Experimental Signatures of Low Energy Gauge Mediated Supersymmetry Breaking

Home , Goldstino

SLAC-PUB-7104

SU-ITP-96-06

SCIPP 96-08

hep-ph/9601367

Exp erimental Signatures of Low Energy

Gauge Mediated Sup ersymmetry Breaking

ab c

Savas Dimopoulos , Michael Dine ,

y z

d e

Stuart Raby , Scott Thomas

Physics Department, Stanford University, Stanford, CA 94309

Theoretical Physics Division, CH-1211, Geneva 23, Switzerland

Santa Cruz Institute for Particle Physics,

University of California, Santa Cruz, CA 95064

Physics Department, Ohio State University, Columbus, OH 43210

Stanford Linear Accelerator Center, Stanford, CA 94309

Abstract

The exp erimental signatures for gauge mediated sup ersymmetry breaking are

presented. The phenomenology asso ciated with this class of mo dels is distinctive

since the gravitino is naturally the LSP. The next lightest sup ersymmetric particle

NLSP can b e a gaugino, Higgsino, or right handed slepton. Decay of the NLSP

to its partner plus the LSP pro ceeds through the Goldstino comp onent of the

gravitino. For a signi cant range of parameters this decay can take place within the

detector, and can b e measured as a displaced vertex or kink in a charged particle

track. In the case that the NLSP is mostly gaugino, we identify the discovery

+ +

mo des as e e ! + E6 , and pp ! l l + E6 . If the NLSP is a right handed

+ + +

slepton the discovery mo des are e e ! l l + E6 and pp ! l l + E6 . An NLSP

which is mostly Higgsino is also considered. Finally, these theories can contain

scalar particles which mediate sub-millimeter range coherent forces of gravitational

strength.

Submitted to Physical Review Letters

? Work supp orted by the Department of Energy.

y Work supp orted by the Department of Energy under contract DOE-ER-01545-646.

z Work supp orted by the Department of Energy under contract DE-AC03-76SF00515.

1. Intro duction

Low energy sup ersymmetry is widely viewed as a plausible solution of the

hierarchy problem. If nature is sup ersymmetric, it is imp ortant to understand how

sup ersymmetry is broken. It is usually assumed that sup ersymmetry breaking is

communicated to ordinary elds and their sup erpartners by sup ergravity. The

breaking scale is then necessarily of order 10 GeV. An alternative p ossibility,

which has b een less thoroughly explored, is that sup ersymmetry is broken at some

lower energy scale, and that the ordinary gauge interactions act as the messengers

of sup ersymmetry breaking. In this case, the scale of sup ersymmetry breaking can

b e as low as 10's of TeV [1].

Indep endent of source and messenger, sup ersymmetry breaking is represented

among ordinary elds the visible sector by soft sup ersymmetry breaking terms

[5]. The most general soft-breaking Lagrangian is describ ed by 105 parameters

beyond those of the minimal standard mo del [6]. In the conventional sup ergravity

context, these are in principle all indep endent, free parameters. However, there are

anumb er of constraints which these parameters must satisfy, coming from direct

exp erimental searches for sup erpartners, electric dip ole moments, and the lack

of avor changing neutral currents. Most mo del builders simply p ostulate a high

degree of degeneracy among squarks and sleptons at a high energy scale to deal with

this problem [5]. In certain classes of sup erstring theories, there are weak hints

for such a universality [7,8]. Alternatively, the various exp erimental constraints

might b e satis ed as a result of avor symmetries or by other means [9-11]. With

gauge mediated sup ersymmetry breaking the entire soft breaking Lagrangian can

b e calculated in terms of a small numb er of parameters. In addition, the regularities

required to avoid avor changing neutral currents are automatically obtained since

the ordinary gauge interactions do not distinguish generations. For these reasons,

we b elieve the gauge-mediated p ossibility should b e taken seriously.

