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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].

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MSUSY? 1000TeV

MSUSY? 100TeV

MSUSY? 10TeV

ΜH? O?m3?2?

tanΒ ? O?1?

0 50 100150200250 300

0

500

1000

1500

2000

2500

3000

m3?2?TeV

mBino

AMSB?GeV

MSUSY? 1000TeV

MSUSY? 100TeV

MSUSY? 10TeV

ΜH? O?m3?2?

tanΒ ? O?1?

0 50100 150200250 300

0

200

400

600

800

1000

m3?2?TeV

mWino

AMSB?GeV

MSUSY? 1000TeV

MSUSY? 100TeV

MSUSY? 10TeV

ΜH? O?m3?2?

tanΒ ? O?1?

050100150200250300

0

1

2

3

4

5

6

7

m3?2?TeV

mgluino?TeV

Figure 1: The anomaly mediated contributions to the gaugino masses (denoted by AMSB).

The each line corresponds to the heavy scalar threshold scale MSUSY = 10,100 and

1000TeV from bottom to up. In the figure, we have taken µH= O(m3/2) and tanβ = O(1),

although they are not sensitive to those parameters.

give detailed analysis on the gaugino mass spectrum in the pure gravity mediation

model.

First, let us consider the anomaly mediated contributions to the gaugino masses.

As we see from Eqs.(4)-(6), the wino is the lightest gauginos for L = 0.This

feature is related to the fact that the SU(2)Lgauge coupling constant is the least

scale dependent out of the three gauge coupling constants. In Fig.1, we show the

anomaly mediated gaugino masses as a function of the gravitino mass. The figure

shows that the gaugino masses are roughly given by,

mbino ? 10−2m3/2,

mwino ? 3 × 10−3m3/2,

mgluino ? (2 − 3) × 10−2m3/2.

(8)

(9)

(10)

with small dependences on the heavy scalar threshold scale, MSUSY. Thus, for the

wino mass mwino= 300GeV, for example, the gluino mass is heavier than 2TeV if

the anomaly mediated contributions dominate the gaugino masses.

Now, let us estimate the typical size of L in the pure gravity mediation model

which parametrize the Higgsino threshold contributions to the gaugino masses. Let

us remember that we require one of the linear combinations of the two Higgs bosons,

h = sinβHu−cosβH∗

ing. In terms of the Higgs mass parameters, the above fine-tuning condition requires,

dremains very light for successful electroweak symmetry break-

(|µH|2+ m2

Hu)(|µH|2+ m2

Hd) − (BµH)2? 0 ,(11)

while the Higgs mixing angle is related to the Higgs mass parameters by,

sin2β =2BµH

m2

A

,(m2

A= m2

Hu+ m2

Hd+ 2|µH|2) .(12)

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tanΒ?1

tanΒ?3

tanΒ?10

tanΒ?30

0.0 0.51.0 1.52.0 2.53.0

?L?m3?2?

Figure 2: The typical values of |L/m3/2| for tanβ = 1,3,10 and 30. The unit of the

vertical axis is arbitrary. We have distributed µHand B from m3/2/3 to 3m3/2and required

|m2

in Eqs.(11) and (12). The ratios of the areas of each histogram roughly represent the

Hu,d/m2

3/2| < 5 which are determined by the electroweak symmetry breaking conditions

relative consistency of the value of tanβ in the pure gravity mediation.

Here, m2

Hu,ddenote the soft SUSY breaking squared masses of the two Higgs doublets,

Huand Hd. These conditions show that the mixing angle β is expected to be of O(1),

since all the mass parameters of the Higgs sector (except for a fine-tuning condition)

are of the order of the gravitino mass in the pure gravity mediation model.5

By putting the typical values of tanβ = O(1) and the Higgs mass parameters of

the gravitino mass scale together into the definition of L in Eq.(7), we find that the

typical value of L is also of the gravitino mass scale. To see this clearly, we show

the typical size of L for tanβ = 1,3,10 and 30 (Fig.2). Here, we have assumed

that µH and B range from m3/2/3 to 3m3/2, respectively.6The figure also shows

that |L/m3/2| ? 0.5 − 2 for tanβ = O(1). Therefore, in the pure gravity mediation

model, we expect L/m3/2= O(1), which leads to comparable contribution to the

wino mass from the Higgsino threshold effects (see Eq.(5)).

In Fig.3, we show the ratio of the wino and bino masses with and without the

5Hereafter, we use a phase convention where BµHis real and positive.

