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arXiv:1005.1255v2 [hep-ph] 20 Aug 2010

UT-10-08

IPMU 10-0079

LHC Reach of Low Scale Gauge Mediation with Perturbatively

Stable Vacuum

Ryosuke Sato and Satoshi Shirai

Department of Physics, University of Tokyo,

Tokyo 113-0033, Japan

Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo,

Chiba 277-8568, Japan

Abstract

Very light gravitino scenario m3/2<

cosmological problem. However in such a scenario, stability of the vacuum is an

important issue. Recently, Yonekura and one of the authors RS have investigated

the parameter space of a low scale gauge mediation with a perturbatively stable

vacuum and found that there are severe upper bounds on the gaugino masses. In

this Letter, we show that such a model can be completely excluded/discovered at

very early stage of the LHC run.

∼16 eV is very interesting, since there is no

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1 Introduction

Low scale gauge mediation is attractive, because it can achieve a very light gravitino mass

m3/2<

∼16 eV, which satisfies all constraints from cosmology [1]. However in this scenario,

stability of the vacuum is an important issue [2]. It is known that there are two kinds

of model which can have the light gravitino and a sufficiently stable vacuum. One is the

model of Refs. [3] using the Izawa-Yanagida-Intriligator-Thomas (IYIT) model [4] as a

SUSY breaking sector, and the other is the model of Refs. [5] gauging a flavor symmetry

of the Intriligator-Seiberg-Shih (ISS) model [6]. The SUSY breaking vacuum of the IYIT

model is absolutely stable. Although the vacuum of the ISS model is only perturbatively

stable, the lifetime of the vacuum is independent of the gravitino mass. Therefore, these

models can have both the light gravitino and the sufficiently stable vacuum at the same

time.

However, in these two models, it was observed that the Minimal Supersymmetric

Standard Model (MSSM) gaugino masses are suppressed. Therefore, these models are

severely constrained by the Tevatron bound [7, 8]. Recently, Yonekura and one of the

present authors RS have studied the parameter space of the low scale gauge mediation

model which has a stable SUSY breaking vacuum [9]. As the result, they have found

almost all the parameter space is excluded by the Tevatron bound when the gravitino

mass is less than 16 eV. However, these models have not been completely excluded. To

exclude them completely, we discuss the discovery region at early stage of the LHC run.

As the result, we show that such a model can be completely excluded/discovered at very

early stage of the LHC run even if we relax the upper bound of the gravitino mass to

32 eV.

This Letter is organized as follows. In section 2, we review the model discussed in

Ref. [9]. In section 3, we estimate the discovery region of the low scale gauge mediation

at the LHC.

2 Model

In this section, we review two kinds of the low scale gauge mediation model.

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Model A (based on the IYIT model)

First, we review the model [3] based on the IYIT model [4] as a SUSY breaking sector.

At low energies, the effective superpotential of the SUSY breaking sector1is given by

W ≃ fZ. (1)

Here, Z is a singlet chiral superfield. The SUSY breaking vacuum of the IYIT model

is stable. We introduce NF flavors of messenger multiplets which transform as 5 and¯5

under the Grand Unified Theory (GUT) gauge group SU(5)GUT. Large NFis desirable to

increase the MSSM gaugino masses. However, the perturbative gauge coupling unification

is lost when NF≥ 5 [10]. Therefore, we choose NF= 4. We will write the messenger quark

multiplets as Ψd,i,˜Ψd,i(i = 1,···,4) and the messenger lepton multiplets as Ψl,i,˜Ψl,i(i =

1,···,4). We assume that the superpotential of the messenger sector and the SUSY

breaking sector is given as follows :

W= fZ +

?

χ=d,l

?

i,j

Mχ,ij(Z)˜Ψχ,iΨχ,j, (2)

(Mχ,ij(Z) = mχ,ij+ kχ,ijZ). (3)

The stability of the SUSY breaking vacuum requires det(m + kZ) = detm [11] and

km−1k = 0 [9]. According to Ref. [9], the gaugino masses are maximized when Mχ(Z) is

given by

Mχ(Z) =

kχZ

mχ

mχ

kχZ mχ

mχ

.(4)

This model has an R-symmetry. Then, we assume the R-symmetry is spontaneously

broken to gain the gaugino masses. We do not specify the mechanism generating the

R-symmetry breaking VEV ?Z?, and treat ?Z? as a free parameter. The parameter f is

determined by f =

?√3m3/2MPl, where MPl≃ 2.4 × 1018GeV is the reduced Planck

mass. After all, we have six parameters, kd, kl, md, ml, ?Z? and m3/2in the model.

