# Report of the Supersymmetry Theory Subgroup

Report of the Supersymmetry Theory Subgroup

J. Amundson (Wisconsin), G. Anderson (FNAL), H. Baer (FSU), J. Bagger (Johns Hopkins), R.M. Barnett (LBNL), C.H. Chen (UC Davis), G. Cleaver (OSU), B. Dobrescu (BU), M. Drees (Wisconsin), J.F. Gunion (UC Davis), G.L. Kane (Michigan), B. Kayser (NSF),

C. Kolda (IAS), J. Lykken (FNAL), S.P. Martin (Michigan), T. Moroi (LBNL), S. Mrenna (Argonne), M. Nojiri (KEK), D. Pierce (SLAC), X. Tata (Hawaii), S. Thomas (SLAC), J.D. Wells (SLAC), B. Wright (North Carolina), Y. Yamada (Wisconsin)

ABSTRACT Spacetime supersymmetry appears to be a fundamental in- gredient of superstring theory. We provide a mini-guide to some of the possible manifesta- tions of weak-scale supersymmetry. For each of six scenarios These motivations say nothing about the scale at which nature we provide might be supersymmetric. Indeed, there are additional motiva- tions for weak-scale supersymmetry.

a brief description of the theoretical underpinnings,

Incorporation of supersymmetry into the SM leads to a so-

the adjustable parameters, lution of the gauge hierarchy problem. Namely, quadratic divergences in loop corrections to the Higgs boson mass a qualitative description of the associated phenomenology at future colliders, will cancel between fermionic and bosonic loops. This mechanism works only if the superpartner particle masses

comments on how to simulate each scenario with existing are roughly of order or less than the weak scale. event generators.

There exists an experimental hint: the three gauge cou- plings can unify at the Grand Uni®cation scale if there ex- I. INTRODUCTION ist weak-scale supersymmetric particles, with a desert be-

The Standard Model (SM) is a theory of spin- 1 matter tween the weak scale and the GUT scale. This is not the 2 fermions which interact via the exchange of spin-1 gauge case with the SM. bosons, where the bosons and fermions live in independent rep-

Electroweak symmetry breaking is a derived consequence resentations of the gauge symmetries. Supersymmetry (SUSY) of supersymmetry breaking in many particle physics mod- is a symmetry which establishes a one-to-one correspondence between bosonic and fermionic degrees of freedom, and pro- els with weak-scale supersymmetry, whereas electroweak vides a relation between their couplings [1]. Relativistic quan- symmetry breaking in the SM is put in ªby hand.º The

tum ®eld theory is formulated to be consistent with the symme- SUSY radiative electroweak symmetry-breaking mecha-

m 150 200

nism works best if the top quark has mass t

tries of the Lorentz/PoincarÂe group ± a non-compact Lie alge-

m =

GeV. The recent discovery of the top quark with t

bra. Mathematically, supersymmetry is formulated as a gener-

4:4 176 GeV is consistent with this mechanism. alization of the Lorentz/PoincarÂe group of space-time symme- tries to include spinorial generators which obey speci®c anti-

As a bonus, many particle physics models with weak- commutation relations; such an algebra is known as a graded scale supersymmetry contain an excellent candidate for Lie algebra. Representations of the SUSY algebra include both cold dark matter (CDM): the lightest neutralino. Such a bosonic and fermionic degrees of freedom. CDM particle seems necessary to describe many aspects of The hypothesis that nature is supersymmetric is very com- cosmology. pelling to many particle physicists for several reasons. Finally, there is a historical precedent for supersymmetry. In

It can be shown that the SUSY algebra is the only non- 1928, P. A. M. Dirac incorporated the symmetries of the Lorentz trivial extension of the set of spacetime symmetries which group into quantum mechanics. He found as a natural conse- forms one of the foundations of relativistic quantum ®eld quence that each known particle had to have a partner particle theory. ± namely, antimatter. The matter-anti-matter symmetry wasn't revealed until high enough energy scales were reached to create

If supersymmetry is formulated as a local symmetry, then a positron. In a similar manner, incorporation of supersymme- one is necessarily forced into introducing a massless spin-2 try into particle physics once again predicts partner particles for (graviton) ®eld into the theory. The resulting supergravity all known particles. Will nature prove to be supersymmetric at theory reduces to Einstein's general relativity theory in the the weak scale? In this report, we try to shed light on some of appropriate limit. the many possible ways that weak-scale supersymmetry might

Theory subgroup conveners. be revealed by colliders operating at suf®ciently high energy.

655 masses, (C. Kolda, S. Martin and S. Mrenna) Boson ®elds Fermionic partners

Gauge multiplets models with non-universal GUT-scale soft SUSY-breaking

a a

(3) g g~

SU terms, (G. Anderson, R. M. Barnett, C. H. Chen, J. Gunion,

i i

~

(2) W W

SU J. Lykken, T. Moroi and Y. Yamada)

~

B B U (1)

Matter multiplets two MSSM scenarios which use the large parameter free-

j

~ dom of the MSSM to ®t to various collider zoo events, (G.

L =(~; e~ ) (; e )

Scalar leptons L

L

+ c

~ Kane and S. Mrenna)

R =~e e

L

R

j

~

~

Q =(~u ;d ) (u; d)

L L

Scalar quarks L R

models with parity violation, (H. Baer, B. Kayser and X.

c

~

U =~u u L

R Tata)and

c

~

~

D=d d

R L

j

0

~ ~

H (H ; H )

Higgs bosons L models with gauge-mediated low energy SUSY breaking

1 1 1

j

+

0

~ ~

H (H ; H )

L (GMLESB), (J. Amundson, C. Kolda, S. Martin, T. Moroi,

2 2 2 S. Mrenna, D. Pierce, S. Thomas, J. Wells and B. Wright). Table I: Field content of the MSSM for one generation of quarks and leptons. Each section contains a brief description of the model, quali- tative discussion of some of the associated phenomenology, and ®nally some comments on event generation for the model under discussion. In this way, it is hoped that this report will be a start- A. Minimal Supersymmetric Standard Model ing point for future experimental SUSY searches, and that it will provide a ¯avor for the diversity of ways that weak-scale super- The simplest supersymmetric model of particle physics which symmetry might manifest itself at colliding beam experiments. is consistent with the SM is called the Minimal Supersymmet- We note that a survey of some additional models is contained in ric Standard Model (MSSM). The recipe for this model is to Ref. [2], although under a somewhat different format. start with the SM of particle physics, but in addition add an ex- tra Higgs doublet of opposite hypercharge. (This ensures can- cellation of triangle anomalies due to Higgsino partner contri- II. MINIMAL SUPERGRAVITY MODEL butions.) Next, proceed with supersymmetrization, following well-known rules to construct supersymmetric gauge theories. The currently most popular SUSY model is the minimal super- At this stage one has a globally supersymmetric SM theory. gravity (mSUGRA) model [3, 4]. Here one assumes that SUSY

Supersymmetry breaking is incorporated by adding to the La- is broken spontaneously in a ªhidden sector,º so that some aux-

10 2

M M ' (10 GeV ) Pl grangian explicit soft SUSY-breaking terms consistent with the iliary ®eld(s) get vev(s) of order Z . symmetries of the SM. These consist of scalar and gaugino mass Gravitational ± strength interactions then automaticallytransmit

SUSY breaking to the ªvisible sector,º which contains all the B terms, as well as trilinear (A terms) and bilinear ( term) scalar

SM ®elds and their superpartners; the effective mass splitting in 100 interactions. The resulting theory has > parameters, mainly from the various soft SUSY-breaking terms. Such a model is the the visible sector is by construction of order of the weak scale, most conservative approach to realistic SUSY model building, as needed to stabilize the gauge hierarchy. In minimal super- but the large parameter space leaves little predictivity. What is gravity one further assumes that the kinetic terms for the gauge needed as well is a theory of how the soft SUSY-breaking terms and matter ®elds take the canonical form: as a result, all scalar

arise. The fundamental ®eld content of theMSSM is listed in Ta- ®elds (sfermions and Higgs bosons) get the same contribution