6More precisely, we assumed that log10µH/m3/2and log10B/m3/2obey the normal distribution

with the mean value 0 and the standard deviation 0.5×log103. For a given tanβ, the Higgs squared

masses are determined by m2

number of random numbers for each tanβ. Afterward, we required |m2

are of the order of the gravitino mass. Thus, the ratios of the areas of each histogram roughly

Hu,(d)= −|µ2

H| + BµHcotβ(−1). In the figure, we generated the fixed

Hu,d/m2

3/2| < 5 so that they

represent the relative consistency of the value of tanβ in the pure gravity mediation. The figure

shows that the model with tanβ = O(10) is less consistent as expected.

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?L?m3?2??1

?L?m3?2??2

arg?L??Π

mwino?mwino

?L?m3?2??3

?L?m3?2??4

?L?m3?2??0

arg?L??0

Π?2

arg?L??Π

5Π?6

2Π?3

Π?3

Π?6

Bino LSP

01234

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

AMSB

mbino?mbino

AMSB

m3?2?MS?50TeV

?4

?2024

10

20

50

100

200

500

1000

2000

L?m3?2

mgaugino?GeV

Figure 3: (Left) The ratios of the wino and bino masses with and without the Higgsino

contributions for given values of L. We have used a phase convention that m3/2is real

and positive. The red lines show the |L| dependences for given phases of L, while the blue

lines show the arg[L] dependences for given values of |L|. (The dashed blue lines show the

values of |L| in between the ones for the two solid lines.). In the gray shaded region for

|L/m3/2| ? 3, the wino is no more the LSP. (Right) The L dependences of the gaugino

masses for m3/2= MSUSY= 50TeV for L > 0(arg[L] = 0) and L < 0(arg[L] = π).

Higgsino contributions for given values of L (left panel). The figure shows that the

wino mass can be about twice as heavy as the anomaly mediated contribution for

|L/m3/2| ? 1 which is expected in the pure gravity mediation model. It should be

noted that the wino becomes no more the LSP where the Higgsino threshold contri-

bution dominates. In such cases, the relic density of dark matter easily exceed the

observed one due to the highly suppressed annihilation cross section of the bino for

O(100)GeV. Fortunately, however, the figure shows that the bino becomes LSP only

for |L/m3/2| > 3 which is less likely in the pure gravity mediation model. Therefore,

in the pure gravity mediation model, the LSP is mostly wino-like, although the wino

mass obtains a comparable contribution from the Higgsino threshold effects.7

In Fig.4, we show the contour plot of the wino mass. In the figure, the blue shaded

region shows the current experimental constraints on the wino mass mwino≥ 88GeV

7In general, a relative phase between L and m3/2is a free parameter, and hence, the three

gauginos have different phases. Such gaugino phases, however, do not cause serious CP-problems,

since the Higgsinos as well as the sfermions are expected to be very heavy in the pure gravity

mediation model. Interestingly, the relative phase of O(1) may lead to the visible electron electric

dipole moment of de/e ∼ 10−30cm[22] for the µ-term in the tens to hundreds TeV range, which

can be reached in future experiments[26].

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mwino?100GeV

300GeV

700GeV

900GeV

500GeV

LEP2 Wino constraint

ATLAS Gluino constraint

20406080 100

?3

?2

?1

0

1

2

3

m3?2?TeV

L?m3?2

Figure 4:

The contour plot of the wino mass for L > 0 and L < 0.Here, we

have taken MSUSY = m3/2(blue lines).

150GeV,250GeV,···.)

mwino ≥ 88GeV for the degenerated neutralino-chargino obtained by LEPII experi-

ment[27]. The orange shaded region denotes the experimental constrain on the gauginos,

mgluino? 750GeV for mLSP< 200GeV reported by the ATLAS collaboration[28].

(The dashed lines corresponds to mwino =

The blue shaded region denotes the experimental constraint,

for the degenerated neutralino-chargino obtained gz by LEPII experiment[27]. The

orange shaded region shows the experimental constrain on the gauginos, mgluino?

