hep-ph/9604354 14 May 1996 our scale of an biguous deviations have b een found tion energies one must address three basic questions theory story The development of the Standard Mo del of particle physics is a remarkable success damental theory at of a comprehensive exp erimental study of thedynamics TeV underlying scale electroweak is symmetry likely breaking to must revealantees b e a of richer new anything sector b eyond say that the study of the TeV scale must reveal the Higgs b oson but with no guar vealed what clusion anism are unknown In order of these questions Mo del parameters the electroweak symmetry breaking particles at and b elow the electroweak scale questions physics b eyond fundamental accuracy Despite At present the dynamics underlying the electroweak symmetry breaking mech Overview eld with a challenge ELECTROWEAK of third are Physics Department Its at ii of the eective theory of the or the origins of to extend many facets have b een tested at particle outstanding what the below nature of What b etter success particles is interactions University of the BEYOND the Standard the We briey summarize current theoretical approaches to answering some the of b est it is a However theoretical studies lead to one very imp ortant con is question Santa Cruz Institute for Standard Mo del to TeV scale the than the the Standard mechanism for of TeV and dynamics Brookhaven National Laboratory Upton NY SYMMETRY the Where do complete However strong theoretical arguments suggest that the one energy of fundamental particles at interactions HOWARD E HABER Standard The answers to these questions are crucial for addressing THE California Santa Cruz CA particle In lowenergy approximation to part SALLY DAWSON Mo del for order description of scale In some cases the mo del has b een veried at in Mo del parameters we go STANDARD physics electroweak electroweak a Mo del to and What is the dynamics resp onsible for thousand The most conservative approach would present day accelerators and BREAKING the from here example a extend Particle Physics of What are Standard as energies the i what is the complete descrip a symmetry the symmetry breaking eective This description MODEL and sup erparticle sp ectrum of Standard one must address the Mo del state AND origins b elow theory breaking a more fundamental of cannot of Mo del PHYSICS of the the electroweak of aairs the In particular fundamental must two basic prop erties Standard no b e to and presents unam higher a be fun iii re

lowenergy sup ersymmetry or a new stronglyinteracting sector of fermions scalars

andor vector resonances The critical path to maintain the longterm vitality of

particle physics must therefore involve the thorough exploration of the TeVscale

in order to elucidate the dynamics of electroweak symmetry breaking and complete

the lowenergy description of particle physics

The origin of the Standard Mo del parameters presents a challenge which may

or may not b e addressed by the next generation of colliders This is b ecause the

energy scale asso ciated with avor physics which controls most of the Standard

Mo del parameters is not constrained by present theories or exp erimental data and

could lie far b eyond the energy scale accessible to future colliders Nevertheless

the elucidation of TeVscale physics may have signicant ramications for our

understanding of avor and physics at even higher energies

This b o ok fo cuses on electroweak symmetry breaking and examines the p o

tential for probing mo dels of physics b eyond the Standard Mo del at future accel

erators A summary of this work was rst presented in Ref Exploration

of TeVscale physics requires a new generation of colliders and detectors b eyond

those currently in op eration or construction The capabilities of the approved fu

ture facilities and a variety of hypothetical future machines were considered these

machines are summarized in Table

Table

p R

Name Type s Yearly Ldt

Approved Pro jects

+ 1

LEP e e GeV pb

1

Tevatron Main Injector pp TeV fb

1

LHC pp TeV fb

Tevatron Upgrades hypothetical

1

TeV pp TeV fb

1

DiTevatron pp TeV fb

+

e e Linear Collider

+ y 1

JLC NLC TESLA e e TeV fb

y

with e e e options

Other Futuristic Colliders

+ + 1

Collider TeV fb

1

Hadron sup ercollider pp TeV fb

The origin of the Standard Mo del parameters is not directly addressed in this

b o ok Nor do es this b o ok examine the p ossibility that new and interesting physics

b eyond the Standard Mo del might p opulate the energy interval above the TeV

scale The Standard Mo del do es not provide any clues as to the energy scale

resp onsible for addressing the origin of the Standard Mo del parameters or a su

p ersymmetric extension thereof The relevant energy scale could lie anywhere

from TeV to the Planck scale M For example in conventional theories of

P

lowenergy sup ersymmetry the origin of the Standard Mo del and sup ersymmetric

parameters lies at or near the Planck scale In contrast theories of extended techni

color typically attempt to solve the avor problem at energy scales b elow TeV

This b o ok fo cuses directly on the TeVscale physics accessible to the next genera

tion of colliders Namely the requirements for completing the TeVscale particle

sp ectrum and unraveling the dynamics of electroweak symmetry breaking are ex

amined We exp ect that future colliders will discover new physics b eyond the

Standard Mo del asso ciated with this dynamics

In Section we b egin with a brief review of the Standard Mo del While

the Standard Mo del is extremely successful in describing the exp erimental data

there are a number of theoretical ob jections asso ciated with the mechanism of

electroweak symmetry breaking The Standard Mo del assumes that electroweak

symmetry breaking is the result of the dynamics of an elementary complex doublet

of scalar elds The neutral comp onent of the scalar doublet acquires a vacuum ex

p ectation value and triggers electroweak symmetry breaking the resulting particle

sp ectrum contains three massive gauge b osons and the massless photon massive

quarks and charged leptons massless neutrinos and a massive Higgs scalar How

ever if one attempts to embed the Standard Mo del in a fundamental theory with

a high energy scale such as the Planck scale M then the masses of elemen

P

tary scalars naturally assume values of order the high energy scale This is due

to the quadratic sensitivity of squared scalar masses to the highest energy scale