2 A m to their squared scalar masses, and that all trilinear param-

ble 1, for one generation of quark and lepton (squark and slep- 0 A

ton) ®elds. Mixings and symmetry breaking lead to the actual eters have the same value 0 , by virtueof an approximate global

(n) physical mass eigenstates. U symmetry of the SUGRA Lagrangian [4]. Finally, mo-

The goal of this report is to create a mini-guide to some of tivated by the apparent uni®cation of the measured gauge cou-

16

M ' 2 10 the possible supersymmetric models that occur in the literature, plings within the MSSM [5] at scale GUT GeV, one

and to provide a bridge between SUSY model builders and their assumes that SUSY-breaking gaugino masses have a common

m M

GUT

=2

experimental colleagues. The following sections each contain value 1 at scale . In practice, since little is known

M M

Planck

a brief survey of six classes of SUSY-breaking models studied about physics between the scales GUT and , one of-

M A at this workshop; contributing group members are listed in ital- ten uses GUT as the scale at which the scalar masses and ics. We start with the most popular framework for experimental parameters unify. We note that R parity is assumed to be con- searches, the paradigm served within the mSUGRA framework. This ansatz has several advantages. First, it is very econom-

minimal supergravity model (mSUGRA) (M. Drees and M. ical; the entire spectrum can be described with a small number

Nojiri), of free parameters. Second, degeneracy of scalar masses at scale M

GUT leads to small ¯avor-changing neutral currents. Finally, and follow with this model predicts radiative breaking of the electroweak gauge

models with additional D-term contributions to scalar symmetry [6] because of the large top-quark mass.

656

Radiative symmetry breaking together with the precisely generation squarks are almost twice as heavy as the gluino, there M

known value of Z allows one to trade two free parameters, might be a signi®cant gluino ªbackgroundº to squark produc-

+ e

usually taken to be the absolute value of the supersymmetric tion at the LHC. A 500 GeV e collider will produce all six

jj B e~ ; e~ ~

R e

Higgsino mass parameter and the parameter appearing chargino and neutralino states. Information about L and

in the scalar Higgs potential, for the ratio of vevs, tan .The masses can be gleaned from studies of neutralino and chargino p

model then has four continuous and one discrete free parameter production, respectively; however, s>1.5 TeV is required to not present in the SM: study sleptons directly. Spectra of this type can already be mod-

elled reliably using ISAJET: the above parameter space set can

m ;m ;A ;tan ; sign():

0 0

1=2

(1) be entered via the S U GRA keyword.

m = m = 200

0

=2 As example B, we have chosen 1 GeV,

This model is now incorporated in several publicly available

A =0 tan =48 < 0 m = 175 t 0 ,,and GeV. Note the large

MC codes, in particular ISAJET [7]. An approximate version

b value of tan , which leads to large and Yukawa couplings, Spythia ISAJET is incorporated into [8], which reproduces as required in models where all third generation Yukawa cou-

results to 10%. Most SUSY spectra studied at this workshop M

plings are uni®ed at scale GUT . Here the gluino (at 517 GeV) have been generated within mSUGRA; we refer to the various lies slightly above ®rst generation squarks (at 480-500 GeV), accelerator subgroup reports for the corresponding spectra. One which in turn lie well above ®rst generation sleptons (at 220- ªgenericallyº ®nds the following features: 250 GeV). The light neutralinos (at 83 and 151 GeV) and light

chargino (at 151 GeV) are mostly gauginos, while the heavy

j SU (2) U (1) j is large, well above the masses of the and

gauginos. The lightest neutralinois therefore mostly a Bino states (at 287, 304 and 307 GeV) are mostly Higgsinos, because

jj = 275 GeV m

=2

(and an excellent candidate for cosmological CDM ± for re- 1 .

~

~

t b ~

1 1

lated constraints, see e.g. Ref. [9]), and the second neu- The masses of 1 (355 GeV), (371 GeV) and (132 GeV) (2) tralino and lighter chargino are dominantly SU gaugi- are all signi®cantly below those of the corresponding ®rst or

nos. The heavier neutralinos and charginos are only rarely second generation sfermions. As a result, more than 2/3 of all

~ b

produced in the decays of gluinos and sfermions (except gluinos decay into a b quark and a squark. Since (s)bottoms ~

possibly for stop decays). Small regions of parameter space have large Yukawa couplings, b decays will often produce the

j' M j heavier, Higgsino-like chargino and neutralinos. Further, all

with W are possible.

neutralinos (except for the lightest one, which is the LSP) have

2 2

0

m m

If , all sfermions of the ®rst two genera-

0

~ + ~

1=2

two-body decays into 1 ; in case of this is the only two- 2

tions are close in mass. Otherwise, squarks are signi®- body mode, and for the Higgsino-like states this mode will be (2) cantly heavier than sleptons, and SU doublet sleptons

enhanced by the large Yukawa coupling. Chargino decays will

are heavier than singlet sleptons. Either way, the lighter +

~ ` `

also often produce real 1 . Study of the invariant mass stop and sbottom eigenstates are well below the ®rst gener- spectrum will not allow direct determination of neutralino mass

ation squarks; gluinos therefore have large branching ratios

` e~

differences, as the are secondaries from tau decays. Even L

+ t

into b or quarks. e

pair events at e colliders will contain up to four tau leptons!

e

0 Further, unless the beam is almost purely right-handed, it

A H

The heavier Higgs bosons (pseudoscalar , scalar ,and

~ 1

might be dif®cult to distinguish between pair production and

H jj tan

charged ) are usually heavier than unless

~

0 pair production. Finally, the heavier Higgs bosons are quite

1 h

1. This also implies that the light scalar behaves like the

m = 126

light in this case, e.g. A GeV.Therewillbealarge

SM Higgs.

+

! number of A events at the LHC. However, because

These features have already become something like folklore. most SUSY events will contain pairs in this scenario, it is not

We want to emphasize here that even within this restrictive clear whether the Higgs signal will remain visible. At present,

1

framework, quite different spectra are also possible, as illus- scenarios with tan can not be simulated with ISAJET,

trated by the following examples. since the b and Yukawa couplings have not been included in

= 750 m = 150 A =

m all relevant decays. This situation should be remedied soon.

0 0

=2

Example A is for GeV, 1 GeV,

300 tan =5:5 <0 m = 165

GeV, ,,and t GeV (pole

j = 120 SU (2) mass). This yields j GeV, very similar to the

III. D -TERM CONTRIBUTIONS TO SCALAR M gaugino mass 2 at the weak scale, leading to strong Higgsino MASSES ± gaugino mixing. The neutralino masses are 60, 91, 143 and 180 GeV, while charginos are at 93 and 185 GeV. They are all We have seen that the standard mSUGRA framework predicts considerably lighter than the gluino (at 435 GeV), which in turn a testable pattern of squark and slepton masses. In this section

lies well below the squarks (at ' 815 GeV) and sleptons (at we describe a class of models in which a quite distinctive modi- 750-760 GeV). Due to the strong gaugino ± Higgsino mixing, ®cation of the mSUGRA predictions can arise, namely contri-

all chargino and neutralino states will be produced with signi®- butions to scalar masses associated with the D -terms of extra (2)

cant rates in the decays of gluinos and SU doublet sfermions, spontaneously broken gauge symmetries [10]. As we will see,

+ ` leading to complicated decay chains. For example, the ` the modi®cation of squark, slepton and Higgs masses can have

invariant mass spectrum in gluino pair events will have many a profound effect on phenomenology.