In this letter, we discuss two striking and distinctive signatures of low energy

gauge-mediated sup ersymmetry breaking. The rst is the sp ectrum of sup erpart-

ner masses. These masses are functions of the gauge quantum numb ers, and are

roughly in the ratio of the appropriate gauge couplings squared. In the simplest

mo dels, de nite relations exist among these masses. As a result, the lightest stan- 1

dard mo del sup erpartner is almost inevitably either a neutralino or a right-handed

slepton. The second imp ortant signature arises from the fact that the lightest

sup ersymmetric particle LSP is the gravitino. The lightest standard mo del su-

p erpartner is then the next to lightest sup ersymmetric particle NLSP. Assuming

that R-parity is conserved, the principle decay of the NLSP is then to its partner

plus a gravitino. The longitudinal comp onent of the gravitino { the Goldstino {

couples to matter with strength prop ortional to F , where F is the scale of su-

p ersymmetry breaking. For a plausible range of F , the decay length can b e 100's

of m to meters. The decays can therefore take place within a detector. This leads

to signatures for sup ersymmetry which are distinct from the conventional minimal

sup ersymmetric standard mo del MSSM, and with p otentially dramatic displaced

vertices.

2. Sup erpartner Sp ectrum

In gauge mediated mo dels, sup ersymmetry is broken in a messenger sector

which transforms under the standard mo del gauge group. The matter elds in this

sector are generally referred to as messenger quarks and leptons. Sup ersymmetry

breaking is transmitted to the visible sector by ordinary gauge interactions. To

preserve the successful sup ersymmetric prediction of the low energy sin it is

sucient that the messengers form a GUT representation. In the simplest versions,

the messenger elds are weakly coupled, and p ossess the quantum numb ers of

a single 5 + 5 of SU 5, i.e. there are triplets, q andq and doublets ` and ` .

They couple to a single gauge singlet eld, S , through a sup erp otential W =

Sqq + S``. The eld S has non-zero exp ectation values for b oth scalar and

1 2

auxiliary comp onents, S and F .Integrating out the messenger sector then gives

rise to gaugino masses at one lo op. For F S , these masses are given by [4]

m = c N : 2:1

where c = ;c = c =1,=F =S , and for a more general messenger sector

1 2 3

N is the equivalentnumber of SU 5 5 + 5 representations. The scalar masses 2

squared arise at two-lo ops [4]

2 2 2

5 Y

3 2 1

2 2

m~ =2 N C +C + : 2:2

3 2

4 4 3 2 4

4 3

where C = for color triplets and zero for singlets, C = for weak doublets

3 2

3 4

and zero for singlets, and Y is the ordinary hyp ercharge normalized as Q = T +

Y . It should b e stressed that F is not necessarily the intrinsic sup ersymmetry

breaking scale, F , since the gauge singlet eld may not b e coupled directly to the

sup ersymmetry breaking sector. For example, in the mo del of Ref. [4], F F .

However, it is also p erfectly p ossible that F F [12]. While F determines the

S S

sup erpartner masses, it is F which determines the Goldstino coupling discussed in

the next section.

These expressions for the masses p ossess a numb er of noteworthy features.

There is a hierarchy of masses, with colored particles b eing the most massive, and

SU 3 SU 2 singlet particles the lightest. The gaugino masses are in the ratio 7 :

2 : 1, just as for sup ersymmetry breaking with universal gaugino masses at a high

scale. For N = 1 the squark, left handed slepton, right handed slepton, and bino

partner of the hyp ercharge gauge b oson masses are in the ratio 11:6: 2:5:1:1:

1. In this case the bino is therefore the natural candidate for the NLSP. The gaugino

masses growas N, while the scalar masses growas N. For N = 2 the ab ove

masses are in the ratio 10:6:2:3:1 :1:3. In this case the right handed slepton

is the candidate for the NLSP.

In more general mo dels the ab ove relations among the masses can b e mo di ed.