750GeV for mLSP? 200GeV reported by the ATLAS collaboration[28]. By remem-

bering that L/m3/2? 2.5 is less likely in the pure gravity mediation, the figure shows

that the gluino mass bound requires m3/2? 30TeV.8

Finally, we discuss the lightest Higgs boson mass in the pure gravity mediation

model. In the pure gravity mediation model, the lightest Higgs boson mass is ex-

pected to be heavier than the conventional MSSM models due to the heavy scalar

bosons[29]. In Fig.5, we show the Higgs boson mass obtained by solving the full

one-loop renormalization-group equations of the Higgs quartic coupling and other

coupling constants given in Ref.[21] with the boundary condition,

?3

at the heavy scalar scale. The threshold corrections at the heavy scalar scale are also

λ =1

45g2

1+ g2

2

?

cos22β ,(13)

taken into account. We also take into account the weak scale threshold corrections

8Fig.2 shows that L/m3/2? 2.5 is possible for tanβ ? 1. As we will see from Fig.5, however, the

lightest Higgs boson mass of our main concern (124GeV< mh< 126GeV) requires m3/2? 100TeV

for tanβ ? 1. Thus, the conclusion m3/2? 30GeV is not changed.

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mh?115.5GeV

mh?127GeV

120GeV

125GeV

130GeV

135GeV

10

102

103

104

1

10

MSUSY?TeV

tanΒ

Figure 5: The contour plot of the lightest Higgs boson mass. (The dashed contours are for

the intermediate values between the two solid contours.) Here, we have fixed m3/2= 50TeV

and taken µH = MSUSY. The gray shaded regions correspond to mh< 115.5GeV and

mh> 127GeV which are excluded by the ATLAS and CMS collaborations at 95%C.L.

for the central value of the top quark mass, mtop= 173.2±0.9GeV. The light gray shaded

region denotes the Higgs mass constraints including the 1σ error of the top quark mass.

The orange band shows the Higgs boson mass 124GeV < mh< 126GeV hinted by the

ATLAS and CMS collaborations for the central value of the top quark mass. The light

orange band is the one including the 1σ error of the top quark mass.

to those parameters in accordance with Ref.[30, 31]. It should be noted that the

predicted Higgs boson mass is slightly lighter than the one in Ref.[31] for a given

(MSUSY,tanβ), since the Higgsino contributions decouple at the very high scale in

the pure gravitino mediation model (see Ref.[1]).

In the figure, the gray shaded regions correspond to mh< 115.5GeV and mh>

127GeV which are excluded by the ATLAS and CMS collaborations[16, 17] at

95%C.L. for the central value of the top quark mass, mtop= 173.2 ± 0.9GeV[32].

The light gray shaded region denotes the Higgs mass constraints including the

1σ error of the top quark mass. The orange band shows the Higgs boson mass

124GeV < mh< 126GeV hinted by the ATLAS and CMS collaborations[16, 17] for

the central value of the top quark mass. The light orange band is the one including

the 1σ error of the top quark mass.

By combined with m3/2? 30TeV which is required from the experimental gluino

mass bound, the hinted Higgs boson in the Fig.5 (124GeV < mh < 126GeV)

constrains the value of tanβ to tanβ ? 7. This shows that the pure gravity mediation

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works quite consistently since tanβ = O(1) is expected in the pure gravity mediation

model.

3Signals of the pure gravity mediation model

In this section, we consider several signals predicted in the pure gravity mediation

model. Before going to discuss those, we summarize current cosmological constraints

on the model. After that, we consider signals related to dark matter detections, where

current astrophysical constraints on the dark matter mass and near-future prospects

to detect the dark matter are discussed. We finally consider collider signals with

particularly focusing on the pair production of the gluino at the LHC experiments

with the center of mass energy of 14TeV.

3.1Cosmological constraints

We first consider the thermal history of the dark matter which is the neutral wino in

the pure gravity mediation model. Its SU(2)Lpartner, the charged wino, is slightly

heavier than the neutral one by 155–170MeV because of contributions from one-

loop gauge boson diagrams[33]. The charged wino decays into a neutral wino and

a pion with the lifetime of O(10−10)sec. It is known that the thermal relic density

of the wino, which is obtained by considering not only self-annihilation processes of

the neutral wino but also co-annihilation processes between the neutral and/or the

charged winos, can be consistent with the observed dark matter density when its

mass is mwino? 2.7TeV. This is because the annihilation cross section of the wino is

highly boosted by the non-perturbative effect called Sommerfeld-enhancement[34].

On the other hand, the wino dark matter is also produced non-thermally through

the late time decay of the gravitino, which also contributes to the relic abundance

of the dark matter. If the contribution is significant, the neutral wino consistent

with the observed dark matter density is much lighter than 2.7TeV[10, 11]. In

particular, in order to have an appropriate reheating temperature for the successful

thermal leptogenesis, there is an upper bound on the wino mass; mwino? 1TeV[1].