0 0 +

! ~ ` ` D

thresholds due to ~ decays. Since ®rst and second In general, -term contributions to scalar masses will arise in

i j

657 (1) supersymmetric models whenever a gauge symmetry is spon- of corrections exactly analogous to (3). Additional U groups

taneously broken with a reduction of rank. Suppose, for ex- are endemic in superstring models, so at least from that point of

SU (3) SU (2) U (1)

ample, that the SM gauge group Y is view one may be optimisticabout the existence of corresponding

U (1) D

supplemented by an additional X factor broken far above -terms and their potential importance in the study of the squark

the electroweak scale. Naively, one might suppose that if the and slepton mass spectrum at future colliders. It should be noted

U (1) U (1)

breaking scale is suf®ciently large, all direct effects of X that once one assumes the existence of additional gauged 's

on TeV-scale physics are negligible. However, a simple toy at very high energies, it is quite unnatural to assume that D -term

model shows that this is not so. Assume that ordinary MSSM contributions to scalar masses can be avoided altogether. (This

2

2

' U (1) X m = m

X i

scalar ®elds, denoted generically by i , carry charges would require an exact symmetry enforcing in the

U (1)

which are not all 0. In order to break X , we also assume the example above.) The only question is whether or not the mag-

D

existence of a pair of additionalchiral super®elds and which nitude of the -term contributions is signi®cant compared to

U (1)

are SM singlets, but carry X charges which are normalized the usual mSUGRA contributions. Note also that as long as the

+1 1 X

(without loss of generality) to be and respectively. Then charges i are family-independent, then from (3) squarks and

U (1)

VEV's for and will spontaneously break X while leav- sleptons with the same electroweak quantum numbers remain

ing the SM gauge group intact. The scalar potential whose min- degenerate, maintaining the natural suppression of ¯avor chang-

i; hi imum determines h then has the form ing neutral currents.

It is not dif®cult to implement the effects of D -terms in sim-

2

g

2

2 2 2 2 2 2 2

X ulations, by imposing the corrections (3) to a particular ªtem-

jj j : V = V + m jj + m jj + j +X j' j

0 i i

2

U (1)

plateº mSUGRA model. After choosing the X charges (2)

of the MSSM ®elds, our remaining ignorance of the mecha-

V

Here 0 comes from the superpotential and involves only and

U (1) D X

nism of X breaking is parameterized by (roughly of

$

2 ; it is symmetric under , but otherwise its precise form 2

m

order M ). The corrections should be imposed at the

2

2 Z i m

need not concern us. The pieces involving m and are soft

M U (1) X

scale X where one chooses to assume that breaks. (If

2

2 2

m M

breaking terms; m and are of order and in general un-

Z

M

Planck GUT X or , one should also in principle incor-

equal. The remaining piece is the square of the D -term associ-

U (1) M X

porate renormalization group effects due to X above ,

U (1)

ated with X , which forces the minimum of the potential to

but these can often be shown to be small.) The other parame-

hihi occur along a nearly D -¯at direction . This scale can

ters of the theory are unaffected. One can then run these param- V

be much larger than 1 TeV with natural choices of 0 , so that the

eters down to the electroweak scale, in exactly the same way as

U (1)

X gauge boson is very heavy and plays no role in collider in mSUGRA models, to ®nd the spectrum of sparticle masses.

physics. D (The solved-for parameter is then indirectly affected by -

However, there is also a deviation from D -¯atness given by

2 2 2 2

2 terms, through the requirement of correct electroweak symmetry

hi hi D =g D =(m m)=2 X X , with ,which X breaking.) The only subtlety involved is an apparent ambigu-

directly affects the masses of the remaining light MSSM ®elds. X

ity in choosing the charges i , since any linear combination of

After integrating out and , one ®nds that each MSSM scalar

U (1) U (1)

X Y

2 and charges might be used. These charges should (mass) receives a correction given by

be picked to correspond to the basis in which there is no mix-

2 (1)

ing in the kinetic terms of the U gauge bosons. In particu-

m = X D X

i (3)

i

U (1) U (1) Y

lar models where X and/or are embedded in non-

2 M D abelian groups, this linear combination is uniquely determined;

where X is again typically of order and may have either

Z (1)

U otherwise it can be arbitrary. sign. This result does not depend on the scale at which X

breaks; this turns out to be a general feature, independent of as- A test case which seems particularly worthy of study is that of

B L U (1)

sumptions about the precise mechanism of symmetry breaking. an additional gauged symmetry. In this case the X

U (1)

Thus X manages to leave its ª®ngerprintº on the masses of charges for each MSSM scalar ®eld are a linear combination of

L Y SO(10)

the squarks, sleptons, and Higgs bosons, even if it is broken at B and . If this model is embedded in (or certain (1)

an arbitrarily high energy. From a TeV-scale point of view, the of its subgroups), then the unmixed linear combination of U 's

5 4

X = (B L)+ Y X

D appropriate for (3) is .The charges for

parameter X might as well be taken as a parameter of our ig-

3 3

1=3 Q ;u ;e

R R

norance regarding physics at very high energies. The important the MSSM squarks and sleptons are for L and

2

+1 L d +2=3

D

L R

point is that X is universal, so that each MSSM scalar (mass) for and . The MSSM Higgs ®elds have charges

H 2=3 H

X

u d

obtains a contribution simply proportional to i , its charge un- for and for . Here we consider the modi®cations to

(m ;m ;A )=

U (1) X

0 0

=2

a mSUGRA model de®ned by the parameters 1 i

der X . Typically the are rational numbers and do not

(200; 100; 0) < 0 tan =2 m = 175

U (1)

GeV, ,and , assuming t all have the same sign, so that a particular candidate X can leave a quite distinctive pattern of mass splittings on the squark GeV.

and slepton spectrum. The effects of D -term contributions to the scalar mass spec-

U (1) e~ ; e~

L R

The extra X in this discussion may stand alone, or may trum is illustrated in Fig. 1, which shows the masses of ,

~

h b

be embedded in a larger non-abelian gauge group, perhaps to- the lightest Higgs boson , and the lightest bottom squark 1

SO(10) D

gether with the SM gauge group (for example in an or as a function of X . The unmodi®ed mSUGRA prediction is

E U (1) D =0 X

6 GUT). If the gauge group contains more than one in found at . A particularly dramatic possibility is that

U (1) U (1) D

addition to Y , then each factor can contribute a set -terms could invert the usual hierarchy of slepton masses, so

658

m ;m

e~ e~

that ~ . In the test model, this occurs for nega-

L R

D D X

tive X ; the negative endpoint of is set by the experimental 400

m ∼ lower bound on ~ . The relative change of the squark masses e 350 ∼L is smaller, while the change to the lightest Higgs boson mass is eR h0

∼ D

almost negligible except near the positive X endpoint where 300 b it reaches the experimental lower bound. The complicated mass 1 spectrum perhaps can be probed most directly at the NLC with 250 precision measurements of squark and slepton masses. Since the usual MSSM renormalization group contributions to scalar 200 masses are much larger for squarks than for sleptons, it is likely Mass (GeV) 150

that the effects of D -term contributions are relatively larger for sleptons. 100

50

At the Tevatron and LHC, it has been suggested in these pro- 0 ceedings that SUSY parameter determinations can be obtained -20000 0 20000 40000 60000 D (GeV2) by making global ®ts of the mSUGRA parameter space to vari- X

ous observed signals. In this regard it should be noted that sig- D

Figure 1: Mass spectrum as a function of X . ni®cant D -term contributions could invalidate such strategies

unless they are generalized. This is because adding D -terms (3) to a given template mSUGRA model can dramatically change certain branching fractions by altering the kinematics of decays 1 involving squarks and especially sleptons. This is demonstrated

for the test model in Fig. 2. Thus we ®nd for example that the

+

+ 0 +

(~ ! ` X) BR(~ ! ` ` X)

product BR can change

2 1

up to an order of magnitude or more as one varies D -terms (with all other parameters held ®xed). Note that the branching ratios ∼ g→bX → + − of Fig. 2 include the leptons from two-body and three-body de- N2 l l X

±

+ +

0 + + 0

+ →

~ 0.5 C1 l X

! ` ~ ~ ! ` ! ` ~

cays, e.g. ~ and .Onthe

1

1 1 j

(~g ! bX ) D other hand, the BR is fairly insensitive to -terms

over most, but not all, of parameter space. Branching Ratio

Since the squark masses are generally much less affected by the D -terms, and the gluino mass only indirectly, the produc- 0 -20000 0 20000 40000 60000 tion cross sections for squarks and gluinos should be fairly sta- 2

DX (GeV )

(~g ! bX ) ble. Therefore, the variation of BR is an accurate

gauge of the variation of observables such as the b multiplicity

D

0

Figure 2: Branching ratios as a function of X .

