LHC Reach of Low Scale Gauge Mediation with Perturbatively Stable Vacuum

Abstract

Very light gravitino scenario m_{3/2} < 16 eV is very interesting, since there is no 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 bound on the gaugino masses. In this paper, we show that such a model can be completely excluded/discovered at very early stage of the LHC run. Comment: 10 pages, 1 figure; v2: minor collections

Full text

Page 1

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

Page 2

1Introduction
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.
2Model
In this section, we review two kinds of the low scale gauge mediation model.
2

Page 3

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).
3

Page 4

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.
3LHC 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
4

Page 5

(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)
5