative contribution to S:the technifermions may have exotic electroweak quantumnumbers or the TC dynamics can be su�ciently unlikeQCD so as to invalidate the naive scaling-up of QCD phe-nomenology. Such alternatives usually also rely on someform of isospin breaking. In multiscale models isospinbreaking at the lowest ESB scale can produce a nega-tive contribution to S without infecting the T parameter,which is sensitive to isospin breaking at the highest ESBscale.

The most recent problem for ETC models arises fromthe measurement of the Z ! b�b partial width at LEP.The experiments �nd a partial width which is slightlylarger than the Standard Model prediction, while almostall the ETC models that have been constructed so farproduce a correction which further reduces this width.The sign of the correction is a consequence of the almostuniversal assumption that SU (2)L commutes with theETC gauge group. The alternative, where SU (2)L isembedded in the ETC gauge group, may be interesting,since this reverses the sign of the correction.

aThe radiative correction parameters, S, T and U are de�nedin the chapter on Precision Tests of Electroweak Physics.

172

Table 6: Discovery reach (in GeV) of di�erent accelerators for particles associated with realistic

models of a strong ESB sector.

(SU (3)C ;

Particle SU (2)V ) Tevatron LHC LEP I LEP II NLC-1000

P 00 (1,1) | 110{150a 8b;28b |c |c;d

P 0 (1,3) | | | | |d

P+P� (1,3) | 400e 45f 100g 500g

P 008 (�T ) (8,1) 400{500h 325i | | |

P 08 d (8,3) 10{20i 325i;j | | |

P+8 P

�8 (8,3) 10{20i;j 325i;j 45f 100g 500g

P+3 P

�3 (3,3) |j |j 100 GeVg 500 GeVg

a Decay mode P 00! , similar to a light neutral Higgs [59].

b Decay mode Z ! P 00, assuming an one-family model, with NTC = 7 and NTC = 8 respectively;no reach for NTC < 7; for larger Z P 00 couplings, the discovery reach extends to 65 GeV [60].c No reach for one-family model; possibility of reach for the Lane-Ramana [61] multiscale model inthe processes e+e� ! P ; Pe+e� [62].d The analogous discovery reach for a CP-odd Higgs scalar can be greatly improved using the NLCoperating in the collider mode (with polarized photon beams) [63].e Estimated from work on charged Higgs (gb! tH�

! t�tb) for tan� ' 1 [64].fLEP I kinematical limit.g Kinematical limits for LEP200 and the NLC-1000.h Contribution to the �tt cross section in multiscale models [65].i QCD pair production of colored PNGBs with decay into 4 jets [66].j QCD pair production of colored PNGBs with decay into t�t, t�b, �+�� or ��� may allow higher reachin mass. This has yet to be studied.

6.3 Phenomenology of Pseudo-Goldstone Bosons

Many ETC models are expected to include a spectrumof pseudo-Nambu-Goldstone bosons (P 's) and vector res-onances (�T 's and !T ) that may carry color quantumnumbers. These particles may be classi�ed by theirSU (3)C and SU (2)V quantum numbers as indicated (forthe P 's) in the �rst column of Table 6, using the nomen-clature of Ref. [67]. Since these particles are stronglyproduced, they have large cross sections at the Teva-tron and LHC. The color triplet (P3) and color octet(P8) pseudo-Nambu-Goldstone bosons will be pair pro-duced from gluon-gluon initial states in hadron collidersand will give rise to 4 jet and t�t �nal states, since inmany models the PNGBs couple preferentially to heavyfermions. Since P3 and P8 couple to the Z boson theycan also be pair produced in e+e� colliders, which areexpected to be sensitive to PNGB masses up to the kine-matic limit. The LHC will be sensitive to P8 masses up to� 325 GeV, while an NLC-1000 would reach � 500 GeV.Since colored PNGBs receive their masses from QCD in-teractions and typically have masses in the 100{300 GeVrange, both the LHC and NLC-1000 can probe the inter-esting region. The expected discovery potential of vari-ous colliders for the pseudo-Nambu-Goldstone bosons isshown in Table 6.

While as yet no completely realistic technicolormodel exists, the models all share the general featureof having a rich spectrum of scalar and vector particleswhich can be probed at either the LHC or a high-energye+e� collider.

7 New Gauge Bosons

7.1 Introduction

Extended gauge symmetries and the associated heavyneutral (Z0) and/or charged (W 0) gauge bosons are afeature of many extensions of the Standard Model (SM).We survey and compare the discovery potential of theexperiments that will be performed over the next decade(Tevatron and LEP 2) and future facilities that are beingplanned and considered for the period beyond.

We present results for heavy gauge boson physicsfor the following representative models: Z� in SO10 !SU5 � U1�, Z in E6 ! SO10 � U1 , Z� =

p3=8Z� �p

5=8Z in superstring inspired models in which E6

breaks directly to a rank 5 group [68], as well as ZLRand W 0

LR in the LR symmetric models [69]. For sim-plicity, we assume that the neutrino produced in the W 0

decay does not produce visible energy in the detector.173

7.2 Discovery Limits of Extra Gauge Bosons

Current limits on the mass of new heavy gauge bosonsare relatively weak. In Table 7 the direct bounds onZ0 production from the main production channel p�p !Z0 ! e+e� from current Tevatron data as well as theindirect unconstrained (no assumption on the Higgs sec-tor) and constrained (speci�c assumption on the Higgssector) bounds from a global analysis of electro-weakdata are presented [70]. From the non-observation ofpp!W 0 ! e�e at the Tevatron, the CDF Collaborationconcludes that MW 0

LR

> 652 GeV [71]. In contrast, theindirect constrained [unconstrained] Tevatron bounds onMW 0

LR

are in the 1.4 TeV [300 GeV] region.

Discovery limits for new gauge bosons at future col-liders are shown in Table 8 [72]. The LHC and a highluminosity 1 TeV e+e� collider have discovery limits fora Z0 which are in many ways comparable. Both mea-surements have strengths and weaknesses. The limitsobtained from the LHC are robust, in the sense thatthey are obtained from a direct measurement with lit-tle background, but they are, however, dependent on thetotal width of the Z0 which is sensitive to assumptionson the particle content of the model. In contrast, limitsobtained for the NLC are indirect, based on statisticaldeviations from the Standard Model and are thereforeboth more model dependent and dependent on havingthe systematic errors under control, but do not dependon the unknown particle content of the model.

If a Z0 were discovered, its mass could be measuredwithout any ambiguity at a hadron collider from the in-variant mass of the lepton pairs which signalled the Z0

discovery. In contrast, at the NLC it is the ratio (g=M 0Z)

2

which enters, so that extracting the Z0 mass is very modeldependent. If evidence were found for a Z0 at the NLC,a model independent determination ofMZ0 would be im-precise at best, except for perhaps a Z0 not much greaterthan the collider energy.

7.3 Z0 Diagnostics at the LHC and NLC

An immediate need after a Z0 discovery would be to de-termine its origins by measuring its couplings to quarksand leptons [73]. Assuming family universality and theZ0 charge commuting with the SU (2)L generators, therelevant quantities to distinguish between di�erent mod-els are the fermion charges, gf

L2(R2) and the gauge cou-

pling strength, g2. Because the signs of the charges willbe hard to determine at hadron colliders the followingfour \normalized" observables are used:

`L =(g`L2)

2

(g`L2)2 + (g`R2)

2;

qL =

(gqL2)2

(g`L2)2 + (g`R2)

2;

~U =(guR2)

2

(gqL2)2;

~D =(gdR2)

2

(gqL2)2: (8)

The values of these couplings at the LHC for the typi-cal models and the corresponding statistical uncertaintiesare given in Table 9 for MZ0=1 TeV.

For MZ0 ' 2 TeV a reasonable discrimination be-tween models and determination of the couplings maystill be possible, primarily from the forward-backwardasymmetry and the rapidity ratio. However, forMZ0 ' 3TeV there is little ability to discriminate between models.The LHC can also address W 0 diagnostics forMW 0 <� 1{2TeV.

If a Z0 were produced on shell at the NLC it wouldbe relatively straightforward to determine its properties.On the other hand, if it is far o�-shell (a more likelypossibility) its properties could be deduced through in-terference e�ects of the Z0 propagator with the and Zpropagators. At the NLC �`; Rhad = �had=�` and A`FBwill be measured and assuming longitudinal polarizationof the electron beam is available A`;hadLR ; A`FB(pol) will bepossible. Although the above quantities can distinguishbetween di�erent models they do not yield informationon all the Z0 couplings.

The following four \normalized" charges and an over-all gauge coupling strength divided by the \reduced" Z0

propagator are probed at the NLC:

P `V =g`L2 + g`R2g`L2 � g`R2

;

PqL =

gqL2

g`L2 � g`R2;

Pu;dR =

gu;dR2

gqL2

;

�A = (g`L2 � g`R2)2g224��

s

M2Z0 � s

: (9)

Recall that couplings (8) probed by the LHC, do notdetermine couplings (9) unambiguously. The couplingswith statistical uncertainties are given in Table 10. TheZ0 charges can be determined to around 10{20 %. Rel-ative error bars are about a factor of 2 larger than thecorresponding ones at the LHC.

7.4 Complementarity

Among existing facilities currently in operation, theTevatron o�ers the highest discovery reach for new gaugebosons with masses up to the 700{900 GeV range al-though LEP 2 can achieve comparable limits for somemodels. In the longer term, hadron colliders, i.e., di�er-ent upgraded versions of the Tevatron and the LHC, as

174

Table 7: Current constraints on MZ0 (in GeV) for typical models (seeRef. [70] for details) from direct production at the Tevatron (Lint = 19:6

pb�1), as well as indirect limits (95 % C.L.) from a global electro-weak

analysis.