~

of SUSY events. Likewise, the ~ production cross section

2 1

does not change much as the D -terms are varied, so the expected trileptonsignal can vary like the product of branching ratios ± by orders of magnitude. While the results presented are for a spe- IV. NON-UNIVERSAL GUT-SCALE SOFT ci®c, and particularly simple, test model, similar variations can SUSY-BREAKING PARAMETERS be observed in other explicit models. The possible presence of

D -terms should be considered when interpreting a SUSY signal A. Introduction at future colliders. An experimental analysis which proves or We considered models in which the gaugino masses and/or

disproves their existence would be a unique insight into physics M

the scalar masses are not universal at the GUT scale, GUT . at very high energy scales. We study the extent to which non-universal boundary condi- tions can in¯uence experimental signatures and detector require- ments, and the degree to which experimental data can distin- To facilitate event generation, approximate expressions for guish between different models for the GUT-scale boundary the modi®ed mass spectra are implemented in the Spythia conditions.

Monte Carlo, assuming the D -terms are added in at the uni®-

cation scale. Sparticle spectra from models with extra D -terms M

1. Non-Universal Gaugino Masses at GUT can be incorporated into ISAJET simply via the M SSM i key- words, although the user must supply a program to generate the We focus on two well-motivated types of models:

relevant spectra via RGE's or analytic formulae. Superstring-motivated models in which SUSY breaking is

659

M m

GUT Z

F M M M M M M

3 2 1 3 2 1

1 1 1 1 6 2 1

24 2 3 1 12 6 1

75 1 3 5 6 6 5

200 1 2 10 6 4 10

O II

53 53

= 4 1 5 6 10

GS

5 5

M m Z

Table II: Relative gaugino masses at GUT and in the four F

possible irreducible representations, and in the O-II model

4

with GS .

moduli dominated. We consider the particularly attractive O-II M

model of Ref. [11]. The boundary conditions at GUT are:

p

0

M 3m [(b + )K]

a GS

3=2

a

2 2 0

m = m [ K ] GS

0 (4)

3=2

Figure 3: Physical (pole) gaugino masses as a function of tan

A =0

0

24 75 200 F

for the 1 (universal), , ,and representation choices.

jB j jj m =1TeV

Also plotted are and . We have taken 0 and

b GS

where a are SM beta function coef®cients, is a mixing pa-

M = 200; 400; 200; 200 GeV

rameter, which would be a negative integer in the O-II model, 3 , respectively.

4

= 1 K ' 4:6 10

and . From the estimates of Ref. [11],

0 3

' 10

and K , we expect that slepton and squark masses M

would be very much larger than gaugino masses. 2. Non-Universal Scalar Masses at GUT F

Models in which SUSY breaking occurs via an -term that is We consider models in which the SUSY-breaking scalar (5)

not an SU singlet. In this class of models, gaugino masses M

masses at GUT are in¯uenced by the Yukawa couplings of the

are generated by a chiral super®eld that appears linearly in corresponding quarks/leptons. This idea is exempli®ed in the F

the gauge kinetic function, and whose auxiliary component 5

U (3)] model of Ref. [12] based on perturbing about the [ sym- acquires an intermediate-scale vev: metry that is present in the absence of Yukawa couplings. One

Z ®nds, for example:

hF i

ab ab

2 a b a b

L d W W + h:c: + :::;

M M

y

Planck Planck

2 2 y 0

m = m (I + c + c + :::)

Q u d

~ (7)

0 u Q d

(5) Q

a;b

F SU (5)

where the are the gaugino ®elds. belongs to an

irreducible representation which appears in the symmetric prod- where Q represents the squark partners of the left-handed quark

3 3 d

uct of two adjoints: doublets. The Yukawas u and are matrices in gen-

4

eration space. The ::: represent terms of order that we

0

c c

(2424) = 1 24 75 200 ; Q

symmetric (6) will neglect. A priori, , , should all be similar in size, in Q

which case the large top-quark Yukawa coupling implies that 1 where only yields universal masses. Only the component of 2

the primary deviations from universality will occur in m ,

~

t

L

F

1 that is ª`neutralº with respect to the SM gauge group should 2

m (equally and in the same direction). It is the fact that

~

b

L

hF i = c c

ab a ab a

acquire a vev, , with then determining the rel-

2 2 2

m m

m and are shifted equally that will distinguish non-

~

~

M

t

b

GUT L

ative magnitude of the gauginos masses at : see Table II. L

A M

0 GUT

Physical masses of the gauginos are in¯uenced by tan - universality from the effects of a large parameter at ;

~ ~

t t R

dependent off-diagonal terms in the mass matrices and by cor- the latter would primarily introduce L mixing and yield a

m m

~ ~

(pol e) m (m ) m low compared to .

t

b

1

g~ g~ g~

rections which boost relative to .If is large, 1

0

m

the lightest neutralino (which is the LSP) will have mass ~

1

min(M ;M ) m M

2 2

1 whilethe lightestchargino will have . B. Phenomenology

~

1

<

200 M M m ' 1

Thus, in the and O-II scenarios with 2 ,

~

1 1. Non-Universal Gaugino Masses

0

0

m ~ ~ tan

~ and the and are both Wino-like. The depen-

1 1

1 We examined the phenomenological implications for the stan-

m 24 75 200

dence of the masses at Z for the universal, , ,and

dard Snowmass comparison point (e.g. NLC point #3) speci-

0

m m

g~

0

choices appears in Fig. 3. The - ~ mass splitting becomes

1

m = 175 GeV =0:12 m = 200 GeV M =

s 0

®ed by t , , ,

3

1 200 75

increasingly smaller in the sequence 24, , , O-II, as

100 GeV tan =2 A =0 <0

, ,0 and . In treating the O-II

could be anticipated from Table II. It is interesting to note that

1

tan M M 2

at high , decreases to a level comparable to 1 and , In this discussion we neglect an analogous, but independent, shift

2

0 0

~ ~ ~ m

and there is substantial degeneracy among the , and . in ~ .

2 1

1

t R

660

8%

0

bbb ! ~ b

1

O II

85% 70% 99% 28%

1 24 75 200 = 4:7

0 0 0 0

GS

~

24 : g~ ! b b ! ~ bb ! h ~ bb ! ~ bbbb

L

2 1 1

m g

~ 285 285 287 288 313

69%

0 0 0

m

b ! ~ ~ ~ b u

~ 302 301 326 394 -

R

1 1 1 m

~ 255 257 235 292 -

43% t

1

0 0

75 : g~ ! ~ g or ~ q q

1 1 m

~ 315 321 351 325 -

t

2

10%

m 0

~ 266 276 307 264 -

b

L

! ~ bb

1 m

~ 303 303 309 328 -

b

R

20%

0 0

! ~ g or ~ q q

m

~

2 207 204 280 437 - 2

`

R

m 10%

~ 216 229 305 313 -

0

`

L

! ~ bb

2 0

m 44.5 12.2 189 174.17 303.09

~

1

17%

m

0

~ q q

97.0 93.6 235 298 337 !

~

1

2

m

100%

96.4 90.0 240 174.57 303.33 99%

0

~

~

1

b ! ~ bb 200 : g~ ! b

L

1 m

275 283 291 311 -

~

51%

2

O II: g~ ! ~ q q

m 0 1

h 67 67 68 70 82

17%

0

! ~ g

Table III: Sparticle masses for the Snowmass comparison point 1

26%

0

~ q q

in the different gaugino mass scenarios. Blank entries for the O- ! 1

II model indicate very large masses. 6%

0

! ~ bb 1

Gluino pair production will then lead to the following strik-

ingly different signals.

m = 600 GeV

model we take 0 , a value that yields a (pole) value

m

1 g of ~ not unlike that for the other scenarios. The masses of the In the scenario we expect a very large number of ®-

supersymmetric particles for each scenario are given in Table III. nal states with missing energy, four b-jets and two lepton-

+ e The phenomenology of these scenarios for e collisions is antilepton pairs.

not absolutely straightforward. 24

For , an even larger number of events will have miss-

p

+

0 0

b

75 ~ ~ ~ s =

In the model, ~ and pair production at ing energy and eight -jets, four of which reconstruct to two

2 2 1 1

0

m 500 GeV

are barely allowed kinematically; the phase space pairs with mass equal to (the known) h .