For example b oth 2.1 and 2.2 are corrected at O F =S . Additional mo di ca-

tions can arise with several gauge singlet elds coupling to q q and `` . In the mo del

with one singlet, the couplings and cancel out in the expressions for the

1 2

masses, but this is not true of the more general case. As a result, b oth the ratios

of the squark and slepton masses and the ratio of these masses to gaugino masses

are mo di ed. More generally scalar masses require only sup ersymmetry breaking,

while gaugino masses require also that U 1 b e broken to at most R-parity.In

principle U 1 could e ectively b e broken at a lower scale than sup ersymmetry,

leading to gauginos which are much lighter than the scalars. 3

Perhaps a more interesting p ossibility is that the messenger sector is strongly

coupled. Gaugino masses can then arise directly from non-p erturbative dynamics

in the messenger sector, m g . The scalar masses require one p erturbative

2 2 2

gauge lo op,m ~ g =4 . So in this case the gauginos are much heavier than

the scalars, and the natural candidate for the NLSP is the right handed slepton.

All of the p ossibilities given ab ove for the messenger sector have in common the

feature that masses for standard mo del sup erpartners go roughly as gauge couplings

squared, although the relation of scalar to gaugino masses is mo del dep endent.

The dimensionful terms whichmust arise in the Higgs sector W = H H ,

1 2

and V = m H H + h:c:, do not follow directly from the anzatz of gauge mediated

1 2

sup ersymmetry breaking, and are mo del dep endent. This is b ecause these terms

require that the Peccei-Quinn symmetry b etween H and H b e broken by non-

1 2

gauge interactions. Sp eci c mo dels with additional singlets and vector quarks have

b een constructed in which and m do arise with reasonable magnitude [4]. In

addition, it is in principle p ossible for high scale physics to generate suitable terms

[4]. Because the prop erties of the Higgs sector are not generic, we leave op en the

p ossibility that the lightest electroweak neutralino is a general mixture of gaugino

and Higgsino.

3. Phenomenology

Perhaps the most dramatic consequence of low energy gauge mediated su-

p ersymmetry breaking is that the gravitino is the LSP. In the global limit the

Goldstone fermion, or Goldstino, of sup ersymmetry breaking is massless. In lo cal

sup ersymmetry, the Goldstino b ecomes the longitudinal comp onent of the grav-

itino, giving a gravitino mass assuming the cosmological constantvanishes of

F F

m = ' 2:5 eV 3:1

100 TeV

where F is the sup ersymmetry breaking scale. The lightest standard mo del su-

p ersymmetric particle is then the NLSP, and can decay to its partner and the

gravitino. The lowest order coupling of the Goldstino is xed by the sup ersym- 4

metric Goldb erger-Treiman low energy theorem to b e given by [13]

L = j @ G + h:c: 3:2

longitudinal Goldstino comp o- where j is the sup ercurrent and G is the spin

nent of the gravitino. The decay to the Goldstino comp onent is then suppressed

only by F rather than M . In the case that the NLSP is mostly bino, B , the

coupling 3.2 leads to a transition magnetic dip ole momentbetween the NLSP

=2 and gravitino, cos m 2 F B GF + h:c:, giving rise to a decay rate

2 5

cos m

B ! G + = 3:3

16F

This translates to a decay length

100 GeV F

c ' 130 m 3:4

m 100 TeV

So there is a range of F and m for which the decay o ccurs within the detector,

with the gravitino carrying o missing energy. For m >m there is also a

0 0

~ ~

non-negligible branching fraction B ! G + Z BrB ! G + Z ! sin for

m m . In the case that the NLSP is a right handed slepton it can decayby

l !G+l with a decay length similar to 3.4. If the NLSP is mostly Higgsino,

R R

0 0 0

it can decaybyH !G+h if m

For m >m decay H ! G + bb is p ossible; however for reasonable values

of the parameters the NLSP decays predominantly to G + through its gaugino

comp onents.

Decay of the lightest standard mo del sup ersymmetric particle to its partner

plus the gravitino within the detector gives signatures which are distinct from the

conventional MSSM. Let us fo cus on the discovery mo des at e e and hadron

colliders. Consider rst the case in which the NLSP is mostly bino. At e e

~ ~

colliders e e ! B B ! + 6E is dominated by t- and u-channel right handed

selectron exchange. The pro duction cross section for this pro cess can b e signi cant.

s =2:2 m , and assuming the sp ectrum resulting from the For example, with

~ ~

simple mo del with N = 1 given in the previous section, e e ! B B ' :87 R 5

2 + +

where R =4 =3s is the e e ! cross section. In many mo dels, since the

bino and slepton masses are related, the total cross section is related to the bino

mass. This pro cess should show signi cant p olarization dep endence sincee ~ is

lighter thane ~ , and the hyp ercharge ofe ~ is twice that ofe ~ .For the parameters

L R L

+ +

~ ~ ~ ~

given ab ove e e ! B B = e e ! B B ' :01. The bino decay is isotropic in

L R

the rest frame, implying that the photons have a at energy distribution in the lab

frame. Cuts on the invariant mass can easily eliminate the background from

+ 0 0

e e ! Z with Z ! .