Indirect IndirectModels Direct (unconstrained) (constrained)

� 425 330 920

415 170 170

� 440 210 600

LR 445 390 1380

Table 8: Discovery limits for MZ0 (in GeV) for typical models achievable at proposed hadron and

e+e� colliders. At hadron colliders the discovery limits for Z 0 [W 0+ +W 0�] are for typical models

with 10 events in e+e� + �+�� [(e+�e+ e���e ) + (�+��+ �����)] from Drell-Yan production of thegauge boson. For e+e� colliders the discovery limits are the 99% C.L. from a �2 �t of the observables:

�(e+e� ! �+��), Rhad = �had=�`, A`FB , and A`

LR.

Colliderps [TeV] Lint [fb�1] � � LR W 0

LR

Tevatron (p�p) 1.8 1 775 775 795 825 920

Tevatron� (p�p) 2 10 1040 1050 1070 1100 1180

DiTevatron (p�p) 4 20 1930 1940 1990 2040 2225

LHC (pp) 14 100 4380 4190 4290 4530 5310

LEP 2 (e+e�) 0.2 0.5 695 269 431 493

NLC (e+e�) 0.5 50 3340 978 1990 2560

NLC (e+e�) 1 200 6670 1940 3980 5090

NLC (e+e�) 2 200 9560 3150 5830 7210

Table 9: Values of the \normalized" couplings (1) for the typical models. Thestatistical error bars indicate how well the coupling could be measured at the

LHC (ps = 14 TeV, Lint = 100 fb�1) for MZ0 = 1 TeV.

� � LR

`L 0:9� 0:016 0:5� 0:02 0:2� 0:012 0:36� 0:007

qL 0.1 0.5 0.8 0.04~U 1� 0:16 1� 0:14 1� 0:08 37� 6:6~D 9� 0:57 1� 0:22 0:25� 0:16 65� 11

Table 10: The value of the couplings (2) for typical models and statistical error bars as determined fromprobes at the NLC (

ps = 500 GeV, Lint = 20 fb�1). MZ0 = 1 TeV. 100% heavy avor tagging e�ciency

and 100% longitudinal polarization of the electron beam is assumed for the �rst set of error bars, while the

error bars in parentheses are for the probes without polarization.

� � LR

P `V 2:0� 0:08 (0:26) 0:0� 0:04 (1:5) �3:0� 0:5 (1:1) �0:15� 0:018 (0:072)

PqL �0:5� 0:04 (0:10) 0:5� 0:10 (0:2) 2:0� 0:3 (1:1) �0:14� 0:037 (0:07)

PuR �1:0� 0:15 (0:19) �1:0� 0:11 (1:2) �1:0� 0:15 (0:24) �6:0� 1:4 (3:3)

P dR 3:0� 0:24 (0:51) �1:0� 0:21 (2:8) 0:5� 0:09 (0:48) 8:0� 1:9 (4:1)

�A 0:071� 0:005 (0:018) 0:121� 0:017 (0:02) 0:012� 0:003 (0:009) 0:255� 0:016 (0:018)

175

well as a high luminosity e+e� collider, i.e., the NLC,would signi�cantly improve limits on the heavy gaugeboson masses. For the typical models such limits are inthe 1{2 TeV region for the Tevatron upgrades, in the 4{5 TeV region for the LHC, and roughly 2{10 times thecenter-of-mass energy for the NLC with 50 fb�1.

The LHC and a high luminosity 1 TeV e+e� colliderhave discovery limits for Z0 which are in many cases com-parable. However, limits obtained for the LHC and thesubsequent measurement of its mass are robust, in thesense that they are obtained from a direct measurementwith little background. In contrast, discovery limits andmass measurements at the NLC are indirect and there-fore model speci�c.

Once discovered, the LHC and the NLC possess com-plementary diagnostic power for the model independentdetermination of the Z0 couplings to quarks and leptons.In conjunction, the two machines may allow for determi-nation of the MZ0 , an overall Z0 gauge coupling strengthas well as a unique determination of all the quark andlepton charges with error bars in the 10{20% range, pro-vided MZ0

<� 1{2 TeV.

8 New particles and Interactions

Many theories beyond the Standard Model (SM) of theelectroweak and strong interactions, such as Grand Uni-�ed Theories (GUT) or composite models, require theexistence of new matter particles with the possibility ofnew interactions not contained in the SM. These parti-cles can be cast into three categories: new elementaryfermions [68,74,75,76,77], difermions [68,78,79] and ex-cited fermions [80,81,82]. If any signals are seen, it willbe crucial to distinguish among the variety of possiblenew states described in this section. In general, totalcross sections, angular distributions and the polarizationof �nal state particles (resulting from new particle de-cays) can be used to discriminate among the di�erentpossibilities [83].

8.1 New Elementary Fermions

The classic examples of new fermions include: sequentialfourth generation fermions (with a right-handed neutrinostate to allow for neutrino masses larger than mZ=2);vector{like fermions with both left- and right-handedcomponents in weak isodoublets [68], mirror fermionswhich have the opposite chiral properties as the SMfermions [75] and isosinglet fermions such as the SO(10)Majorana neutrino [76].

Fermions that have the usual lepton/baryon quan-tum numbers but possess non-canonical SU(2)L�U(1)Yquantum numbers are called exotic fermions. They oc-cur naturally in GUT models that contain a single repre-sentation into which a complete generation of SM quarks

and leptons can be embedded. For instance, in the groupE6 each fermion generation lies in the 27 representation,which contains 12 new fermions in addition to the 15chiral fermions of the SM [68].

It is conceivable that these new fermions acquiremasses not much larger than the Fermi scale, if thesemasses are protected by some symmetry. In fact, this isnecessary if the associated new gauge bosons (which arepresent in the same GUT model that contains the newfermions) are relatively light [84]. In the case of sequen-tial and mirror fermions (at least in the simplest modelswhere the ESB pattern is the same as in the SM), uni-tarity arguments suggest that their masses should notexceed a few hundred GeV [85]. These particles, if theyexist, should therefore be accessible at the next genera-tion of colliders.

Except for singlet neutrinos, the new fermions cou-ple to the photon and/or to the weak gauge bosons W=Z(and for heavy quarks, to gluons) with full strength; thesecouplings allow for pair production with practically un-ambiguous cross sections. In general, new fermions canmix with SM fermions which have the same conservedquantum numbers (such as color and electric charge).This mixing gives rise to new currents, which determinethe decay properties of the heavy fermions and allow fortheir single production. However, avor changing neu-tral currents (FCNC's) will be generated at levels incon-sistent with present experiments unless intergenerationalmixing is highly suppressed or absent. In the latter case,the mixing pattern simpli�es considerably [86]. The re-maining angles are restricted by LEP and low energyexperiment data to be smaller than O(0:04 � 0:1) [86].Note that LEP1 sets bounds of � mZ=2 on the masses ofthese particles [87] (stronger mass bounds from Tevatroncan be set for new quarks); masses up to mZ might beprobed at LEP2.

The new fermions decay through mixing into massivegauge bosons plus their ordinary light partners, F !fZ=f 0W . For masses larger than mw(mZ) the vectorbosons will be on{shell. For small mixing angles, � <0:1, the decay widths are less than 10 MeV (GeV) formF = 0:1(1) TeV. The charged current decay mode isalways dominant and for mF � mZ , it has a branchingfraction of 2/3.

New fermions can be pair-produced in e+e� colli-sions, e+e� ! F �F , through s{channel gauge boson ex-change. The cross sections are of the order of the point{like QED cross section and therefore, are rather large[83]. Because of their clear signatures, the detection ofthese particles is straightforward in the clean environ-ment of e+e� colliders, and masses very close to the kine-matical limit can be probed. Charged fermions can alsobe pair{produced at colliders via ! F �F . The crosssections are comparable (and may be larger for smallerF masses) to the corresponding rates in e+e� collisions.

176

Heavy quarks can be best searched for at hadron collid-ers where the production processes, gg=q�q ! Q �Q, givevery large cross sections: at the LHC with

ps = 14 TeV

and a luminosity of 10 fb�1 quark masses up to 1 TeVcan be reached [88].

If the mixing angles between the SM and heavyfermions are not too small, then singly-produced newfermions in association with their light partners may pro-duce an observable signal. The rate for single productionis very model dependent (in contrast to pair-productionrates mentioned above); however, it has the potentialfor signi�cantly increasing the new fermion mass reachof a given collider. In e+e� collisions, single productionproceeds only via s{channel Z exchange in the case ofquarks and second/third generation leptons, leading tosmall rates. For the �rst generation leptons, however,one has additional t{channel exchanges which increasethe cross sections by several orders of magnitude [83]. Afull simulation of the signals and the backgrounds hasbeen recently carried out; see Ref. [77].

Heavy leptons of the �rst generation can also besingly produced in ep collisions through t{channel ex-change. At LEP�LHC with

ps = 1:2 TeV and

RL = 2

fb�1, the N and E mass reach has been considered inRef. [89]. In Left{Right models, an additional produc-tion mechanism for single N production via t-channelWR-exchange must be included. A detailed Monte Carloanalysis of this process has been carried out in Ref. [90].In e+e� collisions these neutrinos, can be pair producedwith observable cross sections if the WR bosons are nottoo heavy (MWR

< 2 TeV atps = 0:5 TeV). One can

also search for heavy Majorana neutrinos, through theirvirtual e�ects in the process e�e� !W�

RW�R [91].