0 0

~

for ~ is only somewhat better. All the signals would be

1 2

g~g~ 75 The signal for production in the case of is much more rather weak, but could probably be extracted with suf®cient traditional; the primary decays yield multiple jets (some of

integrated luminosity.

0 0

~ ~ ~

which are b-jets) plus , or . Additional jets, lep-

1 2

1

0 0

+

+

~ ! ~

200 e e ! ~ ~

tons and/or neutrinos arise when + two jets, two 1

In the model, production would 2

1 1

p

0

~ ! ~ = 500 GeV

s leptons or two neutrinos or + two jets or lep- 1

be kinematically allowed at a NLC, but 1

0

not easily observed due to the fact that the (invisible) ~ ton+neutrino.

1

would take essentially all of the energy in the ~ decays.

1

200 b

In the scenario, we ®nd missing energy plus four -

+

e !

However, according to the results of Ref. [13], e

p

b

+ jets; only -jets appear in the primary decay ± any other jets

~ ~ s = 500 GeV

would be observable at . 1

1 present would have to come from initial- or ®nal-state radi-

4 m

ation, and would be expected to be softer on average. This

The O-II model with GS near predicts that

~

1

8b

+ is almost as distinctive a signal as the ®nal state found

0

m m e e !

g~

and ~ are both rather close to ,sothat

1 p

in the 24 scenario.

+

0 0

~ ~ ; ~ s =

~ would not be kinematically allowed at

1 1 1 1

0

500 GeV

~ ~

. The only SUSY ªsignalº would be the presence In the ®nal O-II scenario, ! + very soft spectator

1 1

of a very SM-like light Higgs boson. jets or leptons that would not be easily detected. Even the

q g q or from the primary decay would not be very energetic

At the LHC, the strongest signal for SUSY would arise from

m m g

given the small mass splitting between ~ and

~

1

g g~

~ production. The different models lead to very distinct signa-

0

m

~ . Soft jet cuts would have to be used to dig out this

tures for such events. To see this, it is suf®cient to list the pri- 1

g g~ signal, but it should be possible given the very high ~ pro-

mary easily identi®able decay chains of the gluino for each of

m g duction rate expected for this low ~ value; see Ref. [13]. the ®ve scenarios. (In what follows, q denotes any quark other

than a b.) Thus, for the Snowmass comparison point, distinguishing be-

tween the different boundary conditionscenarios at the LHC will

90% 99% 33%

0 0 + +

~

1 : g~ ! b b ! ~ bb ! ~ (e e or )bb

L 1

2 be easy. Further, the event rate for a gluino mass this low is such

0

8% h

0 that the end-points of the various lepton, jet or spectra will

! ~ bb

1 allow relatively good determinations of the mass differences be-

38%

0

~ q qbb

! tween the sparticles appearing at various points in the ®nal state 1

661

decay chain. We are optimistic that this will prove to be a gen-

+

e e + E=

eral result so long as event rates are large. T constraints on supersymmetric parameters

e~ e~

L R

< < < <

m 130 GeV m 112 GeV 100 100

e~ e~

L R

2. Non-Universal Scalar Masses

< < < <

M 92 GeV M 85 GeV 50 60

1 1

Once again we focus on the Snowmass overlap point. We

< < < <

M 105 GeV M 85 GeV 50 40

2 2

M

maintain gaugino mass universalityat GUT , but allow for non-

< < < <

M =M 1:6 M =M 1:15 0:75 0:6

2 1 2 1

universalityfor the squark masses. Of the many possibilities,we

< < < <

35 GeV 35 GeV 65 60

c 6=0 A =0 0

focus on the case where only Q with (as assumed

< < < <

jj=M 0:95 jj=M 0:8 0:5 0:5

1 1

for the Snowmass overlap point). The phenomenology for this

< < < <

3 2:2 tan tan 1 1

A 6=0

case is compared to that which would emerge if we take 0

c =0

with all the i . Table IV: Constraints on the MSSM parameters and masses in

g~ m =m ~

Consider the branching ratios as a function of ~

t

b L

L the neutralino LSP scenario. c

as Q is varied from negative to positive values. As the com-

~

g~ ! b b

mon mass crosses the threshold above which the 1 de-

cay becomes kinematically disallowed, we revert to a more stan- g

dard SUSY scenario in which ~ decays are dominated by modes axino case the LSP is not a candidate for cold dark matter, SUSY

0 0 0

Z

~ q q ~ q q ~ q q ~ bb m

R BR(b ! s );

such as , , and . For low enough ~ ,the

1 2 2 t b

1 can have no effect on or or and stops and

s L

~

~

g~ ! t t g~ ! b b 1 1 mode opens up, but must compete with the gluinos are not being observed at FNAL. In the case where the

mode that has even larger phase space. lightest neutralino is the LSP, the opposite holds for all of these

g~ A observables, and we will pursue this case in detail here.

In contrast, if t is varied, the branching ratios remain es-

~

m g~ ! t t ~

sentially constant until is small enough that 1 is kine- The SUSY Lagrangian depends on a number of parameters, all

t 1

matically allowed. Below this point, this latter mode quickly of which have the dimension of mass. That should not be viewed

~

b b

dominates the 1 mode which continues to have very small as a weakness because at present we have no theory of the origin

~ b

phase space given that the 1 mass remains essentially constant of mass parameters. Probably getting such a theory will depend A

as t is varied. on understanding how SUSY is broken. When there is no data on sparticle masses and couplings, it is appropriate to make sim- C. Event Generation plifying assumptions, based on theoretical prejudice, to reduce the number of parameters. However, once there may be data, it A thorough search and determination of the rates (or lack is important to constrain the most general set of parameters and thereof) for the full panoply of possible channels is required to see what patterns emerge. We proceed by making no assump- distinguish the many possible GUT-scale boundary conditions tions about soft breaking parameters. In practice, even though

from one another. In the program ISAJET, independent weak- the full theory has over a hundred such parameters, that is sel- 4 scale gaugino masses may be input using the M SSM key- dom a problem since any given observable depends on at most

word. Independent third generation squark masses may be input afew.

+ 2

via the M SSM keyword. The user must supply a program to e The CDF event [14] has a 36 GeV e ,a59GeV , photons

generate the relevant weak-scale parameter values from the spe-

E =

of 38 and 30 GeV, and / T 53 GeV. A SUSY interpretation

+ 0

ci®c GUT-scale assumptions. Relevant weak-scale MSSM pa-

q ! ;Z ! e~ e~ e~ ! e ~ ;

is q , followed by each

2

0 0

rameters can also be input to Spythia; as with ISAJET,the 0

! ~ : ~

~ The second lightest neutralino, , must be photino-

2 1 2

user must provide a program for the speci®c model. 0

ee ~

like since it couples strongly to ~ . Then the LSP = must be

1

0 0

(~ ! ~ ):

Higgsino-like [23, 24, 25] to have a large BR The

2 1 V. MSSM SCENARIOS MOTIVATED BY range of parameter choices for this scenario are given in Table DATA IV. If light superpartners indeed exist, FNAL and LEP will pro- An alternative procedure for gleaning information about the duce thousands of them, and measure their properties very well. SUSY soft terms is to use the full (¿ 100 parameters) parameter The ®rst thing to check at FNAL is whether the produced selec-

space freedom of the MSSM and match to data, assuming one

e~ e~ : e~ ; ud !

R L

tron is L or If then the charged current channel

+

has a supersymmetry signal. This approach has been used in the +

W ! e~ ~ e~ e~ e~ ! L

L has 5-10 times the rate of . We expect

L L

0

following two examples. 0

e ~ ~ ! e ~ ; ~ (! ~ :

) Most likely [22] where is the light-

1 1 2 1

~

est chargino. If the stop mass ~ ,then

t

1

~

1

+

0 0 0

e e + E=

A. The CDF T Event >m ~ ! ebc ~ m ~ c ~ )b ! W (! jj)~

so ;if ~ then

t 1 1 1

1

~

1

0

! ej j ~ ; j = u; d; s; c: so ~ where Either way, dominantly

Recently a candidate for sparticle production has been re- 1

e~ ~ ! ee jjE j T

ported [14] by the CDF collaboration. This has been interpreted L /where may be light or heavy quarks. If no

e~

in several ways [15], [16], [17], [18] and later with additional such signal is found, probably the produced selectron was R .