of the underlying fundamental theory In contrast theoretical considerations eg

unitarity require the mass of the Standard Mo del Higgs b oson to b e of order the

electroweak scale To accomplish this in the Standard Mo del one must unnatu

rally adjust the parameters of the highenergy theory a ne tuning of orders

of magnitude in the scalar squared mass parameter is required to pro duce the

required light elementary scalar eld These and other theoretical shortcomings of

the Standard Mo del are outlined in Section

Overcoming these theoretical deciencies requires new physics b eyond the Stan

dard Mo del which controls the dynamics of the electroweak symmetry breaking

The generic prop erties of the new physics that can b e obtained indep endently of

sp ecic mo dels are describ ed in Section In particular exp erimental evidence

for the dynamics underlying electroweak symmetry breaking must b e revealed at

the TeV energy scale or b elow However to make signicant progress one must

introduce a sp ecic mo del framework Two main approaches have b een prop osed

i Invoke sup ersymmetry to cancel quadratic sensitivity of the scalar squared

masses to M Electroweak symmetry breaking is triggered by the dynamics

P

of a weaklycoupled Higgs sector

ii Elementary Higgs scalars do not exist A Higgslike scalar state if it ex

ists would reveal its comp osite nature at the TeVscale where new physics

b eyond the Standard Mo del enters Electroweak symmetry breaking is trig

gered by nonp erturbative strong forces

In order to implement case i one must rst note that sup ersymmetry is not

an exact symmetry of nature otherwise all known particles would have equal

mass sup ersymmetric partners If sup ersymmetry is to explain why the Higgs

b oson mass is of order the electroweak scale then sup ersymmetrybreaking eects

which split the masses of particles and their sup erpartners must b e roughly of

the same order as the electroweak scale Thus if sup ersymmetry is connected

with the origin of electroweak symmetry breaking one exp ects to discover a new

sp ectrum of particles and interactions at the TeVscale or b elow In addition

such mo dels of lowenergy sup ersymmetry are compatible with the existence of

weaklycoupled elementary Higgs scalars with masses of order the electroweak sym

metry breakingscale A comprehensive treatment of Higgs b oson phenomenology

is given in Chapter

No direct exp erimental evidence for the sup ersymmetric particle sp ectrum

presently exists There is however tantalizing indirect evidence Starting from

the known values of the SU SU and U gauge couplings at m and extrap

Z

olating to high energies one nds that the three gauge couplings meet at a single

p oint if one includes the eects of sup ersymmetric particles with masses at or

b elow TeV in the running of the couplings Unication of couplings then takes

16

place at around GeV only a few orders of magnitude b elow M The three

P

gauge couplings do not meet at a single p oint if only Standard Mo del particles

contribute to the running of the couplings This could b e a hint for lowenergy su

p ersymmetry and suggests that the theory of fundamental particles remains weakly

coupled and p erturbative all the way up to energies near M This approach is

P

discussed in Section

New physics is also invoked to explain the origin of electroweak symmetry

breaking in case ii For example in technicolor mo dels which make use of the

mechanism analogous to the one that is resp onsible for chiral symmetry breaking in

QCD electroweak symmetry breaking o ccurs when pairs of technifermions con

dense in the vacuum One then identies a new scale v O TeV

ESB

where new physics b eyond the Standard Mo del must enter Other approaches

such as eective Lagrangian descriptions of the strongly interacting Higgs sector

preon mo dels topmo de condensate mo dels comp osite Higgs mo dels etc also

fall into this category Unfortunately due to the presence of nonp erturbative

strong forces it is often dicult to make reliable detailed computations in such

mo dels Moreover phenomenological diculties inherent in the simplest exam

ples require additional structure eg an extended technicolor sector is needed in

technicolor mo dels to generate fermion masses This approach is discussed in Sec

tion Unfortunately a completely phenomenologically viable fundamental mo del

of stronglycoupled electroweak symmetry breaking has not yet b een constructed

Both sup ersymmetric and technicolor mo dels contain a full sp ectrum of new

particles which may b e accessible at the next generation of colliders The phe

nomenology of these particles play a key role in the search for new phenomena and

is addressed in detail in Chapters Nevertheless these visions may b e to o lim

ited Additional unexp ected new particles and interactions might accompany the

physics underlying electroweak symmetry breaking Clearly in order to extrap o

late our particle theories to higher energies with any condence we must know the

complete TeVscale sp ectrum The Standard Mo del p ossesses three generations

of quarks and leptons and no righthanded neutrinos and an SUU gauge

group Is that all Might there b e additional particles that p opulate the TeV

scale Some p ossibilities considered in Chapters and include i an extended

electroweak gauge group yielding additional gauge b osons eg extra U fac

tors leftright LR symmetry such as SU SU etc ii new fermions

L R

eg a fourth generation mirror fermions which p ossess righthanded couplings

vectorlike fermions massive neutrinos etc iii new b osons extended Higgs

sectors pseudoGoldstone b osons other exotic scalars lepto quarks vector reso

nances etc New TeV scale physics can also b e detected through virtual interac

tions of new particles that contribute to anomalous couplings and other lowenergy

observables as reviewed in Chapters and

Finally we briey summarize in Section the key questions of TeVscale parti

cle physics One of the ma jor goals of this b o ok is to examine how b est to answer

these questions at the next generation of colliders Detector and accelerator issues