8.2 Difermions

Difermions are new bosons (either spin 0 or spin 1) thathave unusual baryon and/or lepton quantum numbers.Examples of these particles are leptoquarks (LQ) withB= �1=3 and L= �1, diquarks with B= �2=3 and L= 0and dileptons with B= 0 and L= �2. They occur insome GUT models (e.g., in E6, the color triplet weakisosinglet new particle can be either a LQ or diquark)and in composite models.

In addition to the usual couplings to gauge bosons,difermions have couplings to fermion pairs which deter-mine their decays. These couplings are a priori un-known, although one typically assumes that the cou-plings between di�erent generations are negligible in or-der to avoid generating tree-level FCNC processes. Asan example, consider the case of LQ's. A systematic de-scription of their quantum numbers and interactions canbe made by starting from an e�ective lagrangian withgeneral SU(3)�SU(2)�U(1) invariant couplings and con-served B and L numbers. This leads to the existence of

5 scalar and 5 vector LQ's with distinct SM transforma-tion properties [76]. In general, present data constraindifermions to have masses larger than 50{150 GeV.

Leptoquarks can be produced in pairs at e+e� collid-ers through gauge boson exchange; signi�cant t-channelquark exchange can be present in some channels if thequark-lepton-LQ couplings are not too small. Depend-ing on the charge, the spin and isospin of the LQ, thecross sections can vary widely [92]. LQ's can also bepair produced in collisions via t-channel LQ-exchange.Single production of scalar and vector LQs has been alsostudied in the e+e�, e and modes of the NLC [93].The kinematical reach is thus extended to �

ps, but

the production rates are suppressed by the unknown LQYukawa coupling to quark{lepton pairs. At e colliders,�rst generation LQ's are observable as long as the cor-responding squared LQ Yukawa coupling is larger thanabout 10�2 e2 (where e2 � 4�� is the electromagneticcoupling strength) [93].

Leptoquarks are color-nonsinglets and hence stronglyinteracting. As a result, LQ's can be produced at hadroncolliders with very large rates. At the LHC, pair produc-tion in the gg=q�q ! LQ �LQ process leads to cross sec-tions ranging from a few nb for masses O(0.1 TeV) to afew fb for masses O(1 TeV). The rate for vector particles(which depends on their anomalous magnetic moment�) is substantially higher than for scalars. At the LHCwith 100 fb�1 the search reach for scalar/vector LQ's is1.4/2.2(1.8) TeV for � = 1 (0), if one assumes a branch-ing fraction of unity for the e+e�+two jet �nal state[94]. Single scalar LQ production, through gu ! e+LQand gd ! ��LQ, can also lead to large cross sections forYukawa couplings of order unity. In this case masses upto � 1.5 TeV can be reached at the LHC [94]. Vectorleptoquarks have larger production rates and the discov-ery reach can be extended to � 2 TeV. Although LQ'scan also be singly produced in association with a WR

in alternative Left-Right models via gu ! WR+LQ, adetailed study of the signal and backgrounds has shownthat the LQ discovery reach in this case is quite limited[95]. For �rst generation leptoquark searches, ep collid-ers are particularly well suited. Such LQ's can be pro-duced as s channel resonances in eq !LQ. For example,at LEP�LHC masses up to 1 TeV can be reached, unlessthe corresponding LQ Yukawa couplings are very small.

Dilepton production has been considered at the NLCin the three collider modes: e+e�; e and . These par-ticles are accessible up to masses close to

ps=2 in pair

production, e+e�= ! X++X��: the rates (especiallyin collisions because of the charge) are very large andthe signatures (four leptons) are spectacular. Dileptonscan also be singly produced in the three modes of the col-lider [96]. Diquarks can be pair produced in e+e� and collisions for masses smaller than

ps=2 with appreciable

rates, with a signal consisting of an excess of 4 jet events.177

They can be also produced at hadron colliders in pairs(or singly for the �rst generation diquark if its couplingto quark pairs is not too small). However, large QCDbackgrounds present a formidable challenge to diquarksearches at the LHC.

8.3 Excited Fermions

The existence of excited particles is a characteristic sig-nal of substructure in the fermionic sector [80]: if theknown fermions are composite (composed of more el-ementary constituents called preons), then they shouldbe the ground state of a rich spectrum of excited stateswhich decay down to the former states via a magneticdipole type de-excitation. Since there is not yet a sat-isfactory and predictive dynamical model for compos-ite fermions, one has to use phenomenological inputs tostudy this scenario. For simplicity, one assumes that theexcited fermions have spin and isospin 1/2; their cou-plings to gauge bosons are vector{like (form factors andnew contact interactions may also be present). Further-more, the coupling which describes the transition be-tween excited and ordinary fermions is taken to be chiraland inversely proportional to the compositeness scale �which is of O(1 TeV).

Excited fermions can be pair-produced in f �f anni-hilation via s-channel gauge boson exchange (V = W ,Z, or gluon), although some suppression due to formfactors is expected [81]. The excited fermions decay intogauge bosons and their ordinary partners, f? ! fV . Thecharged leptons have the electromagnetic decay whichhas at least a branching ratio of 30%, and the excitedquarks decay most of the time into quarks and gluons.These two decays constitute a very characteristic signa-ture and discriminate them from the exotic fermions pre-viously discussed.

In e+e� and collisions, the processes and the crosssections are the same as the ones previously describedfor vector{like exotic fermions (up to possible form-factorsuppressions); hence the detection of f� masses up to thekinematic limit may be possible. Excited fermions can besingly produced with their light partners, but the ratesare suppressed by a factor of 1=�2. At e+e� colliders, forquarks and second/third generation leptons, for whichthe process is mediated by s{channel boson exchange,the cross sections are very small. But for the �rst gener-ation excited fermions, one has substantial contributionsdue to additional t{channel diagrams: W exchange for��e and Z= exchanges for e�, which increase the crosssections by several orders of magnitude. The excited lep-tons can be also singly produced in e collisions (e� asa resonance and �� in association with a W ) with muchlarger rates. All excited fermions can be singly producedin collisions with appreciable cross sections. For � �

few TeV, excited quarks and leptons can easily be foundin such machines, if kinematically allowed [83].

Due to the special couplings of the electron to the ex-cited leptons of the �rst generation, single production ofe� through t-channel and Z exchange, and ��e throughW exchange are possible processes in ep collisions. Thecross sections are large; requiring a few tens of events toestablish a signal, one can probe �� and e� masses upto 800 GeV at LEP�LHC for

RL = 2 fb�1 [97]. Ex-

cited quarks of the �rst generation can also be producedin ep collisions, however background problems make thispossibility less interesting.

Excited quarks can be produced in pp collisionsthrough a variety of mechanisms [81]. The dominantproduction channels are the gluonic excitation of quarksg + q ! q� which occurs through the q�qg magnetic in-teraction, and the excitation through the preon interac-tions qq ! qq� and q�q�. The latter is also responsiblefor excited lepton production, q�q ! ee� and e�e�. Thesignatures of excited quarks are dijet mass bumps, jet +gauge boson and jet + lepton pair combinations. Excitedleptons would reveal themselves in leptons + gauge par-ticles or leptons + quark jets. QCD backgrounds havebeen studied and have been shown to be under control.At the LHC with a luminosity of 10 fb�1, a mass range of5{6 TeV and � 4 TeV can be reached for excited quarksand excited leptons, respectively [89].

8.4 Synopsis

The prospects for the discovery of new fermions (of thesequential, exotic, or excited variety) or di{fermions atfuture high{energy colliders can be summarized as fol-lows:

e+e�, e , , e�e� colliders:

� All new particles considered in this section (exceptfor weak isosinglet neutrinos) can be pair produced ine+e� collisions up to the kinematical limit of

ps=2.

Similarly for new charged particles in collisions.

� Due to their special couplings to the electron, the�rst generation of exotic leptons, excited leptons, lep-toquarks and dileptons can be singly produced if themixing angles, the compositeness scale or the cou-plings to the light fermion pairs are not prohibitivelysmall; one can then reach masses close to the center-of-mass energy of the collider. Here, all four potentialmodes of the NLC can be useful.

� Due to the clean environment of these machines, onecan perform precision measurements which allow oneto probe the indirect e�ects of some of these particlesfor mass scales much higher than the center-of-massenergy.

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ep colliders:

� ep colliders are well suited for the production ofthe �rst generation exotic leptons, excited leptonsand especially leptoquarks, if the mixing angles, thecompositeness scale or the couplings to quark{leptonpairs, respectively, are not too small. At LEP�LHC,masses around 1 TeV can be reached.

pp colliders:

� Proton colliders are ideal machines for the produc-tion of new color non-singlets. At the LHC, parti-cle masses in the TeV range can be probed: � 1TeV for sequential or exotic quarks, � 1.5|2 TeVfor leptoquarks and 5|6 TeV for excited quarks forreasonable values of the compositeness scale.

� New color-singlet particles can also be produced, butwith smaller cross sections than for quarks. Howeverthe signatures are cleaner and might compensate forthe small rates. For instance, some exotic leptons canbe discovered for masses smaller than � 1=2 TeV;through contact interactions, excited electrons canalso be produced for masses in the TeV range.