(~~) (~e e~ )

= L variations [19], [20], [21]. The main two paths are whether the Also, L . Cross sections for many channels are LSP is the lightest neutralino [15], [22], or a nearly massless given in Ref. [22]. gravitino [16, 17, 18, 19, 20] or axino [21]. In the gravitino or The most interesting channel (in our opinion) at FNAL is

662

+

+ 0

ud ! W ! ~ ~ : jjE ;

This gives a signature /T for which a supersymmetry source for the recalcitrant events. The super-

2

i

m q~q~

there is only small parton-level SM backgrounds. If ~ ,symmetry source is best matched by considering production,

t

~

i

0

~ ~

0

q~ ! q ;~ ~ ! `; ` ! ` ~

~ where each . A recommended set

1

b: t ! t ~

one of j is a If (expected about 10% of the time) and,

2

m ' 330 m ' 310

g q~

of parameters is as follows [30]: ~ GeV, q

if ~ are produced at FNAL, there are additional sources of such

m ' 220 m ' 220 m ' 130

~ ~

GeV, GeV, ~ GeV, GeV,

` ` R

events (see below). L

'400 M ' 50 M ' 260 2 If charginos, neutralinos and sleptons are light, then gluinos GeV, 1 GeV and GeV. Note that

this parameter set discards the common hypothesis of gaugino

m '

and squarks may not be too heavy. If stops are light ( ~

t 1

0 mass uni®cation. These parameters can be input into Spythia

~

BR(t ! t ~ ) ' 1=2 M

W ), then [26]. In this case, an ex- i

ISAJET M SSM i tra source of tops must exist beyond SM production, because or (via keywords), taking care to use the non-

2 uni®ed gaugino masses as inputs.

BR(t ! Wb) BR(t !

is near or above its SM value with

)= 1:

Wb With these motivations, the authors of [27] have sug-

R

m + m m m

m VI. PARITY VIOLATION

~

g t q~ g~

gested that one assume ~ and , with

t

m ' 250 300 q

~ GeV. Then there are several pb of top produc- R

R parity ( ) is a quantum number which is +1 for any ordi-

~ ~

q g;~ g~g;~ q~q~ q~ ! q g;~ g~ ! tt tt

tion via channels ~ with and since

(R) nary particle, and -1 for any sparticle. R-violating / interac-

is the gluino's only two-body decay mode. This analysis points tions occur naturally in supersymmetric theories, unless they are

P (tt) P T out that T should peak at smaller for the SM than for

explicitly forbidden. EachR / coupling also violates either lepton

the SUSY scenario, since the system is recoiling against extra B

number L, or baryon number . Together, these couplings vio- m

jets in the SUSY case. The SUSY case suggests that if t or B

late both L and , and lead to tree-level diagrams which would

t t are measured in different channels one will obtain different make the proton decay at a rate in gross violation of the observed values, which may be consistent with reported data. This anal-

bound. To forbid such rapid decay, suchR / couplings are nor-

(t !

ysis also argues that the present data is consistent with BR mally set to zero. However, what if such couplings are actually

0

~

t ~ )=1=2:

i present?

R BR(b ! s )

At present [28] b and differ from their SM

In supersymmetry with minimal ®eld content, the allowableR /

Z predictions by 1.5-2 ,and s measured by the width differs part of the superpotential is

by about 1.5-2 from its value measured in DIS and other ways.

~

t

If these effects are real they can be explained by ~ - loops,

i

0 00

ee

W = L L E + L Q D + U D D :

ij k i j k j k i j k

using the same SUSY parameters deduced from the event i (8)

ij k ij k

R/

tan ; ;

( + a light, mainly right-handed, stop). Although and

L Q E U D

M Here, , , , ,and are super®elds containing, respec-

2 a priori could be anything, they come out the same from

tan 1:5;

the analysis of these loops as from ee ( tively, lepton and quark doublets, and charged lepton, up quark,

i; j; k

m =2;M 60 80

and down quark singlets. The indices , over which sum- 2

Z GeV).

0

W

ee ~ mation is implied, are generational indices. The ®rst term in

The LSP= apparently escapes the CDF detector in the R

1 /

L (L) e + ! e~

event, suggesting it is stable (though only proving it lives longer leads to -violating / transitions such as . The sec-

8

L u + d ! e~ 10

than sec). If so it is a candidate for CDM. The properties ond one leads to / transitions such as . The third one

~

0

B u+ d ! d

of ~ are deduced from the analysis [22] so the calculation of the produces / transitionssuch as . To forbidrapid proton 1

relic density [29] is highly constrained. The analysis shows that decay, it is often assumed that ifR / transitionsare indeed present,

0

0 0

L B

~ Z

the s-channel annihilation of ~ through the dominates, so then only the -violating and terms occur, or only the -

1 1

00

0

m

tan violating term occurs, but not both. While the ¯avor compo-

the needed parameters are , ~ and the Higgsino fraction

1

0 00

0

u; d; s

nents of involving are experimentally constrained

0:1

for ~ , which is large. The results are encouraging, giving

1

24

2 2 10

to be < from proton decay limits, the other components

h 1; h ' 1=4:

with a central value

0 00 00

The parameter choices of Table IV can be input to event of and are signi®cantly less tightly constrained.

0 00

Upper bounds on theR / couplings , ,and have been in- generators such as Spythia or ISAJET (via M SSM i key- ferred from a variety of low-energy processes, but most of these words) to check that the event rate and kinematics of the ee

event are satis®ed and then to determine other related signatures. bounds are not very stringent. An exception is the bound on

0

0 0

9:6

, which comes from the impressive lower limit of

111

! ~ tan

Spythia includes the ~ branching ratio for low

2 1

24

0 0 yr

10 [31] on the half-life for the neutrinoless double beta de-

! ~

values; for ISAJET,the ~ branching must be input us-

2 1

76 76

! Se + 2e cay Ge . At the quark level, this decay is the

ing the F O RC E command, or must be explicitly added into the

0

2d ! 2u +2e = O process .If 6 , this process can be engen-

decay table. 111 R

dered by a diagram in which two d quarks each undergo the /

! u~ + e u~

B. CDF/D0 Dilepton Plus Jets Events transition d , and then the two produced squarks

g u

exchange a ~ to become two quarks. It can also be engen-

~

d ! 2d g~

Recently, CDF and D0 have reported various dilepton plus dered by a diagram in which 2 by exchange, and then

~ ~

R d ! u + e

multi-jet events which are presumably top-quark candidate each of the d squarks undergoes the / transition .

02

events. For several of these events, however, the event kinemat- Both of these diagrams are proportional to . If we assume 111

ics do not match well with those expected from a top quark with that the squark masses occurring in the two diagrams are equal,

' m m m 175 m

~

q~ u~

mass t GeV. The authors of Ref. [30] have shown that , the previously quoted limit on the half-life

L d the match to event kinematics can be improved by hypothesizing implies thatR [32]

663 R

What effects ofR / might we see, and how would / interac-

R

tions affect future searches for SUSY? Let us assume that / cou-

2 1=2

m m

q~ g~

0 4

: j < 3:4 10

j (9) plings are small enough that sparticle production and decay are

111

100 GeV 100 GeV

still dominated by gauge interactions, as in the absence ofR / .

It is interesting to recall that if the amplitude for neutrino- The main effect ofR / is then that the LSP is no longer stable,

less double beta decay is, for whatever reason, nonzero, then the but decays into ordinary particles, quite possibly within the de-

0

6=0

electron neutrino has a nonzero mass [33]. Thus, if ,tector in which it is produced. Thus, the LSP no longer carries

1jj

(E ) SUSY interactions lead to nonzero neutrino mass [34]. away transverse energy, and the missing transverse energy / T

The way [35] in which low-energy processes constrain many signal, which is the mainstay of searches for SUSY when R is

0

of theL / couplings and is illustrated by consideration of nu- assumed to be conserved, is greatly degraded. (Production of

E

clear decay and decay. In the Standard Model (SM), both SUSY particles may still involve missing T , carried away by

of these decays result from W exchange alone, and the compar- neutrinos.)