+

relevant to the search for TeVscale physics at future hadron and e e colliders

are examined in Chapters and The elucidation of the TeVscale will surely

bring forth a new era in the development of the fundamental theory of particles

and their interactions

The Standard Mo del of Electroweak Interactions

The electroweak sector of the Standard Mo del is an SU U gauge theory

L Y

The b osonic sector of the theory contains three massless SU gauge b osons

L

i

W one massless U gauge b oson B and a hypercharge SU doublet of

Y L

complex scalar elds

i

1 2

p

H i

3

The Lagrangian is given by

i i y

1 1

W W B B D D V L

4 4

where

i i i ij k j k

W W W g W W

B B B

i i

1 1

ig W ig YB D

2 2

2 y y 2

V j j j j

The theory dep ends on the following free parameters the SU and U gauge

L Y

coupling constants g and g and the scalar mass and quartic coupling parameters

2

and which app ear in the scalar p otential V Explicit mass terms for the

gauge b osons are forbidden by the gauge invariance Eq is the most general

renormalizable and SU U invariant Lagrangian allowed involving only

L Y

the gauge b osons and scalar elds

2

The state of minimum energy for and is not at zero and the scalar

eld develops a vacuum exp ectation value VEV which can b e taken to b e

p

hi

v

The symmetry breaking scheme exhibited is SU U U In

L Y EM

unitary gauge we can write the scalar eld as

p

H v

The eld H is the Higgs b oson It is a physical scalar which can b e pro duced and

detected exp erimentally It is straightforward to see that the kinetic energy term

for now generates mass terms for three of the gauge b osons W and Z while

the fourth gauge b oson the photon remains massless This is a simple realization

of the Higgs mechanism in which the electroweak symmetry is sp ontaneously

broken while maintaining renormalizability and unitarity of the theory Finding

the physical remnant of this mechanism the Higgs b oson is a vital test of the

correctness of the mo del

The Higgs mechanism is also used to generate quark and charged lepton

masses The SU U gauge invariant Yukawa couplings of the Higgs

L Y

b oson to uptype and downtype fermions are

c

Q d Q u hc L

R u R f d

L L

c

where i transforms as a hypercharge SU doublet and Q u d

2 L L L

L

When is replaced by its VEV Eq generates mass terms for the fermions

with

p

m

f

f

v

Note that within the Standard Mo del there is no explanation for the value of the

fermion masses They are simply input parameters of the theory

One of the most imp ortant prop erties of the Higgs b oson is that its couplings to

fermions and gauge b osons are prop ortional to the corresp onding particle masses

Moreover the overall strength of these couplings is determined in terms of known

masses and couplings The scalar p otential of Eq initially has two free

parameters and We can trade these in for

2

2

v

2 2

v M

H

p

2 1 2

The muon decay rate e determines v G GeV

e F

Thus the only remaining unknown parameter is the Higgs mass As a result

the Standard Mo del Higgs b oson pro duction and decay rates can b e computed

unambiguously in terms of the Higgs b oson mass Chapter of this b o ok discusses

the search for the Standard Mo del Higgs b oson at future colliders

From Eq we see that as the Higgs b oson b ecomes heavy the quartic

coupling in the scalar p otential b ecomes large for O we say that the

scalar sector of the theory is strongly coupled The physics of a strongly interacting

electroweak symmetry breaking sector is discussed in Chapter

Despite the wealth of precision electroweak data at present we have only very

weak exp erimental limits on the Higgs b oson mass From direct searches at LEP

we have the limit

M GeV

H

An improved b ound of around GeV is achievable if no Higgs b oson is discovered

at LEP Standard Mo del Higgs b oson searches at the LHC will b e sensitive

to masses up to around GeV

Precision measurements at LEP give an indirect limit on the Higgs b oson mass

from lo op eects in electroweak radiative corrections

M GeV CL

H

This limit however dep ends sensitively on which pieces of exp erimental data are

included in the t and assumes the correctness of the minimal Standard Mo del

For example if the measurements of the Z bb and Z cc decay rates are omit

ted from the t the CL upp er b ound from Ref b ecomes M GeV

H

Lo op eects which involve the Higgs b oson in a number of low energy pro cesses

are discussed in Chapter although these are relevant mostly in extensions of

the Standard Mo del with nonminimal Higgs sectors

The Standard Mo del is not Complete

Despite the success of the Standard Mo del as a description of the prop erties of fun

damental particles it is clear that the Standard Mo del cannot b e the fundamental

theory of nature There are numerous theoretical ob jections to the Standard Mo del

which we briey summarize here However it should b e emphasized that the va

lidity of the Standard Mo del at all energy scales b elow the Planck scale is not

presently contradicted by any conrmed exp erimental data

For simplicity consider the Higgs sector of the Standard Mo del with gauge

b osons and fermions omitted ie a pure scalar theory in which the p otential

V is given by Eq The quartic coupling runs with the renormalization

scale Q

2

d

2

dt

2 2

and Q is some reference scale This equation is easily where t log Q Q

0

0

solved

2

Q

log

2

2

Q Q Q

0

0

or equivalently

Q

0

Q

2

2 2

Q log Q Q

0

0

We see that Q blows up as Q with Q xed and p ositive Regardless

0

of how small Q is Q will eventually b ecome innite at some large Q called

0

the Landau p ole Alternatively with Q Q as Q ie the the

0

ory if valid to arbitrarily high energy scales b ecomes a noninteracting theory at