Finally, it should be noted that the e�ects of newinteractions may be observable even if all the associatednew particles beyond the SM are too heavy to be ob-served directly. If the mass scale of the new physics, �,is assumed to be much larger than mZ , then one can for-mally integrate out the heavy particles and remove themfrom the full theory. The resulting low-energy e�ectivetheory will di�er from the SM by new (anomalous) in-teractions among SM particles which are suppressed byinverse powers of �. For example, new physics beyondthe SM could generate four-fermion contact interactions[98], which could be detected as deviations from SM pre-dictions in 2-to-2 scattering processes involving quarksand/or leptons [91]. In this way, one may have exper-imental sensitivity to much larger values of � as com-pared to direct searches for new particles. The search foranomalous couplings in the SM may be particularly fruit-ful in the precision study of W and Z self-interactionsand top-quark interactions. Since these are the heaviestparticles of the SM, it is plausible that their interactionscould be modi�ed by the dynamics underlying the gener-ation of mass. The phenomenology of anomalous gaugeboson and top-quark couplings is studied in more detailin the next two chapters.

9 Anomalous Gauge Boson Couplings

9.1 Parametrization of Anomalous Gauge Bosons

Interactions

One of the most direct consequences of the SU (2) �U (1) gauge symmetry of the SM, the non-abelian self-couplings of the W , Z, and photon, remains poorly mea-sured to date. Although information on these couplings

can be extracted from low energy data and high preci-sion measurements at the Z pole, there are ambiguitiesand model dependencies in the results. However, a directmeasurement of these vector boson couplings is possiblein present and future collider experiments, in particularvia pair production processes like e+e� ! W+W� and

p p(�) ! W+W�; W ; WZ. The �rst and major goalof such experiments will be the veri�cation of the SMpredictions at a quantitative level.

For our discussion of experimental sensitivities weemploy a parametrization of the WWV couplings (V = ; Z) in terms of a phenomenological e�ective La-grangian [99]:

iLWWV = gWWV

�gV1�W y��W

�V � �W y�V�W

���

+ �VWy�W�V

�� +�V

m2W

Wy��W

�� V

��

�(10)

Here the overall coupling constants are de�ned asgWW = e and gWWZ = e cot �W . The couplings gV1 , �V ,and �V need to be determined experimentally. Withinthe SM, at tree level, they are given by gZ1 = g

1 = �Z =

� = 1; �Z = � = 0. g 1 = 1 is �xed by electromagneticgauge invariance; gZ1 , however, may well be di�erent fromits SM value 1 and appears at the same level as � or �Z .

The e�ective Lagrangian of Eq. (10) parametrizes themost general Lorentz invariant and C and P conservingWWV vertex which can be observed in processes wherethe vector bosons couple to e�ectively massless fermions.Terms with higher derivatives are equivalent to a depen-dence of the couplings on the vector boson momenta andthus merely lead to a form-factor behavior of these cou-plings [99]. Analogous to the general WWV vertex it ispossible to parametrize anomalous Z V; V = ; Z cou-plings in terms of two coupling constants, hV3 and hV4 , ifCP invariance is imposed. All Z V couplings are C odd;hV3 corresponds to a dimension 6, hV4 to a dimension 8operator [99].

Tree level unitarity uniquely restricts the WWV

and Z V couplings to their SM gauge theory valuesat asymptotically high energies. This implies that de-viations of gV1 , �V , �V and hVi , i = 3; 4 must beparametrized by form factors which indicates that the ef-fective Lagrangian describing the anomalous vector bo-son self-interactions breaks down at some high energyscale. SM one-loop e�ects lead to corrections of O(�)with a form factor scale, �FF , of order the electroweaksymmetry breaking scale.

Models which have been considered so far, such astechnicolor or supersymmetric models, predict rathersmall deviations from the SM values, of O(10�2) or less.If we regard the Standard Model as an e�ective �eld the-ory, then new physics can be parametrized in a model in-dependent way by additional gauge-invariant operators.

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Regardless of whether Higgs physics is strongly or weaklyinteracting, there are restrictions on the strength of suchcontributions which, however, depend on naturalness as-sumptions. Detailed analyses [100,101] show that theserestrictions leave a slim chance only that new physics willbe discovered through anomalous couplings at machineswhich are less capable than the LHC or NLC.

9.2 Search for Anomalous Gauge Boson Couplings at

Present and Future Colliders

The direct measurement ofWWV and Z V couplings inpresent and future collider experiments in general makesuse of the high energy behavior of the non-standard con-tributions to the helicity amplitudes which grow like apower of the parton center of mass energy. In di-bosonproduction, this leads to an excess of events at large W ,Z and photon transverse momenta as well as at largeinvariant masses of the di-boson system. Furthermore,the various non-standard couplings contribute to di�er-ent helicity amplitudes in the high energy limit. An-gular distributions of the W and Z-boson decay prod-ucts, therefore, are helpful as polarization analyzers, inparticular in e+e� collisions. Quantitative bounds on�gZ1 = gZ1 � 1, ��V = �V � 1 and �V are obtained bycomparing the shape of the measured and the predicteddistributions.

Present and future 95% con�dence level (CL) lim-its on a variety of WWV and Z V couplings are listedin Table 11. In addition, the limits on the couplings�� and � are displayed in bargraph form in Fig. 5.The present limits are from di-boson production at theTevatron [102] and from single photon production atLEP [103]. The future limits are estimated for experi-ments at the Tevatron, LEP II, the LHC and a futurelinear e+e� collider (NLC). In contrast to the boundson anomalous WWV couplings, the limits on the Z Vcouplings hVi0, i = 3; 4 depend signi�cantly on the formfactor scale �FF . Here they are assumed to appear inthe form hVi = hVi0=(1 + s=�2

FF )ni , i = 3; 4 with n3 = 3

and n4 = 4.

A direct measurement of the WW vertex isachieved via W production. The best current boundson WWV couplings, however, depend signi�cantly oninformation obtained from W+W� and WZ productionat the Tevatron in the channel p�p ! W+W�; W�Z !`��jj. In deriving these bounds, �� = ��Z and� = �Z is assumed.

The present limits on anomalous WWV and Z V

couplings can be improved by one order of magnitudeor more in future Tevatron experiments if an integratedluminosity of 1 fb�1 can be achieved. Raising the inte-grated luminosity to 10 fb�1 typically leads to a factor� 2 improvement over the limits which can be achievedwith 1 fb�1. Fitting several di�erent distributions simul-

Figure 5: Present and future 95% CL bounds on �� (a) and

� (b).

taneously might lead to further improvements. Boundson �gZ1 and ��V are expected to be comparable to thosewhich can be obtained at LEP II. For �V , the limits fromfuture Tevatron experiments should be better.

The future bounds listed in Table 11 for W+W�

and W�Z �nal states were obtained assuming �Z = � ,�gZ1 = �� =2 cos

2 �w and �gZ1 + ��Z = �� . Theserelations are motivated by an e�ective Lagrangian basedon a complete set of SU (2)�U (1) invariant operators ofdimension 6 [101]. If one assumes � = �Z , � = �Z and�gZ1 = 0 instead, the limit on �� can be improved byabout 40%.

At the LHC, with an integrated luminosity of100 fb�1, values of ��Z, �g

Z1 and �Z of O(10�2) can

be probed. Similar sensitivities can be achieved for theWW couplings. A linear e+e� collider with a center ofmass energy of 500 GeV or more in general can probeanomalous couplings of order 10�3 [104,50].

The present bounds on Z V couplings can be im-proved only by about a factor 2 at best in Z productionat LEP II. Future experiments at the Tevatron will be

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Table 11: Present and future 95% CL bounds on WWV and Z V couplings.

Experiment Channel Limit

D� p�p!W� ! `�� �1:6 < �� < 1:8

(present limit) ` = e; � �0:6 < � < 0:6

CDF p�p! W+W�; W�Z ! `��jj �1:0 < ��V < 1:1

(present limit) � = �Z, � = �Z , gZ1 = 1 �0:8 < �V < 0:8

D� p�p! Z ! `+`� �1:9 < hV30 < 1:8

(present limit) ` = e; �, �FF = 0:5 TeV �0:5 < hV40 < 0:5

L3 e+e� ! ��� �0:9 < hZ30 < 0:9

(present limit) �2:3 < hZ40 < 2:3

Tevatron p�p! W� ! e�� , �0:38 < �� < 0:38

(CDF sim.)ps = 2 TeV,

RLdt = 1 fb�1 �0:12 < � < 0:12

Tevatron p�p!W+W�; W�Z ! `��jj; `+`�jj �0:31 < �� < 0:41

(CDF sim.)RLdt = 1 fb�1, �FF = 2 TeV �0:19 < � < 0:19

Tevatron p�p!W�Z ! `�1 �1`+2 `

�2 �0:26 < ��Z < 0:70

(NLO theor.)RLdt = 1 fb�1, �FF = 1 TeV �0:24 < �Z < 0:32

Tevatron p�p! Z ! e+e� �0:105 < hV30 < 0:105

(CDF sim.)RLdt = 1 fb�1, �FF = 1:5 TeV �0:0064 < hV40 < 0:0064

Tevatron p�p! Z ! e+e� �0:044 < hV30 < 0:044

(CDF sim.)RLdt = 10 fb�1, �FF = 1:5 TeV �0:0025 < hV40 < 0:0025

LEP II e+e� !W+W� ! `��jj, �0:13 < �� < 0:14

(L3 sim.)ps = 190 GeV,

RLdt = 500 pb�1 �0:13 < � < 0:14

LEP II e+e� ! Z ! ��� ,ps = 180 GeV, �0:50 < hZ30 < 0:50

(L3 sim.)RLdt = 500 pb�1, �FF = 1 TeV �0:45 < hZ40 < 0:45

LHC pp!W�Z ! `�1 �1`+2 `

�2 , �0:006 < ��Z < 0:0097

(NLO theor.)RLdt = 100 fb�1, �FF = 3 TeV �5:3 � 10�3 < �Z < 6:7 � 10�3

LHC pp! Z ! e+e� �5:1 � 10�3 < hV30 < 5:1 � 10�3

(LO theor.)RLdt = 10 fb�1, �FF = 1:5 TeV �9:2 � 10�5 < hV40 < 9:2 � 10�5

NLC e+e� !W+W� ! `��jj, �0:0024 < �� < 0:0024ps = 500 GeV,

RLdt = 80 fb�1 �0:0018 < � < 0:0018

NLC e+e� !W+W� ! `��jj, �5:2 � 10�4 < �� < 5:2 � 10�4ps = 1500 GeV,

RLdt = 190 fb�1 �3:8 � 10�4 < � < 3:8 � 10�4

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sensitive to values of hV30 � 0:11 and hV40 � 0:006 (with�FF = 1:5 TeV).