+ e

ison of their rates tells us about the CKM quark mixing matrix. At future e colliders, sparticle productionmay include the

+ + + + +

+ 0 0

R

e ! ~ ~ ~ ~ e~ e~ e~ e~ e~ e~ e~ e~

However, in the presence of / couplings, nuclear decay can processes e , , , , , ,

i j

i j L L L R R L R R

~ ~

+ + + +

d s~ b

receive a contribution from , ,or exchange, and decay

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ L

, , , , L . Here, the are charginos,

L L R R L L R R i

0

e ~ ~

from ~, ,or exchange. The information on the CKM ele-

and the ~ are neutralinos. Decay of the produced sparticles will i

ments which has been inferred assuming that only W exchange E

often yield high- T charged leptons, which can be sought in

is present bounds these new contributions, and it is found, for seeking evidence of SUSY.Now, suppose the LSP is the lightest 0

example, that [35] 0

L R ~

neutralino, ~ .Ifthe/,/couplings are nonzero, the can

1 1

0

! e; ee

have the decays ~ .

1

m k

e~

R

; j j < 0:04 k 12 (10) These yield high-energy leptons, so the strategy of looking for

100 GeV the latter to seek evidence of SUSY will still work. However, if

00 0

B R ~ k the / ,/couplings are nonzero, the can have the decays

for each value of the generation index . In a similar fashion, 1

0

! cds; cds ~ . When followed by these decays, the production

a number of low-energy processes together imply [35] that for 1

+ 0 0

0

e e ! ~ ~

L

ij k process yields six jets which form a pair of three- 1

many of the / couplings and , 1

ij k

0

m

jet systems. The invariant mass of each system is ~ ,andthere

1

m

~

0) f

( is no missing energy. This is quite an interesting signature.

j < (0:03 ! 0:26) :

j (11)

ij k

100 GeV

R

NonvanishingL / and / couplings would also make possi-

+ e

ble resonant sneutrino production in e collisions. [35] For

m

~

0 Here, is the mass of the sfermion relevant to the bound on +

f

e e ! ~ ! ~ ; ~

example, we could have .Atthe

1

1

(0) the particular . ij k resonance peak, the cross section times branching ratio could be

Bounds of order 0.1 have also been placed on theL / couplings large [35]. 0

by searches for squarks formed through the action of these jk

1 In future experiments at hadron colliders, one can seek evi-

+ p

couplings in e collisions at HERA [36]. dence of gluino pair production by looking for the multilepton

00 Constraints on theB / couplings come from nonleptonic signal that may result from cascade decays of the gluinos. This

weak processes which are suppressed in the SM, such as rare B

signal will be affected by the presence ofR / interactions. The

K D D

decays and K and mixing [37]. For example, the R

worst case is where the LSP decays viaB / ,/couplings to yield

+ +

0

! K K decay B is a penguin (loop) process in the SM, hadrons. The presence of these hadrons can cause leptons in

but in the presence ofR / couplings could arise from a tree-level SUSY events to fail the lepton isolation criteria, degrading the

k

u k =1;2 3 diagram involving ~ ( ,or ) exchange. The present R multilepton signal [40]. This reduces considerably the reach in

upper bound on the branching ratio for this decay [38] implies

m g

~ of the Tevatron. At the Tevatron with an integrated lumi-

1 1

that [37]

m g

nosity of 0.1 fb ,thereisno reach in ~ , while for 1 fb it

m =2m

q~ g~

m

k is approximately 200 GeV [40], if .AttheLHC

u~

00 00 1=2

R

1

j < 0:09 ; k =1;2;3:

j (12)

12 k 23

k with an integrated luminosity of 10 fb , the reach extends be-

100 GeV

m =1TeV B R g

yond ~ , even in the presence of / and / interactions 0

0 [41].

m = 100 < 0:29 < 0:18 q

Recently, bounds and for ~

12k 22k R GeV have been obtained from data on D meson decays [34]. If / couplings are large, then conventional SUSY event gener-

For a recent review of constraints on R-violating interactions, ators will need many production and decay mechanisms to be re-

see Ref. [39]. computed. The results would be very model dependent, owing R

We see that if sfermion masses are assumed to be of order 100 to the large parameter space in theR / sector. If / couplings are

R

GeV or somewhat larger, then for many of the / couplings ij k , assumed small, so that gauge and Yukawa interactionsstill dom-

0 00

and , the existing upper bound is 0.1 for a sfermion inate production and decay mechanisms, then event generators

ij k ij k mass of 100 GeV. We note that this upper bound is comparable can be used by simply adding in the appropriate expected decays

to the values of some of the SM gauge couplings. Thus,R / inter- of the LSP (see the approach in Ref. [40, 41]). For ISAJET, actions could still prove to play a signi®cant role in high-energy the relevant LSP decays must be explicitly added (by hand) to collisions. the ISAJET decay table.

664

q

5

0

= c = c =1 g = g =

VII. GAUGE-MEDIATED LOW-ENERGY c

2 3 1 where 1 (we de®ne ), and SUPERSYMMETRY BREAKING 3 F=S. The two-loop squark and slepton masses squared at the messenger scale are [42]

A. Introduction

"

2

2 2 2

3 Y

3 2 1 2

Supersymmetry breaking must be transmitted from the 2

C m~ =2 +C +

3 2

4 5 2 4 supersymmetry-breaking sector to the visible sector through 4

some messenger sector. Most phenomenological studies of (15)

4

C = C = 2

supersymmetry implicitly assume that messenger-sector inter- where 3 for color triplets and zero for singlets,

3 3

actions are of gravitational strength. It is possible, however, that for weak doublets and zero for singlets, and Y is the ordi-

4

1

Q = T + Y

the messenger scale for transmitting supersymmetry breaking nary hypercharge normalized as 3 . The gaugino 2 is anywhere between the Planck and just above the electroweak and scalar masses go roughly as their gauge couplings squared.

scale. The Bino and right-handed sleptons gain masses only through

U (1)

The possibility of supersymmetry breaking at a low scale Y interactions, and are therefore lightest. The Winos and

SU (2) has two important consequences. First, it is likely that the left-handed sleptons, transforming under L ,aresome- standard-model gauge interactions play some role in the mes- what heavier. The strongly interacting squarks and gluino are

senger sector. This is because standard-model gauginos cou- signi®cantly heavier than the electroweak states. Note that the F=S

ple at the renormalizable level only through gauge interactions. parameter = sets the scale for the soft masses (indepen-

2

F S M i If Higgs bosons received mass predominantly from non-gauge dent of the i for ). The messenger scale ,maybe

interactions, the standard-model gauginos would be unaccept- anywhere between roughly 100 TeV and the GUT scale. =

ably lighter than the electroweak scale. Second, the gravitino is The dimensionful parameters within the Higgs sector, W

2

H H V = m H H + h:c:

d u d u and , do not follow from the naturally the lightest supersymmetric particle (LSP). The light- 12 est standard-model superpartner is the next to lightest super- ansatz of gauge-mediated supersymmetry breaking, and require symmetric particle (NLSP). Decays of the NLSP to its partner additional interactions. At present there is no good model which

plus the Goldstino component of the gravitino within a detector gives rise to these Higgs-sector masses without tuning parame-

2 m ters. The parameters and are therefore taken as free pa- lead to very distinctive signatures. In the following subsections 12

the minimal model of gauge-mediated supersymmetry breaking, rameters in the minimal model, and can be eliminated as usual

tan m and the experimental signatures of decay to the Goldstino, are in favor of and Z .

presented. Electroweak symmetry breaking results (just as for high-scale 2

breaking) from the negative one-loop correction to m from

H u stop-top loops due to the large top quark Yukawa coupling. Al-

B. The Minimal Model of Gauge-Mediated though this effect is formally three loops, it is larger in magni- 2

Supersymmetry Breaking tude than the electroweak contribution to m due to the large

