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ICRR-report-605-2011-22

IPMU11-0016

Pure Gravity Mediation with m3/2= 10–100TeV

Masahiro Ibe(a,b), Shigeki Matsumoto(b), and Tsutomu T. Yanagida(b)

(a)ICRR, University of Tokyo, Kashiwa, 277-8582, Japan

(b)IPMU, TODIAS, University of Tokyo, Kashiwa, 277-8583, Japan

Abstract

Recently, the ATLAS and CMS collaborations reported exciting hints of a

Standard Model-like Higgs boson with a mass around 125GeV. Such a Higgs

boson mass can be easily obtained in the minimal supersymmetric Standard

Model based on the “pure gravity mediation model” where the sfermion masses

and the Higgs mass parameters are in tens to hundreds TeV range while the

gauginos are in the hundreds GeV to TeV range. In this paper, we discuss

detalis of the gaugino mass spectrum in the pure gravity mediation model. We

also discuss the signals of the model at the current and future experiments such

as cosmic ray observations and the LHC experiments. In particular, we show

that the parameter space which is consistent with the thermal leptogenesis

can be fully surveyed experimentally in the foreseeable future.

arXiv:1202.2253v1 [hep-ph] 10 Feb 2012

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1 Introduction

The pure gravity mediation model investigated in Ref.[1] is a surprisingly simple

model of the supersymmetric Standard Model (SSM). There, the scalar bosons obtain

supersymmetry (SUSY) breaking masses from a SUSY breaking sector via tree-level

interactions in supergravity[2]. The Higgs mixing mass parameters, µ-term and B-

term, are also generated via tree-level interactions of supergravity[3]. Due to the

tree-level mediation, the scalar boson masses and the Higgs mixing mass parameters

are expected to be of the order of the gravitino mass, m3/2. The gaugino masses are,

on the other hand, generated at the one-loop level[4, 5, 6]. Thus, the pure gravity

mediation model predicts a hierarchical spectrum. The greatest benefit of the pure

gravity mediation is that the model requires no additional fields to realize the above

spectrum. Therefore, the pure gravity mediation model is the bare-bones model of

the supersymmetric Standard Model.

The pure gravity mediation model is particularly successful when the gravitino

mass is in the range of m3/2= 10–100TeV. The first advantage is the alleviation

of the cosmological gravitino problem[7, 8]. Especially, the model does not suffer

from the gravitino problem even for a very high reheating temperature after inflation,

TR?√3×109GeV, which is essential for the successful thermal leptogenesis[9]. The

second advantage is that the model has a good candidate for dark matter. For the

above gravitino mass range, the lightest superparticle (LSP) which is neutral wino

in the pure gravity mediation obtains a mass in hundreds GeV to TeV range. The

neutral wino in this mass range is a good candidate of weakly interacting particle

dark matter[10, 11]. Moreover, as emphasized in Ref.[12, 1], the relic density of the

neutral wino can be consistent with the observed value when we assume the thermal

leptogenesis. Therefore, the pure gravity mediation model goes quite well with the

thermal leptogenesis. Another but an important advantage in cosmology is that the

model does not suffer from the cosmological Polonyi problem[13] since no singlet

SUSY breaking fields are required in the model.1In addition to those advantages

in cosmology, the problems of flavor-changing neutral currents and CP violation in

the SSM are highly ameliorated thanks to the large masses for squarks and sleptons.

The unification of the gauge coupling constants at the very high energy scale also

provides a strong motivation to the model.2

1See also Ref.[14] for the Polonyi problem in dynamical supersymmetry breaking models.

2In fact, the gauge coupling constants unify at around 1016GeV at a few percent level even for

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In Ref.[1], two of the authors (M.I. and T.T.Y) discussed the lightest Higgs boson

mass of the minimal SSM (MSSM) based on the pure gravity mediation model.

There, we showed that the lightest Higgs boson mass is required to be below about

128GeV if we assume the thermal leptogenesis. This requirement has been shown to

be consistent with the most recent experimental constraints on the Higgs boson mass,

mh> 115.5GeV and mh< 127GeV at 95%C.L. reported by ATLAS[16] and CMS

collaborations[17]. Furthermore, as shown in Ref.[1], the pure gravity mediation

model can easily explain the rather heavy Higgs boson mass around 125GeV which

is tantalizingly hinted by ATLAS and CMS collaborations.

In this letter, we discuss phenomenological, cosmological and astrophysical as-

pects of the pure gravity mediation model. In particular, in this paper, we concen-

trate ourselves on the the parameter space of the model which is consistent with the

thermal leptogenesis. As we will show, such a parameter space can be fully tested by

the observation of the cosmic rays, especially by the observation of the anti-proton

flux in the foreseeable future. We also discuss the strategies of the discoveries and

the measurements of the gauginos at the Large Hadron Collider (LHC) experiments.

There, the distinctive gaugino mass spectrum in the pure gravity mediation model

plays important roles.

The organization of the paper is as follows. In section2, we review the model with

pure gravity mediation. There, we discuss the details of the gaugino spectrum. In

section3, we discuss the phenomenological, cosmological and astrophysical aspects

on the model. The final section is devoted to our conclusions.