Within the next few years experiments at the Teva-tron and at LEP are expected to con�rm the non-abelianself-couplings of the SM at the 10% level. The O(�) de-viations predicted by the SM and most models of newphysics, however, can only be probed at the LHC or ahigh energy linear e+e� collider. Of course, if the scale ofnew physics is directly accessible at these machines onewould rather focus on the spectrum of new particles anddirect measurements of their interactions with the gaugeboson sector.

10 Top Quarks as a Window to Electroweak

Symmetry Breaking

Among the various matter fermions, the top quark mustbe considered the most mysterious. It is the heaviestknown elementary particle, with mass 30{40 times thatof the next heaviest quark. It is more strongly coupled tothe mechanism of electroweak symmetry breaking thanthe weak gauge bosons themselves. It is plausible, infact, that the top quark is an essential component of thismechanism. On a more mundane level, the top quark isthe only quark or lepton whose couplings to the StandardModel are not constrained to percent accuracy by theLEP experiments. Thus, the couplings of the top caneasily yield surprises.

Most of this section is concerned with the searchfor anomalies in the couplings of the top quark to theStandard Model gauge bosons. We will consider �rst thepossibility of large deviations from the standard proper-ties of the top quark and then the precision experimentsthat could show signs of smaller deviations. Finally, wewill discuss the possibility that the top quark has decaymodes outside the Standard Model.

10.1 Anomalous Top Couplings { s-Channel Resonance

The original CDF announcement of evidence for the topquark [105,106] came with an anomaly, the measurementof a production cross section 2{3 times larger than thetheoretical prediction. The more recent announcementsof the observation of the top quark by CDF [107] and D�[108] give a production cross section of 6.5�1:8 pb, whichis consistent with the Standard Model unless the topquark mass is above 185 GeV. Nevertheless, the possibil-ity of order-1 deviations of the top quark couplings fromthe predictions of the Standard Model is extremely tan-talizing and might well open a new window into physicsof avor.

At the Tevatron collider, the dominant mechanism oft�t production is through q�q annihilation; at a top massof 175 GeV, the gg fusion cross section is a factor 10smaller. To dramatically enhance this cross section, it is

natural to consider models with an s-channel resonancein t�t production, with a mass of 500{600 GeV, just abovethe t�t threshold. Two groups of authors have proposedexplanations of this type based on pre-existing theoreti-cal models [109,65].

Higher luminosity running at the Tevatron colliderwill clarify this situation. The clearest prediction of themodel is an excess of events at large t�t invariant mass andhigh t transverse momentum. Taking the model [109]with a 600 GeV resonance for de�niteness, event sam-ples of 0.1 fb�1, 3 fb�1, and 100 fb�1 lead to roughly10, 300, and 10,000 observed t�t events with m(t�t) > 600GeV, assuming e�ciency (1/10) for detection, above abackground 5 times lower. These samples correspondto the goals for the current Tevatron collider run, thenew Main Injector upgrade, and the TeV� luminosity up-grade. With the same event samples, one could put lowerlimits on the mass of an s-channel resonance at roughly700, 1000, 1500 GeV.

At the LHC, the production cross section for t�t is90% gg fusion, but the observed rates are large, of order106 t�t pairs per year. The cross section measurement atthe LHC clearly distinguishes the q�q from the gg modelfor the s-channel resonance; these models predict crosssections di�ering by a factor of 10. The mass reach of theLHC with 10 fb�1 is about 1000 GeV in the q�q model and2000 GeV in the gg model, with stronger constraints at100 fb�1.

Since both models involve resonances that do notcouple to leptons, their direct e�ect on t�t production isnot easily tested at an e+e� collider. However, for bothmodels, an e+e� collider with an energy about 1 TeVcould provide important complementary information onthe associated production of the new resonances with t�tand on the pair-production of related new particles withelectric charge and exotic color.

10.2 Anomalous Top Couplings { E�ective Lagrangian

If the top quark production cross section proves not tobe anomalous at the zeroth order, how well can the topquark couplings be searched for anomalies at higher or-der? An appropriate framework for discussing this ques-tion is an e�ective Lagrangian governing the top quarkcoupling to gauge bosons. For example, the coupling ofthe W boson to t�b may be written

�L =gp2FW1 (q2)�t �bLW� +

1

4mt

FW2 (q2)�t���bLFW�� :

(11)Analogous formulae de�ne the F1 and F2 form factors ofg, , and Z. Phenomenological couplings of this formhave been studied by many authors [110]. Electroweakinteractions typically give contributions to these formfactors at the 1% level or below. However, it is likely thatthere are larger contributions from models in which the

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top quark is strongly coupled to the symmetry breakingsector. For example, extended technicolor models givecontributions to the various F1 form factors of tL, tR,and bL which are typically of order 5% but whose pat-tern depends on the details of the model [111].

We consider �rst the measurement of these form fac-tors in hadron-hadron collisions. It is possible that theseform factor corrections are large; in fact, it has been pro-posed [112] that a nonzero color anomalous magnetic mo-ment F g2 � 0:25 could provide an alternative explanationof the large cross section reported by CDF. On the otherhand, if the form factor e�ect is smaller, one's abilityto measure it quickly becomes limited by the 15% QCDuncertainty in the t�t production cross section. In a one-parameter �t based on the total cross section, the Teva-tron could bound the F2 of the ttg coupling to �0:15(95% conf.) with 0.1 fb�1 and reach the systematicslimit of �0:10 with 0.5 fb�1 [113]. The same systematicslimit appears at the LHC. Yuan has suggested that theF1 coe�cients of the Wt�b couplings can be constrainedby measuring the cross section for single top production:gW ! t�b; this cross section, however, has a theoreticaluncertainty of order 30% [114]. One parameter of t�t pro-duction at hadron colliders which seems very promisingfor a precision constraint is the measurement of the lon-gitudinal/transverse polarization of W bosons from topdecay; a 3 fb�1 event sample at the Tevatron should bringthe statistical uncertainty below 4% [115].

The environment o�ered by e+e� colliders o�ersmany advantages for a precision study of the top cou-plings. In addition to low backgrounds and the ability toreconstruct t�t in the 6-jet mode, top production is char-acterized by order-1 forward-backward and polarizationasymmetries which re ect sizeable interference of the and Z exchange diagrams. Top quarks produced in theforward direction carry the electron polarization and thusprovide a polarized sample for studies of the decay formfactors.

For comparison with the estimate given above, thetotal cross section measurement at an e+e� collider with20 fb�1 should bound a common F2 for the tt and t�tZcouplings, in a one-parameter �t, at �0:03. However,much more detailed studies are possible, at least withlarge event samples. For example, consider a variationin the Zt�t coupling leaving the t�t coupling �xed. Theleft- and right-handed form factors of Zt�t coupling canbe constrained in a two-parameter �t for an event sam-ple of 100 fb�1 at 500 GeV, to deviations of �0:08 (95%conf.). (The systematic contribution to this error shouldbe small, and will be analyzed carefully for the �nal re-port.) For comparison with the parameter of top decaysdiscussed above, Fujii has found that the fraction of lon-gitudinal W bosons in t decay can be determine with astatistical precision of 2% with 10 fb�1 of data at 350GeV. By studying top pair production with an extra jet,

one can obtain [116] a direct limit on the color anoma-lous magnetic moment F g2 , to be compared with thatfrom hadron colliders; with 200 fb�1, the constraint is�0:16 (95% conf.).

The F1 associated with the Wt�b vertex can be ob-tained from a measurement of the total width of the topquark, assuming that no exotic decay modes are seen.This quantity can be measured at the threshold for t�tproduction by three techniques: the width of the 1S reso-nance or shoulder, the momentum distribution of recon-structed top quarks decaying to Wb, and the forward-backward asymmetry of top production due to the in-terference of overlapping S and P wave states. Fujii,Matsui, and Sumino [117] have found that, by combiningthese techniques, the width of the t can be determinedwith 100 fb�1 of data to an accuracy of 4%, plus an er-ror from the uncertainty in �s that boost this numberto about 10%. We should also note that, in models witha relatively light Higgs boson, of mass about 100 GeV,the height of the 1S enhancement at the t�t thresholdmeasures the t�t Higgs coupling constant, to about 25%accuracy.

In addition to magnetic dipole (F2) couplings, thetop quark may also have electric dipole couplings whichviolate CP. Direct measurements of the form factors givelimits on the CP-violating couplings similar to those citedabove. This is probably not adequate for those modelsof CP violation involving CP-violating Higgs bosons cou-pling strongly to the top quark. However, Schmidt andPeskin have suggested observing the energy asymmetryin e+ vs. e� decay products of t�t. Combined with thehigh statistics available at the LHC, this technique couldreasonable reach the CP asymmetries of 10�3�10�4 pre-dicted by the models [118].