low energy a socalled trivial theory To avoid this theoretical embarrassment

one typically attempts to choose parameters in such a way that the Landau p ole

lies ab ove the Planck scale In that case one can hop e that a more fundamental

Planck scale theory avoids this problem If the Landau p ole lies b elow the Planck

scale one must invoke additional interactions which would either alter the renor

malization ow of the coupling or fundamentally change the degrees of freedom of

the theory at some intermediate energy scale near or b elow the predicted lo cation

of the Landau p ole The inclusion of gauge b oson and fermion elds do es not

alter these conclusions In order to avoid a Landau p ole b elow the Planck scale

the Higgs b oson of the Standard Mo del must b e relatively light with mass less

than ab out GeV This is sometimes interpreted as an upp er b ound on the

Standard Mo del Higgs b oson mass

If no Higgs b oson is discovered with a mass lying b elow GeV one would

conclude that there must b e a new energy scale in particle physics that lies b elow

the Planck scale Still if this new scale were much larger than TeV it would

have no discernible eect on exp erimental observables at present colliders as well

as at colliders of the foreseeable future

There have b een many other attempts to limit the allowed mass region of the

Higgs b oson and to pinp oint the energy scale at which either the Higgs b oson or

new physics must b e revealed Another simple b ound is based on p erturbative

unitarity The J partial wave for the elastic scattering of longitudinal W

2

b osons in the high energy limit s m is

W

2 2 2

G M M M s

F

H H H

+ +

p

W W W a W log

0

L L L L

2 2

s M s M

H H

2

one nds At very high energies s M

H

2

G M

F

H

+ +

p

W W W a W

0

L L L L

1

Applying the condition for p erturbative unitarity jRe a j gives the restriction

0

2

M GeV The most restrictive b ound is derived from a coupled channel

H

analysis and gives

p

2 2

M GeV

H

G

F

Similar b ounds are found from lattice studies It is imp ortant to understand

that this do es not mean that the Higgs b oson cannot b e heavier than GeV

it simply means that for heavier masses p erturbation theory is not valid and the

electroweak sector of the theory is strongly interacting

We can apply an alternate limit to Eq and take the Higgs b oson much

p

2

s one nds s For M heavier than the energy

H

G s

F

+ +

p

W W W a W

0

L L L L

p

s TeV Again applying the p erturbative unitarity condition one nds

c

p

s to denote the critical energy scale at which where we have used the notation

c

p erturbative unitarity is violated In this case the most restrictive b ound emerges

from considering the isospin zero channel and yields

p

2

s s TeV

c

G

F

Eq is the basis for the often rep eated assertion that there must be new physics

at the TeV scale Eq is telling us that without a Higgs b oson there must

b e new physics that restores p erturbative unitarity somewhere b elow an energy

scale of around TeV This is precisely the energy scale that will b e prob ed at

the next generation of colliders Therefore we exp ect to either discover the Higgs

b oson b elow around GeV or to discover evidence for a strongly interacting

electroweak symmetry breaking sector How this strongly interacting sector might

manifest itself is the sub ject of Chapters and

A further theoretical ob jection to the Standard Mo del is that p erturbative

lo op corrections to the Higgs b oson squared mass are quadratically divergent and

counterterms must b e adjusted order by order in p erturbation theory to cancel

these divergences If one attempts to embed the Standard Mo del in a fundamental

theory with a high energy scale then the masses of elementary scalars naturally

assume values of order the high energy scale This is a reection of the quadratic

sensitivity of squared scalar masses to the highenergy scale of the underlying

fundamental theory In contrast the unitarity arguments ab ove imply that the

mass of the Higgs b oson of the Standard Mo del must b e of order the electroweak

scale To achieve this requires an unnatural cancelation of terms each b eing of

order the high energy scale but whose sum is of order the electroweak scale

Considering the problems of triviality p erturbative unitarity and the quadratic

divergence in the unrenormalized Higgs b oson squared mass leads us to conclude

that the Standard Mo del is at b est a go o d lowenergy approximation to a more

fundamental theory of particle interactions valid in a limited domain of low

energies of order TeV and b elow In light of the many theoretical ob jections

to the simplest version of the Higgs mechanism theorists have considered several

alternatives for electroweak symmetry breaking In all cases new physics b eyond

the Standard Mo del must arise at or b elow the TeV scale

Mo del Indep endent Asp ects of New TeV Scale Physics

We b egin our discussion of TeV scale physics b eyond the Standard Mo del by

considering the features that are indep endent of the assumptions ab out the source

of the new physics This is usually accomplished by studying the gauge b oson two

three and fourp oint functions and lo oking for deviations from the Standard Mo del

values If we assume that the electroweak gauge group is SU U and that

L Y

the scale of new physics is much greater than m then the eects of new physics

W

are largest in the corrections to the twopoint functions of the gauge b osons As

discussed in Chapter these eects and can b e parametrized in terms of three

parameters S T and U or the related parameters and The LEP

1 2 3

exp eriments have placed stringent b ounds on these parameters which can then b e