The signature + E6 can also arise in the conventional MSSM in some regions

of parameter space if the LSP is mostly Higgsino. In this case the NLSP is not much

heavier than the LSP, is also mostly Higgsino, and has a signi cant branching ratio

+ 0 0

~ ~ ~ ~

H ! H + . e e ! H H then gives rise to this mo de. In the gauge mediated

2 1

2 2

case however, since E6 is carried by the essentially massless gravitinos, the photon

p p

1 1

energy is b ounded by s1 E s1 + , where = 1 4m =s

4 4

is the bino velo city. In the conventional case since 6 E is carried by the massive

2 2

, where =m LSP the photon energy end p oints are smaller by a factor 1 m

0 0

~ ~

H H

2 1

in this case is the H velo city. This allows the decay to a gravitino to b e

distinguished from decay to the LSP in the conventional MSSM. In addition, in

this region of parameter space the lightest chargino is just slightly heavier, is also

~ ~

mostly Higgsino, and decays predominantly by H ! H W . In the MSSM the

+ + + 0

~ ~

additional signatures e e ! H H ! 4j + E6 , jjl+ E6 , and l l + E6 are likely

to b e accessible at comparable s. This is in contrast to the gauge mediated case

with a mostly bino NLSP.

As discussed in the previous section, with a weakly coupled messenger sector

giving an NLSP which is mostly bino, it is likely that the right handed sleptons

are not to o much heavier than the NLSP. In this case, in addition to bino pair

pro duction, slepton pair pro duction may b e kinematically accessible. Cascade

+ +

~ ~

decay through the bino then gives rise to e e ! l l ! l l + E6 .

R R

~ ~

! If the NLSP is a right handed slepton, the discovery mo de is e e ! l l

R R

l l + E6 . As for the decay to photons, the leptons have a at energy distribution,

with end p oints determined by . The nal states with e, , and , s and m

should app ear with very nearly equal m . Cuts on 6 E can easily eliminate the

+ 0 + 0

background e e ! Z l l with Z ! . This signature can also arise in 6

the conventional MSSM where the missing energy is carried by the massive LSP.

However, the lepton energy endp oints again distinguish this from an essentially

massless gravitino. It is interesting to note that if F is much larger than a few

1000 TeV the decayof l takes place well outside the detector. The signature

for sup ersymmetry is then massivecharged particles, rather than the traditional

missing energy.

>m , the discovery mo de is e e ! If the NLSP is mostly Higgsino, and m

0 0

~ ~

H H ! 4b+ E6 , with of course two pairs of b jets reconstructing the Higgs mass.

In this part of parameter space the next heaviest neutralino and lightest chargino

are mostly Higgsino, not much heavier than H , and have the same decay mo des

0 + +

~ ~ ~

to H as in the MSSM. The signatures e e ! H H ! 4b4j + 6 E ,4bjjl+ 6E,

+ 0

and 4bl l + 6 E should therefore also b e accessible at comparable s, with the

additional jets and leptons fairly soft.

The discovery mo des at hadron colliders can b e somewhat di erent than for

~ ~

e e colliders. If the NLSP is very nearly purely bino, pp ! B B ! + 6

E pro ceeds predominantly through t- and u-channel squark exchange, and is

therefore highly suppressed b ecause of the large squark masses. However, sleptons

can b e pair pro duced by the Drell-Yan pro cess. Cascade decay through the bino

~ ~

then leads to pp ! l l ! l l + E6 . One such sp ectacular ee event has in

R R

fact b een observed at the Tevatron by the CDF collab oration event 257646 in run

68739. The kinematics of this event are consistent with cascade decay through the

bino to gravitino. The obvious background from pp ! WW has a very small

pro duction rate, and would give rise to other decays mo des which are not observed

~ ~

[14]. In contrast, the pro duction cross section for pp ! l l with m ' 95 GeV is

R R

2 1

roughly 10 pb [15]. With 90 pb of integrated luminosity, the single observed

event could b e consistent with right handed slepton pair pro duction.