10.3 Exotic Decays of the Top Quark

The top quark may also connect to exotic states by itsdecays. Many exotic decay modes of top have been con-sidered in the literature. Here are the most importantones:

t! H+b: This mode is interesting because it is thebest way to �nd H+ at hadron colliders. In addition, theratio of t-quark branching ratios to H+b and W+b de-pends on tan �, providing one of the best ways to measurethis parameter of an extended Higgs sector. The decaymode should be found at LHC with 1033 luminosity, orwith a 500 GeV e+e� collider with 1 fb�1 of data.

t ! e�0et: This is a supersymmetric decay of topwhich occurs in a reasonable volume of parameter space,with a branching ratio of roughly 5% if et is much lighterthan t [119].

t! ch0, t! cZ, t! cg, etc.: These avor changingneutral current modes are extremely rare in the StandardModel, with branching ratios < 10�10. If these modes

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are dramatically enhanced by new physics, they mightbe observed at the LHC.

t! sW+. This mode is expected to be at the 0.1%level in the Standard Model. If this mode is enhanced tothe few-percent level, it should be observable at an e+e�

collider [120].

11 Virtual E�ects of New Physics

11.1 Overview

The study of virtual e�ects can open an important win-dow on electroweak symmetry breaking and physics be-yond the Standard Model (SM). The examination of indi-rect e�ects of new physics in higher order processes o�ersa complementary approach to the search for direct pro-duction of new particles at high energy accelerators. Infact, tests of loop induced couplings can provide a meansof probing the detailed structure of the SM at the levelof radiative corrections where Glashow-Iliopoulos-Maiani(GIM) cancellations are important. In some cases theconstraints on new degrees of freedom via indirect e�ectssurpass those obtainable from collider searches. In othercases, entire classes of models are found to be incom-patible. Given the large amount of high luminosity datawhich will become available during the next decade, thisapproach to searching for physics beyond the SM willbecome a valuable tool.

11.2 Precision Electroweak Measurements

Virtual e�ects from new physics are easily detected inprecision electroweak measurements. These include themeasurements of the Z line{shape and asymmetries atSLD/LEP, deep inelastic muon{neutrino scattering, andatomic parity violation. Because of the accurate theo-retical predictions in the electroweak sector of the SM,especially in purely leptonic processes that are free ofQCD corrections, any observed deviations must be ex-plained as due to new physics not encompassed withinthe SM.

Radiative corrections from new physics are oftenclassi�ed into two groups; the `oblique' and the `direct'corrections. `Oblique' refers to the vacuum polarizationcorrections to the gauge boson propagators. They areindependent of the external particles and thus are uni-versal to all electroweak processes. `Direct' refers to thevertex and box corrections which are speci�c to each pro-cess. Because of the universality of oblique corrections,it is possible to express them in a model independentfashion with a few phenomenological parameters. Underthe two assumptions that the electroweak gauge group isthe standard SU (2)L�U (1)Y , and that the scale of newphysics is large compared to the electroweak scale, thevirtual e�ects of new physics can be expressed in terms

of 3 parameters, often called S, T , and U [121]. Usinga set of measurements to which the direct correctionsfrom new physics are expected to be small, one can placetight constraints on the values of S and T . These includethe purely leptonic processes at SLD/LEP, and atomicparity violation measurements. Currently, the strongestconstraint on S and T comes from the SLD/LEP mea-surement of sin2 �e�w and �(Z ! `+`�).

If one relaxes the second assumption that the scale ofnew physics is large compared to the electroweak scale,then it becomes necessary to introduce three additionalparameters called V , W , and X [122]. If one relaxesthe �rst assumption and extends the electroweak gaugegroup to SU (2)L�U (1)Y �U (1)Y 0 , SU (2)L�SU (2)R�U (1)B�L, SU (3) � U (1), etc. then it becomes necessaryto take into account the exchange of the additional gaugebosons as well as their virtual loop e�ects so these modelscannot be treated within the S{T formalism and eachcase must be analyzed separately.

A process where the direct corrections from newphysics is expected to be sizable is Z ! b�b. This isdue to the fact that the b{quark is the isospin partner ofthe t{quark so the same mechanism which generates thelarge t{quark mass will also generate a large vertex cor-rection to this process. This is true in the SM which hasa vertex correction proportional to m2

t , and also in Tech-nicolor models and SUSY models. If such new vertexcorrections exist, then one should be able to see a devi-ation from the SM prediction after the universal obliquecorrection e�ects have been folded out. Such a deviationat the 2�-level is presently observed at LEP in the ratioRb = �b�b=�had.

11.3 Rare Processes in the Quark Sector

Rare K processes have played a strong and historicalrole in constraining new interactions. The box and pen-guin diagrams which typically mediate these processesreceive contributions from the SM, as well as potentiallysizeable contributions from new physics. For example,the strongest limit (albeit assumption dependent) on themass of a right-handed W -boson is derived from its con-tributions to K0{ �K0 mixing, and the requirement of neardegeneracy of squark masses results from a super-GIMmechanism imposed in the K sector. Rare K decay ex-periments at Brookhaven and KTeV at the Tevatron willprovide further probes in the near future. The decayK+ ! �+��� is an interesting mode as it is theoreticallyclean and experiment will reach the SM level during thenext decade. K0

L ! ��e� is forbidden in the SM andprovides a probe of lepton number violation, leptoquarkexchange, and family symmetries.

Short distance SM contributions to rare charm pro-cesses are small due to the e�ectiveness of the GIM mech-anism (as there are no large quark mass splittings in the

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loops). Long distance e�ects usually dominate and aredi�cult to reliably calculate. Observation of D ! �

would provide an excellent test of the techniques used inthese calculations, and could be used to reliably evaluatethe related long distance contributions to B ! K� ; � .However, there is a window for the clean observationof possible new physics contributions in some processes,such asD0{ �D0 mixing, D ! Xu`

+`�, andD ! ��. Thetypes of non-standard scenarios which give the largestcontributions to these reactions are

� two-Higgs-doublet models in the large tan � region,

� multi-Higgs doublet models with avor changing cou-plings,

� new Q = �1=3 quarks,� supersymmetric models with non-degenerate

squarks, and

� variants of left-right symmetric models.

Several high volume charm experiments are planned forthe future, with 107�8 charm mesons expected to be re-constructed. D0{ �D0 mixing can then be probed another1{2 orders of magnitude below present sensitivities.

A large amount of data in the B-meson system willbe acquired during the next decade at SLC/LEP, CESR,the Tevatron, and the SLAC and KEK B Factories.Here, one-loop processes occur with sizeable rates inthe SM, due to large top-quark contributions. Manyclasses of new models can give signi�cant and testablecontributions to rare B processes. The inclusive processB ! Xs and the related exclusive decay B ! K�

has been observed by CLEO and is the �rst direct ob-servation of a penguin mediated process. It has providedstrong restrictions on parameters in several theories be-yond the SM [123], with the bounds being competitivewith those from direct collider searches. For example,it constrains the mass of a charged Higgs boson to be> 260GeV for mt = 175 GeV, and provides complemen-tary bounds to those obtained at colliders on an anoma-lous WW vertex. The inclusive processes b! s``; s���are also excellent probes of new physics. They are sen-sitive to the form of possible new interactions since theyallow measurements of various kinematic distributionsas well as the total rate. Techni-GIM models predictB(b ! s�+��) � O(10�4) and appear to already be incon ict with the present experimental limits.

CP violation in the B system will be examined at theSLAC and KEK B Factories. Signals for new sources ofCP violation include,

� non-closure of the 3 generation unitarity triangle,

� non-vanishing CP asymmetries for the channelsB0d ! ��0;K0

SK0S ,

� inconsistency of separate measurements of the anglesof the unitarity triangle, and

� a deviation of CP rates from SM predictions.

The large data sample and asymmetric con�guration ofthe B Factories will provide a series of unique consistencytests of the quark sector and will challenge the SM in anew and quantitatively precise manner.

Loop-induced top-quark decays are small in the SMdue to the e�ectiveness of the GIM mechanism. Branch-ing fractions for t! c ; cZ; cg; ch lie in the range 10�12{10�8. Long distance e�ects are expected to be negligible.Contributions from new physics can enhance these ratesby 3-4 orders of magnitude. The tree-level decay t! ch,if kinematically accessible, is possible in multi-higgs mod-els without natural avor conservation. t! ~t~�0 can oc-cur in SUSY if the stop-squark is light. These wouldprovide clean signals for new physics and may be observ-able at a high luminosity Tevatron.

11.4 Electric Dipole Moments

Electric dipole moments (EDMs) of atoms, molecules,and the neutron are the most sensitive test of low en-ergy avor conserving CP violation. Such CP violationfrom the CKM angle is highly suppressed (by at least3 loops), while other sources of CP violation are gener-ally not so suppressed. Atoms with an unpaired elec-tron (such as 133Cs) are generally most sensitive to theelectron EDM, while the neutron and atoms with pairedelectrons (such as 199Hg) are sensitive to CP violation inthe strongly interacting sector. Although no EDM hasyet been observed, the current bounds already put strin-gent constraints on CP-violating extentions of the SM.For example in supersymmetric theories the bound of1:3� 10�27 e cm for the EDM of 199Hg places a limit onnew CP-violating phases that can arise in gaugino massterms and in o�-diagonal squark masses and squark in-teractions. These new phases must be less than a fewtenths of a percent for MSUSY ' 100 GeV. This boundalso limits the CP-violating phases in the Higgs potentialin multi-Higgs theories to be less than roughly 10�1 formHiggs ' 100 GeV. The bound from the neutron gives aslightly less stringent limit. Improvement in most exper-iments is anticipated over the next few years. New tech-niques, such as atomic traps, may allow improvementof up to a few orders of magnitude. If positive mea-surements are eventually made the QCD vacuum anglecontribution can be distinguished from new physics bycomparing atoms or molecules with paired and unpairedelectrons.