interpreted as b ounds on various types of new physics

It has b ecome conventional in the literature to parametrize the three gauge

+ +

b oson vertices W W and ZW W in the following manner

y y Z y y

W W W W A L ig cos g W W W W Z ieg

WWV W

1

1

y y

ig cos W W Z ie W W A

W Z

+ + Z

W W Z W W g cos g

W

5

Z

y y

e W A g cos W Z W W

W

2 2

m m

W W

This is the most general renormalizable Lorentz invariant and CP invariant inter

action Lagrangian for onshell gauge b osons Electromagnetic gauge invariance

Z Z

g and g requires g In the Standard Mo del g

Z Z

1 1

5 1

and within the context of a given mo del the co ecients can b e predicted Typi

cally these co ecients are rather small of O if they arise for example from

Z

and lo op eects A discussion of the limits that can b e placed on g

Z

1

at various accelerators is given in Chapter Any measurement of these co e

Z

cients that deviates from the Standard Mo del values would indicate new physics

but could not distinguish the source of the new physics

A chiral Lagrangian approach is often used to parametrize new physics b eyond

the Standard Mo del To lowest order this nonlinear Lagrangian is simply the

Standard Mo del with no Higgs b oson and massive W and Z gauge b osons The

2

advantage of this approach is that it is a consistent expansion in s where

is the high energy scale that characterizes the scale where new physics o ccurs In

this picture the couplings of the two three and four gauge b oson interactions are

2

related There are ve free parameters in the Lagrangian to O s assuming

an SU U gauge theory a custo dial SU symmetry which guaran

L Y C

tees that the electroweak parameter is equal to as required by exp erimental

data and CP conservation One of these parameters often called L in the

10

literature is related to the S parameter measured at LEP while the other four

give nonStandard Mo del three and four gauge b oson couplings Limits on these

couplings are discussed in Chapter For the three gauge b oson couplings it is

straightforward to map the chiral Lagrangian parameters into the parametrization

of Eq It is also p ossible to couple a generic heavy M TeV I scalar

or I spinone b oson to the chiral Lagrangian and derive valid lowenergy

predictions even though the system is strongly interacting

To make further progress one must consider sp ecic mo dels of the electroweak

breaking sector If the electroweak symmetry breaking sector is weakly coupled

then it is straightforward to predict the chiral Lagrangian parameters in terms of

the fundamental parameters of the underlying theory If the electroweak symmetry

breaking sector is strongly coupled this task is far more dicult We now turn to

sp ecic mo dels for the TeV scale physics

LowEnergy Sup ersymmetric Mo dels

Lowenergy sup ersymmetry is a theory of fundamental particle interactions in

which the sup ersymmetry breaking scale is assumed to b e connected with elec

troweak symmetry breaking and hence is assumed to lie b etween GeV and

a few TeV The simplest version of such a theory is the minimal sup ersymmetric

extension of the Standard Mo del MSSM which consists of taking the Standard

Mo del and adding the corresp onding sup ersymmetric partners In addition

the MSSM contains two hypercharge Y Higgs doublets which is the minimal

structure for the Higgs sector of an anomalyfree sup ersymmetric extension of the

Standard Mo del The sup ersymmetric structure of the theory also requires at

least two Higgs doublets to generate mass for b oth uptype and downtype

quarks and charged leptons All renormalizable sup ersymmetric interactions

consistent with global B L conservation B baryon number and L lep

ton number are included Finally the most general softsup ersymmetrybreaking

terms are added the mass scale asso ciated with such terms is taken to b e of

order TeV or b elow

As a consequence of B L invariance the MSSM p ossesses a discrete R

3(B L)+2S

parity invariance where R for a particle of spin S Note

that this formula implies that all the ordinary Standard Mo del particles have

even Rparity whereas the corresp onding sup ersymmetric partners have o dd R

parity The conservation of Rparity in scattering and decay pro cesses has a crucial

impact on sup ersymmetric phenomenology For example starting from an initial

state involving ordinary Reven particles it follows that sup ersymmetric particles

must b e pro duced in pairs In general these particles are highly unstable and decay

quickly into lighter states However Rparity invariance also implies that the

lightest sup ersymmetric particle LSP is absolutely stable and must eventually

b e pro duced at the end of a decay chain initiated by the decay of a heavy unstable

sup ersymmetric particle In order to b e consistent with cosmological constraints