2 Pure gravity mediation model

2.1Mass spectrum

In the pure gravity mediation model, the only new ingredient other than the MSSM

fields is a (dynamical) SUSY breaking sector. There, the scalar bosons obtain the soft

SUSY breaking squared masses mediated by tree-level interactions in supergravity.

With a generic K¨ ahler potential, all the soft squared masses of the scalar bosons are

a rather large µ-term of 10–100TeV. It should be noted that the scale of the coupling unification

is slightly lower than the conventional SSM for m3/2= 10–100TeV about a factor of two or so.

Thus, the model predicts a slightly shorter proton lifetime via the so-called dimension six operators,

τp? 1035yrs, which is within the reach of the Hyper-Kamiokande Experiment[15].

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expected to be of the order of the gravitino mass[2]. The soft SUSY breaking scalar

trilinear coupling, the A-terms, are, on the other hand, expected to be suppressed

in supergravity at the tree-level.

In the pure gravity mediation model, the Higgs mixing µ and B parameters can

be also generated via tree-level interactions in supergravity. In fact, if the Higgs

doublets are not charged under any special symmetries, we expect the following

K¨ ahler potential,

K ? cHuHd+

c?

M2

PL

X†XHuHd+ h.c.. (1)

Here, X denotes a chiral SUSY breaking field in a (dynamical) SUSY breaking sector,

MPLis the reduced Planck scale, and c and c?are coefficients of O(1). Through the

above K¨ ahler potential, the µ- and the B-parameters[3, 18]

µH

= cm3/2, (2)

BµH

= cm2

3/2+ c?|FX|2

M2

PL

, (3)

where FXis the vacuum expectation value of the F-component of X. Therefore, the

µ- and B Higgs mixing parameters are also expected to be of O(m3/2).3

For the gaugino masses, on the other hand, tree-level contributions in the super-

gravity are extremely suppressed since we have no SUSY breaking fields which are

singlet under any symmetries. At the one-loop level, however, the gaugino masses are

generated without having singlet SUSY breaking fields, which is called the anomaly

mediated contributions[4, 5]. Besides, the gauginos also obtain contributions from

the heavy Higgsino threshold effects at the one-loop level. Putting these one-loop

contributions together, the gaugino masses at the energy scale of the scalar boson

masses, MSUSY= O(m3/2), are given by[4, 10]

M1 =

33

5

g2

1

16π2

g2

2

16π2

?

m3/2+1

11L

?

,(4)

M2 =

?m3/2+ L?

g2

3

16π2m3/2.

,(5)

M3 = −3(6)

Here, the subscripts Ma, (a = 1,2,3) correspond to the gauge groups of the Standard

Model U(1)Y, SU(2)Land SU(3), respectively. In the above expressions, the terms

3If the SUSY breaking sector has a singlet Polonyi field, the so-called Giudice-Masiero mecha-

nism[19] can also generate the µ and B Higgs mixing parameters of O(m3/2). In that case, however,

the model suffers from the Polonyi problem[13].

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proportional to m3/2denote the anomaly mediated contributions and the terms pro-

portional to L denote the Higgsino threshold contributions. The parameter L is

given by

L ≡ µHsin2β

m2

A

|µH|2− m2

A

ln|µH|2

m2

A

, (7)

where mAdenotes the mass of the heavy Higgs bosons, and tanβ is the ratio of the

vacuum expectation values of the up-type Higgs boson Huand the down-type Higgs

boson Hd. As we will see in the next subsection, the size of L is expected to be of

the order of the gravitino mass in the pure gravity mediation model[1]. Therefore,

the wino mass obtains comparable contributions from the anomaly mediated effects

and the Higgsino threshold effects. This facts have a great impacts on the testability

of the pure gravity mediation model at the LHC experiments.

Before closing this section, we should emphasize the difference of the pure gravity

mediation model from the the Split Supersymmetry[20, 21, 22]. In the first place, the

Split Supersymmetry mainly considers a scalar mass scales much higher than that

in the pure gravity mediation model, i.e. MSUSY? 104−6GeV. Thus, the anomaly-

mediated gaugino masses should be suppressed in the Split Supersymmetry, while

we rely on the anomaly-mediated gaugino masses in the pure gravity mediation

model.4

Thus, the pure gravity mediation model is more close to the PeV-scale

Supersymmetry[24] and the Spread Supersymmetry[25]. Another important and

more practical difference is the size of µ-term. In the Split Supersymmetry, it is

assumed that the higgsinos are also in the TeV range. Thus, the absence of the

Higgsino in the TeV range will be a crucial observation to distinguish the pure

gravity mediation model from the Split Supersymmetry. Furthermore, as we will see

below, such a large µ-term leads to a peculiar gaugino spectrum in the pure gravity

mediation model. Thus, we can also distinguish these models by carefully examining

the gaugino mass spectrum.

2.2 Details on gaugino masses

As discussed above, the pure gravity mediation model predicts that the sfermions,

Higgsinos and the heavier Higgs bosons in the MSSM have masses of the order of the

gravitino mass, m3/2= 10–100TeV. Therefore, the only accessible particles at the

collider experiments in the foreseeable future are the gauginos. In this subsection, we

4See discussions on the possible cancellation of the anomaly-mediated gaugino masses[22, 23].

4