11.5 Double Beta Decay

Neutrinoless double beta decay requires the violation oflepton number and is thus a clear signal for physics be-yond the SM. Such a decay could arise from a nonzeroMajorana mass for the electron neutrino. In theorieswith spontaneously broken lepton number, the decay

185

could also be accompanied by the emission of a Ma-joron. The current half life limit for 76Ge gives a boundon the e�ective Majorana neutrino mass of m� < 1{2 eV.The neutrino-Majoron coupling is also constrained to beg�;� < 10�4. The current generation of enriched Ge ex-periments could reach the 0.3 eV level in m� . A largeexperiment, NEMO III, using 100Mo, is being designedto reach the 0.1 eV level.

12 Experimental Issues at Hadron Colliders

The frontiers of particle physics have been signi�cantlypushed forward by discoveries made at colliders with thehighest available center-of-mass energies. Since the early1980's, hadron colliders have become the tool of choicefor extending our knowledge of the high energy frontier.The ability of collider detectors to cover a broad range ofnew phenomena over a wide range of mass scale allowsmany of the most important measurements to be madeand limits to be set in an economical way. A mix ofboth \discovery" and precision measurements have beensuccessfully carried out at such machines over the lastten years. Progress has depended upon a mix of boththeoretical and experimental developments.

During the last ten years, the theoretical communityhas been able to re�ne our knowledge of hadron-hadroninteractions to enable calculations with increasing preci-sion. The soundness of the theoretical framework putsthe hadron-hadron collider on a �rm footing for reliableestimation of event rates and backgrounds for a varietyof new phenomena.

The experimental community has likewise made im-portant advances during this period. Operating experi-ence at hadron colliders with precision tracking detectorshas been gained. These devices open up the possibilityof tagging jets containing b-quarks, a capability that con-siderably broadens the physics reach of collider detectorsas the recent CDF top quark evidence has shown. Inaddition, the broad-based program of detector R&D forSSC and LHC detectors has deepened our understand-ing of how to handle the high occupancies and radiation uxes at high luminosity hadron colliders. The knowl-edge gained from the detector R&D and design stud-ies gives us con�dence that the theoretically predictedphysics capabilities of the hadron collider machines canbe exploited in detectors that are practical to build andoperate.

12.1 Machine Environment

The LHC program is designed to study physics beyondthe Standard Model over a wide mass range for all typesof hypothetical particles. To achieve a substantial reachfor the production and observation of new particles, LHCplans to run at a luminosity of 1034cm�2s�1 with a 25 ns

bunch spacing. There will be on average 25 interactionsper crossing contributing considerable complexity to thedetection of interesting phenomena. Future luminosityupgrades at Fermilab may also generate conditions com-parable to these. The challenge met by the SSC and LHCR&D programs was to create detector designs that couldsurvive in these harsh conditions of high occupancy andhigh radiation, while providing adequate resolution androbust triggering capability.

The general results of the R&D program showed thatexisting detector technologies could be successfully em-ployed to meet the SSC/LHC requirements. The higheroccupancies expected are accommodated in �rst orderby more �nely segmenting the detector. The main R&Dchallenges then lay in the area of electronics and DAQdesign. The widespread use of custom integrated circuitsin the detector front-end electronics allows practical de-signs to handle the high rates and �ne segmentation at�nite cost. Modest extension of existing multi-level trig-ger designs are able to handle the expected event rates.

The high radiation levels in high-luminosity hadronmachines have been a cause for concern for both the SSCand LHC experimental groups. Again, the R&D pro-gram has shown that radiation resistant versions of themost sensitive detector elements can be fabricated withonly modest extension of existing capability. In partic-ular, many front end electronic circuits that would beexposed to the harsh radiation conditions have been fab-ricated in radiation-hard versions and shown to work.Also, the level of thermal neutron ux inside the innertracking cavity and within the detector hall is broughtwithin acceptable limits for detector operation by appro-priate shielding design, especially in the region aroundthe machine �nal focusing quads. Thus, while the prob-lem of radiation resistance remains an ongoing area offurther development for the experimenters, solutions toall the most critical problems appear to be in hand. Formore speci�c details on proposed solutions, see the SSCand LHC detector design reports.

12.2 Detectors

Two large general purpose detectors are being designedfor the LHC, namely ATLAS and CMS. Both experi-ments have been designed to detect all hypothesized par-ticles accessible to the LHC. Many studies have beencarried out by these collaborations, and are detailed inthe ATLAS and CMS letters of intent. Generally, tofully exploit the potential physics reach of future hadroncolliders, detectors must feature good charged particletracking, precision electromagnetic calorimetry, full an-gular coverage for the hadronic calorimetry, and a robustmuon detection system.

How physics processes set the requirements on the186

detector design has been fairly thoroughly explored bythe SSC and LHC experimental groups. As examples,detection of the signal H ! for low mass Higgs re-quires shower counter resolution in the range �E=E =10%=

pE � :7%, measurement of photon position with

accuracy in the range � 5 mm/pE, and timing resolu-

tion adequate for tagging from which bunch the photonoriginated. Measurement of high mass like-sign W pro-duction requires measurement of the sign of the chargeof the W decay lepton out to p? � 500 GeV/c. Angularcoverage for both electrons and muons must extend torapidities of � 2:5 for good angular acceptance for theH ! 4` signals. Many other physics processes have beenstudied to set detailed design parameters for the detec-tors.

SSC and LHC R&D programs were required to showthat detectors with the requisite capabilities are practicalto construct. The SSC and LHC proposals have shownthat detectors with resolutions comparable to existingdetectors are adequate for the task. In large measure,the higher event rates expected at future machines arehandled by �ner segmentation of the detector elements,as mentioned earlier.

The existence of multiple interactions per crossingprovides a further complication of this problem, mainlyby degrading the pattern recognition capabilities of thedetector. Each physics process must be studied with adetailed detector simulation to quantify the capability ofthe design to detect the signal of interest. Such studieshave been carried out in detail, with full event reconstruc-tion, for many of the important Standard Model Higgsdetection modes. Numerous other physics processes havealso been studied at this level of detail. However, the fullextent of the capabilities of the designs as they currentlystand has not been explored. In several areas, prelimi-nary parton-level estimations of detector capability willbe supplemented by more detailed simulations later. Ar-eas of active investigation by the LHC collaborations in-clude b-jet tagging capability at high luminosity, forwardjet tagging capability, and alternate modes for MSSMHiggs detection.

12.3 Outlook

During the last �ve years, important progress has beenmade in understanding the experimental challenges ofhadron colliders. This progress includes improved the-oretical understanding of the basic Standard Modelphysics processes which occur at such machines, im-proved experimental technique through the operating ex-perience gained mainly at Fermilab, and improved in-strumentation mainly through the program of SSC andLHC R&D. Over the next �ve years, we expect to main-tain a program of continual upgrade at FNAL, and con-tinue preparations for LHC. New limits will be set at

FNAL during this period on physics beyond the Stan-dard Model. In addition, measurement of the top andWmasses with improved precision will provide indirect in-formation on the electroweak symmetry breaking sector.Within the next ten years, we hope to see the turn-onof the LHC with a �rst real chance for direct productionof more massive Higgs particles, and considerable risk ofdiscovery for physics beyond the Standard Model.

13 Experimental Issues at e+e� Linear Colliders

13.1 The Physics Environment

Experimental studies at e+e� colliders over the past twodecades have provided key observations and insights tothe nature of the fundamental particles and interactionsof the Standard Model. Electron-positron collisions yieldevents with simple and transparent structures. Anni-hilation events carry the full energy of the beam, andproduce �nal states with few partons. Searches for newphenomena give complete and unambiguous results, andprecision studies of strong and electroweak interactionsare made with a minimum of bias and background. Thephysics environment at TeV-scale colliders will continueto be as ideally suited to the exploration of particlephysics [124].

The Standard Model �nal states that will predom-inate at a

ps = 500 GeV e+e� collider are udscb pair

production (9 units of R), W+W� (20 units of R), ZZ(1.2 units of R), and t�t (1 unit of R), where R = 87 fb/sif s is in TeV2. These processes correspond to relativelysimple �nal states, and, with a typical large solid-angledetector, event structures can be sorted to reduce the 50or so pions, kaons, and photons to a few 4-vectors that ac-curately describe the underlying partons. With the par-tons reconstructed with high precision, topological andkinematic constraints can be utilized to take completeadvantage of the simplicity of the physics environmentat e+e� colliders.

Polarization of the electron beam in a linear collideris a unique tool that provides new and important views ofparticle physics. It can be utilized to isolate longitudinalW boson states, probe the helicity structure of the inter-actions of the top quark, reveal the underlying symmetryof SUSY, and determine the gauge structure of new inter-actions that might be found in high energy collisions - toname just several targets of opportunity. Sources of in-tense bunches of polarized electrons are presently used atthe SLC where beam polarizations of 80% are routinelydelivered to the collision point. Development of sourcesis continuing and it is reasonable to expect polarizationsof 90-95% in the future. Instrumentation has been de-veloped to measure beam polarization with accuracies ofa per cent or better.