the LSP is almost certainly electrically and color neutral Consequently the

LSP is weaklyinteracting in ordinary matter ie it b ehaves like a heavy stable

neutrino and will escap e detectors without b eing directly observed Thus the

a

canonical signature for Rparity conserving sup ersymmetric theories is missing

transverse energy due to the escap e of the LSP

The parameters of the MSSM are conveniently describ ed by considering sepa

rately the sup ersymmetryconserving sector and the sup ersymmetrybreaking sec

tor Sup ersymmetry breaking is accomplished by including the most general set

of softsup ersymmetry breaking terms these terms parametrize our ignorance of

the fundamental mechanism of sup ersymmetry breaking Among the parameters

of the sup ersymmetry conserving sector are i gauge couplings g g and g

s

corresp onding to the Standard Mo del gauge group SUSUU resp ec

tively ii Higgs Yukawa couplings and which are matrices in

e u d

avor space and iii a sup ersymmetryconserving Higgs mass parameter The

sup ersymmetrybreaking sector contains the following set of parameters i gaug

ino Ma jorana masses M M and M asso ciated with the SU SU and

3 2 1 C L

U subgroups of the Standard Mo del ii scalar mass matrices for the squarks

Y

and sleptons iii Higgssquarksquark trilinear interaction terms the socalled

Aparameters and corresp onding terms involving the sleptons and iv three

scalar Higgs mass parameterstwo diagonal and one odiagonal mass terms for

the two Higgs doublets These three mass parameters can b e reexpressed in terms

of the two Higgs vacuum exp ectation values v and v and one physical Higgs

1 2

mass Here v v is the vacuum exp ectation value of the Higgs eld which cou

1 2

2 2

ples exclusively to downtype uptype quarks and leptons Note that v v

1 2

2

GeV is xed by the W mass while the ratio

tan v v

2 1

is a free parameter of the mo del

The sup ersymmetric constraints imply that the MSSM Higgs sector is automat

ically CPconserving at treelevel Thus tan is a real parameter conventionally

chosen to b e p ositive and the physical neutral Higgs scalars are CPeigenstates

Nevertheless the MSSM do es contain a number of p ossible new sources of CP

violation For example gaugino mass parameters the Aparameters and may

b e complex Some combination of these complex phases must b e less than of order

2 3

for a sup ersymmetrybreaking scale of GeV to avoid generating

electric dip ole moments for the neutron electron and atoms in conict with ob

served data However these complex phases have little impact on the direct

searches for sup ersymmetric particles and are usually ignored in exp erimental

analyses

a

Some mo del builders attempt to relax the assumption of Rparity conservation Mo dels of

the type must break B L and are therefore strongly constrained by exp eriment In such

mo dels the LSP is unstable and sup ersymmetric particles can b e singly pro duced and destroyed

in asso ciation with B or L violation These features lead to a phenomenology of brokenRparity

mo dels that is very dierent from that of the MSSM

Before describing the sup ersymmetric particle sector let us consider the Higgs

sector of the MSSM There are ve physical Higgs particles in this mo del a

0

charged Higgs pair H two CPeven neutral Higgs b osons denoted by h and

0 0

0 0

and one CPo dd neutral Higgs b oson A The prop erties m H where m

H h

of the Higgs sector are determined by the Higgs p otential which is made up of

quadratic terms whose squaredmass co ecients were mentioned ab ove Eq

and quartic interaction terms The strengths of the interaction terms are directly

related to the gauge couplings by sup ersymmetry As a result tan dened in

Eq and one Higgs mass determine the Higgs sp ectrum an angle which

indicates the amount of mixing of the original Y Higgs doublet states in the

physical CPeven scalars and the Higgs b oson couplings When onelo op radiative

corrections are incorp orated additional parameters of the sup ersymmetric mo del

enter via virtual lo ops The impact of these corrections can b e signicant

0

m If true this would For example at treelevel the MSSM predicts m

Z

h

imply that exp eriments to b e p erformed at LEP op erating at its maximum energy

0

and luminosity would rule out the MSSM if h were not found However this Higgs

mass b ound can b e violated when the radiative corrections are incorp orated For

0

example in the following approximate upp er b ound was obtained for m

h

e e

0

m in the limit of m m M where topsquark t t assuming m

Z Z t L R

A

e

t

mixing is neglected

2

2 4 2 2 2 4

M

g m m m m m

Z t Z t t

2 2 e

t

m m ln

0

Z h

2 4 2 2

2

m m m m

t

W Z Z

More rened computations which include the eects of topsquark mixing

at onelo op renormalization group improvement and the leading twoloop con

0

GeV for m GeV and a topsquark mass of tributions yield m

t

h

M TeV Clearly the radiative corrections to the Higgs masses have a signi

e

t

cant impact on the search for the MSSM Higgs b osons at LEP

Consider next the sup ersymmetric particle sector of the MSSM further de

tails can b e found in Ref The gluino is the color o ctet Ma jorana fermion

partner of the gluon with mass M jM j The sup ersymmetric partners of the

3

eg

electroweak gauge and Higgs b osons the gauginos and higgsinos can mix As a

result the physical mass eigenstates are mo deldep endent linear combinations of

these states called charginos and neutralinos which are obtained by diagonalizing

the corresp onding mass matrices The chargino mass matrix dep ends on M

2

+

e

tan and m The corresp onding chargino mass eigenstates are denoted by

W

1

+ + +

f f

e

and some authors use the notation W and W with masses

2 1 2

n

2

2 2 2 2 2 2 2

1

jj jM j m jj jM j m M

+ +

2 2

W W

2 e e

1 2

o

12

2 2 4 2 2

jj jM j m sin m sin ReM

2 2

W W

+ +

If CPviolating eects are M where the states are ordered such that M

e e

2 1

ignored in which case M and are real parameters then one can choose a

2

convention where tan and M are p ositive Note that the relative sign of M and

2 2

is meaningful The sign of is conventiondependent the reader is warned that

b oth sign conventions app ear in this b o ok The sign convention for implicit in

Eq is used by the LEP collab orations in their plots of exclusion contours

+

e e

in the M vs plane derived from the nonobservation of Z The

2

1 1

neutralino mass matrix dep ends on M M tan m and the weak mixing

1 2 Z

0

e

angle The corresp onding neutralino eigenstates are usually denoted by

W

i

e

i some authors use the notation Z according to the convention that

i

0

e

M M M M Typically is the LSP

0 0 0 0

e e e e 1

1 2 3 4

It is common practice in the literature to reduce the sup ersymmetric parame

ter freedom by requiring that all three gaugino mass parameters are equal at some