This fact means that the most of the dark matter observed today is not from thermal

relics but produced non-thermally by the late time decay of the gravitino.

Since the neutral wino has a large annihilation cross section into a W-boson pair,

which is of the order of 10−24–10−25cm3/s when mwino? 1TeV, it may affect several

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phenomena in the early universe [35]. For instance, the annihilation may affect

abundances of light elements, and, in fact, observations of the elements put a bound

on the mass of the neutral wino as mwino ? 200GeV in order not to destroy the

elements during Big-Bang Nucleosynthesis (BBN)[36]. The annihilation also affects

the recombination history of the universe. If the annihilation is significantly large, it

modifies the spectrum of cosmic microwave background[37]. This fact leads to the

constraint as mwino? 200GeV, which is comparable to that from BBN.

3.2Dark matter detections

Since the µ-parameter is of the order of 10–100TeV in the pure gravity mediation

model, the effect of the mixing between wino and higgsino components on the light-

est supersymmetric particle (dark matter) is negligibly small. The scattering cross

section between the dark matter and a nucleon is then estimated to be 10−47cm2[38],

which seems to be very challenging to discover the dark matter in on-going direct

detection experiments. This is a sharp contrast to the cases of Split Supersymme-

try model and conventional anomaly mediation models. Since the µ-parameter does

not have to be huge in these models, the tree-level diagram that the higgs boson is

exchanged in the t-channel contributes to the scattering cross section significantly,

which enables us to detect the dark matter in near future[35]. Direct detection ex-

periments of dark matter can be therefore used as a test of the pure gravity mediation

model.

On the contrary to the direct detection of dark matter, we can expect rich signals

at indirect detection experiments, because the dark matter is almost purely wino in

the pure gravity mediation model and its annihilation cross section is boosted by

the Sommerfeld effect[39]. Among several on-going experiments, the most stringent

constraint on the dark matter is obtained by the Fermi-LAT experiment observing

gamma-rays from milky way satellites[40]. This constraint is depicted in Fig.6 as a

solid (green) line. No astrophysical boost factor is assumed here. Theoretical predic-

tion of the neutral wino is also shown in the figure, which is obtained by calculating

its annihilation cross section involving the Sommerfeld effect at one-loop level[41].

Notice, however, that there may be some uncertainties on the constraint, since the

constraint is based on several assumptions such as the use of fixed dark matter profile.

According to Ref.[42] in which those uncertainties (involving dark matter profiles)

on the gamma-ray experiment are discussed, we also show the region (green-shaded

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10

−27

10

10

10

10

−26

−25

−24

−23

100

3

200

Dark Matter Mass (GeV)

300

400

500

Annihilation Cross Section (cm /s)

AMS−02 (Anti−p)

PAMELA (Anti−p)

Fermi−LAT

Wino Dark Matter

Figure 6: Constraints and future prospects of indirect detection experiments of dark

matter. Theoretical prediction of the neutral wino dark matter is also shown.

one) above the constraint in order to take the uncertainties into account. It can be

seen that the neutral wino should be, at least, heavier than 300GeV.

Another interesting indirect detection is the PAMELA experiment observing the

cosmic-ray ¯ p (anti-proton) flux[43]. Current constraint on the dark matter from the

experiment is also shown in Fig.6 as a blue-shaded region. Since the ¯ p flux depends

on how ¯ p propagates under the complicated magnetic field of our galaxy and which

dark matter profiles we adopt[44], the constraint has large uncertainties as can be

seen in the figure. The mass of the dark matter is, however, constrained to be

mwino? 230GeV in spite of the uncertainties. On the other hand, the observation

of the cosmic-ray ¯ p flux in near future is very hopeful. This is because the AMS-

02 experiment, which has already been started[45], has better sensitivity than the

PAMELA experiment and it is also expected that astrophysical uncertainties related

to the ¯ p propagation are reduced. The future sensitivity to detect the dark matter in

this experiment is also depicted in the figure as a red-shaded region with assuming

an appropriate propagation model[44]. It can be seen that the sensitivity is much

below the prediction of the dark matter. It is also worth noting that the whole mass

range of the dark matter consistent with the thermal leptogenesis will be fully tested

by the future observation of the cosmic-ray ¯ p flux, because the annihilation cross

section of the dark matter is not suppressed because of the Sommerfeld effect. It

may be even possible to determine mwinoby observing the ¯ p spectrum.