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13.2 Detectors

The analysis of events at future e+e� colliders requiresgood tracking of high-momentum leptons and good re-construction of quark jets. The isolation of heavy quarkswith precision vertex detectors will continue to play animportant role in the analysis of events. Particles thatgo unseen in the detector, such as neutrinos and beam-strahlung photons, can be fully reconstructed in manyinstances by applying energy-momentum and mass con-straints.

Most studies of physics at future electron-positroncolliders have used Monte Carlo simulations of detectorswith capabilities that have already been achieved at LEPand SLC. The parameters of a \Standard Detector" arelisted in Table 12. We see that the charged-particle track-ing and electromagnetic and hadronic calorimetery doesnot extend any technology beyond that now in existence.

Table 12: \Standard Detector" Parameters. All momenta and

energies are in GeV. The symbol � means quadratic sum.

Calorimetry

�E=E (electromagnetic) 8%=pE � 2%

�E=E (hadronic) 60%=pE � 2%

Cell size (electromagnetic) 2�

Cell size (hadronic) 4�

Tracking

�Pt=Pt 10�3 � PtVertex resolution (impact) 20�m�

�100�mP

�Hermiticity

Calorimetery and tracking �e� > 10�

Table 13: \Improved Detector" Parameters. All momenta

and energies are in GeV. The symbol� means quadratic sum.

Calorimetry

�E=E (electromagnetic) 8%=pE � 1%

�E=E (hadronic) 35%=pE � 2%

Cell size (electromagnetic) 1�

Cell size (hadronic) 2�

Tracking

�Pt=Pt 2� 10�4 � PtVertex resolution (impact) 5�m�

�50�mP

�Hermiticity

Calorimetery and tracking �e� > 10�

We can anticipate that improvements in the tech-niques and technologies used in the design and construc-tion of particle detectors will occur. At center of mass

energies of several hundred GeV, most applications ofelectromagnetic and hadronic calorimetery do not su�erfrom lack of shower statistics, but it is increasingly im-portant to minimize systematic errors in the reconstruc-tion of the energies and positions of neutral hadrons andphotons. The charged particles of greatest interest aresimilarly energetic, so that the scattering of tracks in thematerial of the detector becomes less problematic. Themore aggressive set of goals shown in Table 13 might berealizable and certainly would enhance the physics out-put of the experiment. More systematic and quantitativestudy is needed to arrive at a complete set of design pa-rameters, but it is clear that existing detectors are notfar from ideal.

13.3 Event Rates and Time Structures

The total e+e� annihilation cross section at high ener-gies is approximately 30 units of R, or 10�35cm2 at 500GeV. Colliders at these energies are designed to generateluminosities typically 5� 1033cm�2s�1, with an interest-ing event produced every 10 seconds or so. Small-angleBhabha scattering of electrons and positrons into the re-gion covered by detector elements (above 10 degrees polarangle) occurs with a cross section 5-10 times the annihila-tion rate. This serves as a good monitor of the luminosityand energy spectra of collected data samples.

Cross sections for backgrounds produced by the co-herent beam-beam interaction and low-energy peripheraltwo-photon reactions are also larger than those of anni-hilation events. For example, numerically the total crosssection for the reaction ee ! eeee is � 10�26cm�2 (atbeam energy of 500 GeV). Most of this cross section cor-responds to production of e+e� pairs near threshold, butthe total rate can be su�ciently large that care must betaken in the design of the accelerator and detector to min-imize the probability that soft particles from these inter-actions will overlap with the desired annihilation events.Accelerator and detector designs have evolved that ac-count for these processes.

The luminosity per bunch crossing and the time in-terval between crossings varies considerably from one ma-chine design to another. Those based on superconductinglinacs yield the lowest luminosity per crossing and spac-ing between bunches of up to a microsecond. The dutycycle and time structure of these machines are similarto those found at LEP for example, and place similardemands on detector data acquisition systems. Collid-ers that utilize linacs with high frequency rf (at X-Bandfor example), create brighter collisions in short trains oftypically 100 bunches pulsed at repetition rates of 100{200 Hz. Bunches within a train will be spaced by a fewnanoseconds. Detector trigger and data acquisition sys-tems will have long periods to analyze and format infor-mation from each repetition cycle, but it will be advanta-

188

geous for detectors to be able to assign observed chargedand neutral particles to their proper bunch-bunch inter-action. Detectors have been built with this capability,and these issues have been considered in the evaluationof physics analyses at colliders with center of mass ener-gies as high as 1.5 TeV.

13.4 Beamstrahlung

Another property of high-energy linear colliders is thatof \beamstrahlung" | the radiation emitted by beamparticles as they pass through the electromagnetic �eldof the opposing bunch. Corrections for the e�ects ofinitial-state radiation in e+e� collisions has long beena well-understood process, and similar techniques will beneeded at future colliders to account for the smearing ofannihilation center of mass energies by beamstrahlung.All proposed e+e� machines are designed so that thesmearing of the center of mass energy by beamstahlungis never greater than, and often less than, the smearingby initial state bremsstrahlung.

The consequences of these e�ects on the analysis ofdata have been studied by many groups, and techniquesto correct data, and even individual events, for radiationof energy by the incident particles prior to collision havebeen developed. It is extremely rare that more than onehard photon is emitted in any event, and those that areradiated travel along the incident beam direction, so itis often possible to simply include the radiation as anunknown parameter in a likelihood �t to the event topol-ogy. This works well for analyses of exclusive �nal statessuch as W+W�, ZH0, and t�t pairs.

13.5 Machine-Induced Backgrounds

While the physics environment created by electron-positron annihilation is remarkably neat and orderly, thesingle-pass nature of a linear collider poses a very spe-cial challenge to the experimenter and machine designer.Unlike a storage ring in which the circulating beam isquickly reduced to only those particles that are well-contained within the phase space of the physical anddynamic apertures of the machine, a pulsed collider willtransmit particles that are very near to its aperture limit.Such particles will create backgrounds in experimentaldetectors either through the emission of synchrotron ra-diation as they pass through magnetic �elds near thedetector, or by the creation of secondary debris whenthey strike physical elements along the beamline. Thedetector must be properly masked, and the beam mustbe properly collimated to remove beam extremities, or\tails", well upstream of the interaction region. It is im-portant that the design of the collider include accommo-dation for special optical sections to allow for completecollimation of the phase space of the beam.

The experience of the MARK II and SLD detectors[125] at the SLC has been an invaluable guide to theproblems that will be encountered by experiments at fu-ture linear colliders. Successful operation of these ex-periments and the lessons that have been learned fromthe SLC provide a good basis for design and operationof experiments at the NLC.

14 Conclusions

Exploration of the TeV scale requires a new generation ofcolliders and detectors beyond those currently in opera-tion, and is essential for the long-term vitality of particlephysics. In this report, we describe an in-depth studyof the phenomenology of electroweak symmetry break-ing and quantify the \physics reach" of present and fu-ture colliders. Our investigations focus on the StandardModel (with one Higgs doublet) and beyond: models oflow-energy supersymmetry, dynamical electroweak sym-metry breaking, and other approaches containing newparticles and interactions. Implications for future exper-iments at hadron and e+e� colliders are considered. Onthe basis of this work, we present the following conclu-sions and recommendations.

The participation of the United States in the LHCprogram should be vigorously supported. An extensivestudy of the electroweak symmetry breaking sector andthe elucidation of physics beyond the Standard Modelwill require a robust experimental program at the LHC.The LHC possesses an impressive discovery potential forHiggs bosons, low-energy supersymmetry, and a large va-riety of beyond the Standard Model phenomena, witha mass reach in many cases �ve to ten times the cor-responding mass reach at existing facilities. Of course,with the LHC approximately ten years from its initialrun, one should not overlook the possibility that initialevidence for physics associated with electroweak symme-try breaking and/or physics beyond the Standard Modelcould be uncovered at upgrades of existing facilities.

Detailed simulations of high-energy particle physicsprocesses at hadron colliders are often required to obtainan accurate assessment of the new physics discovery ca-pabilities of future experiments. These include realistictreatments of hadronic jets (beyond parton-level MonteCarlo analyses) and full detector simulations. An activecollaboration between experimentalists and theorists iscrucial to the further development of strategies to ex-tract evidence for electroweak symmetry breaking andbeyond the Standard Model physics at future colliders.

There are many instances of the complementarity offuture hadron colliders and future e+e� colliders. Ahigh-energy e+e� collider will provide a unique low-background environment for the study of the productionand decay of heavy gauge bosons and top quarks and ofnew physics beyond the Standard Model. A Next Lin-

189

ear Collider (NLC) at 0.5 TeV is an ideal laboratory forthe study of intermediate-mass Higgs bosons, while at1.5 TeV, it can begin to probe the physics of a strongly-coupled electroweak symmetry breaking sector. Exper-imental studies at the NLC would provide outstandingopportunities for discovery, while signi�cantly enhanc-ing the ability of the LHC to interpret evidence for newphysics.

Other possible future collider scenarios are beginningto be examined. Physics studies at a number of hypothet-ical Tevatron upgrades beyond the Main Injector havebeen initiated. A full study of the scienti�c potential ofsuch machines is necessary to provide input into any fu-ture cost/bene�t evaluation that might be undertaken inthe future.

In plotting out the course for future colliders, theUS must work closely with its international partners.By avoiding the duplication of resources and taking intoaccount the complementarity of various approaches, itshould be possible to propose a set of future facilitiesthat can fully explore the TeV energy scale and elucidatethe physics of electroweak symmetry breaking. In doingso, we can push the frontiers of particle physics forwardand keep our �eld intellectually vital and exciting.

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