grand unication scale Then at the electroweak scale the gaugino mass param

eters can b e expressed in terms of one of them say M and the gauge coupling

2

constants

2 2 2 2

M g g M M g g M

3 2 1 2

s

Having made this assumption the chargino and neutralino masses and mixing

angles dep end only on three unknown parameters the gluino mass and tan

However the assumption of gaugino mass unication could prove false and must

eventually b e tested exp erimentally

The sup ersymmetric partners of the quarks and leptons are spinzero b osons

the squarks charged sleptons and sneutrinos For a given fermion f there are two

e e

sup ersymmetric partners f and f which are scalar partners of the corresp onding

L R

e

e

left and righthanded fermion There is no However in general f and

R L

e e e

f are not masseigenstates since there is f f mixing which is prop ortional in

R L R

strength to the corresp onding element of the scalar squaredmass matrix

m A tan for downtype f

d d

2

M

LR

m A cot for uptype f

u u

where m m is the mass of the appropriate down up type quark or lepton

d u

Here A and A are unknown softsup ersymmetrybreaking Aparameters and

d u

and tan have b een dened earlier The signs of the A parameters are also

conventiondependent see Due to the app earance of the fermion mass in

Eq one exp ects M to b e small compared to the diagonal squark and

LR

slepton masses with the p ossible exception of the topsquark since m is large

t

and the b ottomsquark and tauslepton if tan The diagonal L and Rtype

squark and slepton masses are given by

2 2 2 2 2

M M m m cos T e sin

3 f W

F f Z

e

f

L

2 2 2 2 2

M M m e m cos sin

f W

R f Z

e

f

R

where M M M for Ltype squarks sleptons with the appropriate choice of

F

e e

Q L

1

for uptype and downtype squarks and sleptons M M M and M T

R 3

e e e

2

U D E

e

e e

for u d and e resp ectively and m and e are the corresp onding quark lepton

R R R f f

mass and charge in units of e The softsup ersymmetrybreaking parameters M

e

Q

M M M and M are unknown parameters Note that generational indices

e e e e

U D L E

have b een suppressed further complications such as intergenerational mixing are

p ossible although there are some constraints from the nonobservation of avor

changing neutral currents FCNC One way to guarantee the absence of

signicant FCNCs mediated by virtual sup ersymmetric particle exchange is to

p osit that the diagonal softsup ersymmetrybreaking scalar squaredmasses are

universal in avor space at some energy scale normally taken to b e at or near

the Planck scale Renormalization group evolution is used to determine the

lowenergy values for the scalar mass parameters listed ab ove This assumption

substantially reduces the MSSM parameter freedom

Two additional theoretical frameworks are often introduced to reduce further

the MSSM parameter freedom The rst involves grand unied theories

GUTs and the desert hypothesis ie no new physics b etween the TeVscale

and the GUTscale Perhaps one of the most comp elling hints for lowenergy su

p ersymmetry is the unication of SUSUU gauge couplings predicted

by sup ersymmetric GUT mo dels with the sup ersymmetry breaking scale of

order TeV or b elow The unication which takes place at an energy scale of or

16

der GeV is quite robust and dep ends weakly on the details of the GUTscale

theory In contrast gauge coupling unication in the simplest nonsup ersymmet

ric GUT fails by many standard deviations The second framework involves

minimal sup ergravity theory where the soft sup ersymmetrybreaking parameters

are often taken to have the following simple form Referring to the parameter list

given ab ove Eq the Planckscale values of the softsup ersymmetrybreaking

terms dep end on the following minimal set of parameters i a universal gaugino

mass m ii a universal diagonal scalar mass parameter m iii a universal

12 0

Aparameter A and iv three scalar Higgs mass parameterstwo common di

0

2 2

agonal squaredmasses given by j j m and an odiagonal squaredmass given

0

0

by B which denes the Planckscale sup ersymmetrybreaking parameter B

0 0 0

where is the Planckscale value of the parameter Renormalization group evo

0

lution is used to compute the lowenergy values of the sup ersymmetrybreaking pa

rameters and determines the sup ersymmetric particle sp ectrum Moreover in this

approach electroweak symmetry breaking is induced radiatively if one of the Higgs

diagonal squaredmasses is forced negative by the evolution However the mini

mal approach ab ove is probably to o restrictive Theoretical considerations suggest

that the universality of Planckscale softsup ersymmetry breaking parameters is

not generic Recent developments are reviewed in Chapter

The verication of lowenergy sup ersymmetry requires the discovery of the

sup ersymmetric particles Once sup erpartners are discovered it is necessary to

test their detailed prop erties to verify the sup ersymmetric nature of their inter

actions Furthermore one can explicitly test many of the additional theoretical

assumptions describ ed ab ove that were introduced to reduce the sup ersymmetric

parameter freedom The phenomenology of sup ersymmetric particles is discussed

in detail in Chapter The phenomenology of the Higgs sector may also provide

0 0

crucial evidence for an underlying lowenergy sup ersymmetry If m m then

A h

0

the prop erties of h will b e nearly indistinguishable from the Higgs b oson of the

minimal Standard Mo del Small deviations from the Standard Mo del Higgs

sector could signal the existence of additional Higgs states as exp ected in the

0

O m then the full nonminimal Higgs sector could b e revealed MSSM If m

Z

A

so on after the initial discovery of the rst Higgs state The phenomenology of the