1For concreteness, we take the IYIT model as the SUSY breaking sector, but one can take other

SUSY breaking models of which the effective superpotential is given by Eq. (1).

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We have some comments on the possible region of these parameters. The Yukawa

interaction is not asymptotic free. Then, if we require the Yukawa interaction of the

messenger sector is perturbative up to the GUT scale 2 × 1016GeV, there are upper

bounds of the Yukawa coupling constants kdand kl. See Fig. 2 in Ref. [9]. The condition

that the Standard Model gauge symmetry is not broken, i.e., the messenger scalar VEV

?˜Ψχ

?Ψχ? =

?

= 0 requires that mχ≥

?

kχf.

Model B (based on the ISS model)

Next, we review the model using the ISS model [6]. The SUSY breaking vacuum of the

ISS model is meta-stable. The vacuum can be sufficiently stable if the cutoff scale Λcut

is much larger than the messenger mass scale Mmes. However, to gain the large gaugino

masses comparable to ones of the model A, this model requires very low cutoff scale

Λcut/Mmes<

∼O(10) [9]. This means large vacuum tunneling rate. Therefore, it is doubtful

whether we can get the large gaugino masses when we require the stability of the SUSY

breaking vacuum. See Ref. [9] for details.

In both of the models, The sfermions are much heavier than the gauginos. Then, the

role of the gaugino masses are important when we discuss the discovery region. Because

the gaugino masses in the model B are smaller than the model A, the model B are

excluded/discovered if the model A are excluded/discovered.In the following of the

paper, we discuss the discovery region of the model A.

3 LHC signature

In this section, we estimate the discovery region at√s = 7 TeV and integrated luminosity

L = O(1) fb−1. We have used the programs Pythia 6.4.19 [12] and fast detector simulation

AcerDET-1.0 [13]. In the fast simulation, the detection efficiency of a photon which passes

a certain isolation criteria is 100 %. However as discussed in Ref. [14], full simulation result

indicates lower efficiency. Hereafter we assume selection efficiency of the isolated photon

with pT> 20 GeV is 65 %.

In the light gravitino scenario discussed in the previous section, one of important

features of LHC signature is prompt decay of the next to lightest supersymmetric particle

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(NLSP) into the gravitino. The decay length of the NLSP is written as

cτNLSP≃ 18 µm

?m3/2

1 eV

?2?mNLSP

100 GeV

?−5

, (5)

which is much smaller than the detector size.Therefore all MSSM particles decay

promptly.

Neutralino NLSP

In almost all the parameter region of the present model, the NLSP is a bino-like neutralino.

Let us comment on the other possibilities for the NLSP. In some parameter region, the

NLSP is a higgsino-like or wino-like neutralino, but the mass of the NLSP is small,

m˜ χ0

1<

∼90 GeV. This region is excluded by the CDF bound [8]. Also, there is a region

where the lightest chargino is the NLSP, but the mass is small, m˜ χ±

region is excluded by the LEP bound [15]. Finally, it is possible to realize the gluino

1

<

∼90 GeV. This

NLSP. In this case, the expected collider signature is di-jet and missing energy. However,

the upper bound on the gluino NLSP is about 200 GeV and it is excluded by the Tevatron

di-jet search [16]. Hereafter, we assume that the NLSP is a bino-like neutralino.

Event selection

The prompt decay of the lightest neutralino ˜ χ0

1→ γ˜G3/2gives very strong clue for the

SUSY discovery, i.e., high pTphotons and missing energy. The gluino pair production

pp → ˜ g˜ g and wino-like neutralino and chargino production pp → ˜ χ˜ χ are dominant SUSY

production. The produced gluino decays into the lighter SUSY particle with high energy

jets. For this mode, multi-jets and large missing energy are expected in addition to the

photon signal. Following Ref. [14], we impose the following cuts

• At least two isolated photons with pT> 20 GeV.

• At least four jets with pT> 50 GeV.

• The leading jet with pT> 100 GeV.

• ET,miss> max(100 GeV,0.2Meff), where

Meff≡

?

4 leading jets

pT,j+ ET,miss+

?

leptons

pT,ℓ. (6)

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