H u

The standard-model gauge interactions act as messengers of squark masses. Upon imposing electroweak symmetry break-

(1 2)m

ing, is typically found to be in the range ~ (de- `

supersymmetry breaking if ®elds within the supersymmetry- L

breaking sector transform under the standard-model gauge pending on tan and the messenger scale). This leads to a light-

0 est neutralino, ~ , which is mostly Bino, and a lightest chargino,

group. Integratingout these messenger-sector ®elds gives rise to 1

~ , which is mostly Wino. With electroweak symmetry break- standard-model gaugino masses at one-loop, and scalar masses 1 squared at two loops. Below the messenger scale the particle ing imposed, the parameters of the minimal model may be taken

content is just that of the MSSM plus the essentially massless to be

; = F=S ; sign ; ln M ) Goldstino discussed in the next subsection. The minimal model ( tan (16)

of gauge-mediated supersymmetry breaking (which preserves The most important parameter is which sets the overall scale

the successful predictions of perturbative uni®cation) consists for the superpartner spectrum. It may be traded for a physical

5 + 5

0

m m

of messenger ®elds which transform as a single ¯avor of ~

mass, such as ~ or . The low energy spectrum is only

`

L

1

` SU (5) q q `

M ln M

of , i.e. there are triplets, and , and doublets, and . ln 3

weakly sensitive to i , and the splitting between and

S

ln M

These ®elds couple to a single gauge singlet ®eld, , through the 2 may be neglected for most applications.

superpotential

W = Sqq + S``: 2 3 (13) C. The Goldstino In the presence of supersymmetry breaking the gravitinogains

A non-zero expectation value for the scalar component of S

a mass by the super-Higgs mechanism

= S

de®nes the messenger scale, M , while a non-zero

expectation value for the auxiliary component, F , de®nes the

F F

p

m = ' 2:4 eV

supersymmetry-breaking scale within the messenger sector. For G (17)

2

(100 TeV )

3M

p

2

S F , the one-loop visible-sector gaugino masses at the

messenger scale are given by [42] 18

M ' 2:4 10

where p GeV is the reduced Planck mass. With

low-scale supersymmetry breaking the gravitino is naturally the

i

= c m i (14)

i lightest supersymmetric particle. The lowest-order couplings of

4

665

1

0

the spin- longitudinal Goldstino component of the gravitino, Detecting the ®nite path length associated with ~ decay rep-

1

2

0

G ~ !

, are ®xed by the supersymmetric Goldberger-Treiman low resents a major experimental challenge. For the case

1

+ G energy theorem to be given by [43] , tracking within the electromagnetic calorimeter (EMC)

is available. A displaced photon vertex can be detected as a non-

1

= j @ G + h:c: L zero impact parameter with the interaction region. For example,

p

(18) F

with a photon angular resolution of 40 mrad/ E expected in the

j < 1 CMS detector with a preshower array covering j [44], a where j is the supercurrent. Since the Goldstino couplings

(18) are suppressed compared to electroweak and strong inter- sensitivity to displaced photon vertices of about 12 mm at the 3 actions, decay to the Goldstino is only relevant for the lightest level results. Decays well within the EMC or hadron calorimeter

standard-model superpartner (NLSP). (HC) would give a particularly distinctive signature. In the case

0 0 0

! (h ;Z )+G of decays to charged particles, such as from ~

With gauge-mediated supersymmetry breaking it is natural 1

0

! + G ! f f or ~ with , tracking within a silicon ver- that the NLSP is either a neutralino (as occurs in the minimal 1

model) or a right-handed slepton (as occurs for a messenger sec- tex detector (SVX) is available. In this case displaced vertices

down to the 100 m level should be accessible. In addition, de-

+ 5

tor with two ¯avors of 5 ). A neutralino NLSP can decay

0 0 0 0

0 cays outside the SVX, but inside the EMC, would give spectac-

! ( ; Z ;h ;H ;A )+G

by ~ , while a slepton NLSP de- 1

~ ular signatures.

! ` + G cays by ` . Such decays of a superpartner to its partner

plus the Goldstino take place over a macroscopic distance, and p for F below a few 1000 TeV, can take place within a detec- 2. Slepton NLSP tor. The decay rates into the above ®nal states can be found in

Ref. [16, 17, 18, 19]. It is possible within non-minimal models that a right-handed

~

` ! ` + G

slepton is the NLSP, which decays by R . In this case

+ +

` ` X + E6 e e D. Experimental Signatures of Low-Scale the signature for supersymmetry is T .At col- liders such signatures are fairly clean. At hadron colliders some

Supersymmetry Breaking

tt

of these signatures have backgrounds from WW and produc-

~ ~

` ` X =4` L

The decay of the lightest standard-model superpartner to its tion. However, L production can give , which has

~ ~

` ` R partner plusthe Goldstinowithin a detector leads to very distinc- signi®cantly reduced backgrounds. In the case of R produc-

tive signatures for low-scale supersymmetry breaking. If such tion the signature is nearly identical to slepton pair production

0 0

~

! ` +~ ~

with ` with stable. The main difference here is 1 signatures were established experimentally, one of the most im- 1

portant challenges would be to measure the distribution of ®nite that the missing energy is carried by the massless Goldstino.

~

! ` + G path lengths for the NLSP, thereby giving a direct measure of the The decay ` over a macroscopic distance would give supersymmetry-breaking scale. rise to the spectacular signature of a greater than minimum ion- izing track with a kink to a minimum ionizing track. Note that if 1. Neutralino NLSP the decay takes place well outside the detector, the signature for In the minimal model of gauge-mediated supersymmetry supersymmetry is heavy charged particles rather than the tradi-

0 tional missing energy.

breaking, ~ is the NLSP. It is mostly gaugino and decays pre-

1

0

! + G R

dominantly by ~ . Assuming parity conservation, 1

and decay within the detector, the signature for supersymmetry E. Event Generation

X +E6 X

at a collider is then T ,where arises from cascade de-

0 For event generation by ISAJET, the user must provide a pro-

cays to ~ . In the minimal model the strongly interacting states 1

are much too heavy to be relevant to discovery, and it is the elec- gram to generate the appropriate spectra for a given point in the

0 M SSM i

+ above parameter space. The corresponding parame-

e ~ troweak states which are produced. At e colliders can be

1 ters can be entered into ISAJET to generate the decay table, ex-

e~

probed directly by t-channel exchange, yielding the signature

+ 0 0

! G +

cept for the NLSP decays to the Goldstino. If NLSP

e e ! ~ ~ ! + E6

T . At a hadron collider the most

1 1

+

0 0 G

at 100%, the F O RC E command can be used. Since the par-

qq ! ~ ~ ; ~ ~ ! X + E6

promising signals include T ,

2 1 1 1

+ ticle is not currently de®ned in ISAJET, the same effect can be

= WZ;WW;W` ` ;:::

where X . Another clean signature is

+

+ 0 ~

~ obtained by forcing the NLSP to decay to a neutrino plus a pho-

` ! ` ` + E6 qq ! `

T . One event of this type has in

R R fact been reported by the CDF collaboration [14]. In all these ton. If several decays of the NLSP are relevant, then each de- signatures both the missing energy and photon energy are typ- cay along with its branching fraction must be explicitly added to

the ISAJET decay table. Decay vertex information is not saved

0

m =2

ically greater than ~ . The photons are also generally iso- lated. The background1 from initial- and ®nal-state radiation typ- in ISAJET, so that the user must provide such information. In ically has non-isolated photons with a much softer spectrum. Spythia,theG particle is de®ned, and decay vertex informa-

0 tion is stored.

In non-minimal models it is possible for ~ to have large Hig-

1

0 0

! h + G

gsino components, in which case ~ can dominate. In

1

bbbbX + E6 b

this case the signature T arises with the -jets recon- VIII. CONCLUSIONS

0 m

structing h in pairs. This ®nal state topology may be dif®cult to reconstruct at the LHC ± a systematic study has not yet been In this report we have looked beyond the discovery of super- attempted. symmetry, to the even more exciting prospect of probingthe new

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The phenomenology of some scenarios is less dramatic and th

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668