MSSM Higgs b osons is considered in Chapter

Mo dels with Dynamical Electroweak Symmetry Breaking

One of the main examples of dynamical electroweak symmetry breaking is the tech

nicolor approach which p ostulates the existence of technicolor gauge interactions

acting among a set of new massless technifermions The technifermions

TF

carry the ordinary quantum numbers under SU SU U plus their

C L Y

own technicolor charges The Standard Mo del particles are all singlets under the

technicolor gauge group The technicolor gauge group and technifermion repre

sentations are chosen so that the theory p ossesses a custo dial SU symmetry

C

2 2 2

cos In the simplest version there are m which ensures that m

W

Z W

N technifermions which transform in the fundamental N representation of the

TF

SUN technicolor group The theory thus has a chiral SUN SUN

TF L TF R

global symmetry The technicolor interaction is chosen to b e asymptotically free

and to have a particle sp ectrum such that at an energy scale of O T eV it b e

comes strong At this energy scale one assumes that condensates of technifermions

form

h i

TF

TF

2

This breaks the chiral symmetry to a vectorlike SUN and gives rise to N

TF

TF

Goldstone b osons called technipions in much the same way that the light pseu

doscalar mesons arise in QCD Three of the technipions b ecome the longitudinal

comp onents of the W and Z and hence these gauge b osons acquire mass In order

to obtain the observed W and Z masses the technicolor scale is xed to b e

s

v

TC

N

TF

Since the minimal anomaly free choice of technifermions has eight avors of tech

nifermions with the Standard Mo del quantum numbers of a single generation of

quarks and leptons one indeed nds TeV

TF

After the W and Z get mass by absorbing three Goldstone technipion states

the remaining technipions are physical particles The number of such technipi

ons dep ends on the gauge group chosen for the technicolor interaction and on the

representations chosen for the technifermions The minimal constraints such as

the requirement that the technicolor interaction b ecomes strong at ab out a TeV

require a gauge group such as SU or larger and yields a rich sp ectrum of techni

pions Since the technifermions also carry ordinary electroweak and color charges

the technipions o ccur in multiplets of these groups Much of the phenomenology of

technicolor mo dels involves the search for technipions which typically have masses

at the electroweak scale

The technicolor sp ectrum mimics the QCD sp ectrum and so there are for

example mesons with the quantum numbers of the and Large N arguments

s

lead to the estimate

M TeV

TC

N

which is yet another indication that the relevant scale for electroweak symmetry

breaking is TeV Extensive eort has b een sp ent predicting exp erimental sig

natures for the technirho and the techniomega see Chapter for further

details

The basic technicolor mechanism leaves the quarks and leptons massless and

extended technicolor interactions ETC must b e introduced to give the fermions

mass There is no version of ETC that naturally gives fermions mass without also

generating avor changing neutral currents FCNC in conict with exp erimental

data no simple equivalent of the GIM mechanism has b een found The ETC

interactions contribute for example to the K K mass dierence which requires

L S

M TeV in order to suppress this interaction to an acceptable level

ETC

The simplest technicolor mo dels give fermion masses

i h

m

f

2

M

ETC

3

Taking TeV and M TeV we i where naively h

TC ETC

TC

see that it is imp ossible to generate large enough masses for the s and c quarks

let alone the third generation quarks One solution is to have a hierarchy of

scales with a dierent ETC scale for each generation Obtaining the observed top

quark mass and generating the observed topb ottom mass splitting is still dicult

The simple picture describ ed ab ove can b e avoided in walking technicolor

mo dels which change the naive scaling of Eq If the technicolor mo del

has a large mass anomalous dimension then a larger value of M can b e used

ETC

to obtain the observed quark masses which in turn will suppress problems with

FCNCs The low ETC scale required to get m GeV will lead to a predicted

t

value for the Z b b branching ratio in conict with the LEP data in most mo dels

of extended technicolor although this can b e avoided in some mo dels where the

ETC gauge group do es not commute with the electroweak SU group

The large mass of the top quark has led to suggestions that it may b e fun

damentally dierent from the ve lighter quarks Another example of dynamical

symmetry breaking is a class of mo dels in which the top quark forms a conden

sate at some high energy scale htti This approach yields a CPeven

t

neutral scalar b ound state whose prop erties are indistinguishable from those of

the Standard Mo del Higgs b oson In these mo dels the scalar mass is xed by the

dynamics and tends to b e around GeV However this is typically achieved

only when m in which case there is a netuning problem identical to that

t Z

encountered in the Standard Mo del Attempts have b een made to incorp orate the

top quark condensate in a dynamical scheme where netuning is avoided by taking

O TeV and embedding this structure in a theory of extended technicolor

t

Interesting mo dels have b een constructed Nevertheless the dynamical

electroweak symmetry breaking approach suers from the fact that no simple and

calculable minimal extension of the Standard Mo del has b een found that satises

all present exp erimental constraints

Capsule Summary

To summarize the primary goals of TeVscale exploration are to reveal the nature

of the Higgs sector and discover the underlying dynamics of electroweak symmetry

breaking to discover whether new particles and interactions b eyond the Standard

Mo del exist at the TeVscale eg conrm or rule out lowenergy sup ersymmetry

and to uncover new insights for physics at even higher energy scales which im

pact on unication the origin of avor etc Exploration of the TeVscale requires

a new generation of colliders and detectors b eyond those currently in op eration

or construction This b o ok presents an indepth study of the phenomenology of

electroweak symmetry breaking and quanties the physics reach of present and

future colliders Its fo cus is on the Standard Mo del with one Higgs doublet and

b eyond mo dels of lowenergy sup ersymmetry dynamical electroweak symmetry

breaking and other approaches that invoke new particles and interactions We

hop e that this volume will serve a useful purp ose and provide a foundation for

developing the future direction of particle physics at the dawn of the st century

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