If the sleptons are much heavier than the gauginos, and the NLSP is mostly

bino, pair pro duction of winos b ecomes the dominant pro duction mechanism, pp !

0 0

~ ~ ~ ~ ~

W ! W W . The dominant wino decay mo des are W ! BW and W !

0 0 +

~ ~ ~ ~ ~

BZ through mixing with the Higgsino states, and W ! Bl and W ! Bl l

through o shell sleptons. Cascade decays through the bino then lead to the

0 + 0

~ ~

signatures pp ! W W ! 4j + 6E , jjl + 6E , and l l l + 6E . The last

T T T

one is similar to the standard tri-lepton signature of chargino pair pro duction [16]. 7

Here the additional hard photons signi cantly reduce the background. If the NLSP

is mostly Higgsino or a right handed slepton, the signatures at hadron colliders are

similar to those at e e .

By far the most dramatic signature of low energy sup ersymmetry breaking is

the p ossibility of measuring directly the decay of the NLSP to its partner plus the

gravitino. If the NLSP is a neutralino this app ears as a displaced vertex, while for

a slepton NLSP it app ears as a kink in a charged particle track. Measurementof

the decay distribution would allow a direct determination of the sup ersymmetry

breaking scale. For the decay of right handed sleptons to leptons, or the decayof

Higgsinos to the lightest Higgs b oson, tracking of the resulting charged particles in

a silicon vertex detector and central tracking region would allow measurements of

c between roughly 100 m { 10 m. In the case of decay to a photon, the tracking

ability for the displaced vertex is generally not go o d. However if such a signal

were established exp erimentally, detectors could b e optimized to convert photons

within the tracking region. So dep ending on the sp eci c decay mo des of the NLSP,

displaced vertices for F between roughly 100 { 1000's of TeV could b e accessible

to collider exp eriments.

This range of exp erimentally accessible F is in fact consistent with astro-

physical and cosmological considerations. Unless there is an in ation with low

reheat temp erature, avoiding overclosure of the universe from relic gravitinos re-

quires F 2 10 TeV. In many theories a p otentially dangerous R-axion arises

in the sup ersymmetry breaking sector [17]. For F ab ove a few TeV, R-violating

interactions suppressed by a single p ower of the Planck scale make the R-axion

to o heavy to b e pro duced during helium ignition in red giants [18]. In addition

it is either trapp ed or to o heavy to deplete the neutrino pulse from SN1987A. Fi-

nally, for weakly coupled mo dels with a single additional scale, such as the simple

example in the previous section with F F , electroweak scale sup erpartners are

obtained for F 100 TeV.

A nal p ossible consequence of these theories is that scalar mo duli with Planck

suppressed couplings to matter obtain masses of order or smaller than the gravitino

mass as the result of sup ersymmetry breaking. These elds can mediate coherent

forces in the sub-millimeter range, which has not b een explored exp erimentally.

New techniques employing small cryogenic mechanical oscillators [19] or atomic 8

b eams [20] may allow the detection of such short range gravitational strength

forces.

Low energy gauge-mediated sup ersymmetry breaking clearly makes distinct

and dramatic predictions for future exp eriments. The new particle sp ectrum is

predicted in terms of a small numb er of parameters. For a quite plausible range of

these parameters, it predicts signatures distinctly di erent than those of the con-

ventional MSSM. Most dramatic of these is the p ossibility of measuring displaced

vertices or kinks in charged particle tracks from decays to the gravitino.

Wewould like to thank G. Anderson, R. Barbieri, G. Giudice, H. Hab er, L.

Hall, M. Peskin, A. Pomarol, and J. Wells for valuable discussions.

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