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2

3

?1

0.8

10

10

10

1

10

~~

PP gg + X

Gluino mass (TeV)

Cross section (fb)

s = 14 TeV

1/2

1.0

1.21.4

1.6

1.8

2.0

1

3

2.5

1.5

0.5

200

400

600

800

1000

Gluino mass (TeV)

Wino mass (GeV)

2

L/m = 0 (AMSB)

3/2

3/2

L/m = 1

3/2

L/m = 2

Wino mass > Gluino mass

L/m > 2

3/2

Wino mass < 300 GeV

Current LHC bound

Figure 7: (Left panel) Cross section of the gluino pair production at the LHC experiment

with the center of mass energy of 14TeV. (Right panel) Gluino and wino masses within

the parameter region of mgluino? 3TeV. Shaded regions are not favored because of the

gluino LSP (mgluino> mwino), too large L (L/m3/2> 2), and dark matter constraints

(mwino< 300GeV). Current bound of the LHC experiment (7TeV) is also shown.

Finally, we comment on other indirect detections of dark matter. It is well known

that there is an anomaly at the cosmic-ray e+flux[46]. Since it is difficult to account

for the anomaly by the neutral wino dark matter with the mass of 300–1000 GeV [47],

it should be explained by some astrophysical activities. The observation of the e+

flux is therefore not better than that of the ¯ p flux to test the pure gravity mediation

model. The observation of the ν flux from the galactic center may give an good

opportunities to test the neutral wino dark matter[35], though the signal strength

depends on the dark matter profile at the center. On the other hand, the observation

of the ν flux from the sun seems to be challenging, because the flux is proportional

to the spin-dependent scattering cross section of the dark matter and it is estimated

to be as small as 10−48cm2in the pure gravity mediation model[38].

3.3 Collider signals

In the pure gravity mediation model, the ratio between gluino and wino masses can

be smaller than that of the conventional anomaly mediation model. The gluino may

therefore be produced at the LHC experiment even if the wino mass is constrained

to be mwino? 300GeV. On the other hand, all the sfermions as well as the higgsinos

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are of the order of 10–100TeV in the model and they are never produced at the

LHC. As a result, the dominant collider signal of the model is the pair production of

the gluinos, whose production cross section is shown in Fig.7 (left panel). Once the

gluino is produced, it eventually decays into a neutral wino by emitting Standard

Model particles. It is known that, when the sfermions are much heavier than the

gluino, the radiative decay of the gluino into a gluon and a neutralino (˜ g → g˜ χ0) can

have a sizable branching fraction[48]. In the pure gravity mediation model, however,

the µ-parameter is also as large as the sfermion masses and the branching fraction

is much suppressed. The non-observation of the radiative decay therefore enables us

to distinguish the pure gravity mediation model from other models predicting heavy

sfermions without the large µ-parameter.

Gluinos in the pure gravity mediation model therefore decay into two quarks

with a neutralino/chargino (˜ g → q¯ q?+ ˜ χ0/˜ χ±

but the charged wino, decays into a neutral wino (dark matter) by emitting a soft

i). The chargino, which is nothing

pion. On the other hand, when the neutralino is the bino, it decays through several

modes; a charged wino + a W-boson (˜B →˜ W±W∓), a neutral wino + a higgs boson

(˜B →˜ W0h), or a charged/neutral wino + two leptons (˜B →˜ Wl¯l?), whose branching

fractions depend highly on model parameters. In Fig.7 (right panel), we show the

range of gluino and wino masses within the parameter region of our interest for the

LHC experiment. It is also worth noting that, as shown in the previous section, the

bino mass is roughly given by mbino? mgluino/3 in the most parameter region. Thus,

the mass degeneracy between gluino and neutralino/chargino is not severe, which is

very attractive from the viewpoint of discovering the signal.

The most efficient mode to discover the signal of the pure gravity mediation

model is the pair production of the gluinos followed by the decay ˜ g → q¯ q?˜ χ with

q(q?) being a quark except the top quark and ˜ χ being a neutralino/chargino, so that

the signal event is composed of four jets + missing energy. The branching fraction

of the decay is about 73.4% when all squark masses are degenerated. In Fig.7

(right panel), the current bound on the (mgluino,mwino)-plane, which is obtained by

the LHC experiment with the center of mass energy of 7TeV and 1.04fb−1data,

is depicted with assuming that mwino∼ mbinoand 100% branching fraction of the

decay ˜ g → q¯ q?˜ χ[49]. It can be seen that the region constrained by the current LHC

data has already been excluded by dark matter experiments. It has been also shown

that the gluino mass up to 1.2TeV can be discovered at the LHC experiment with

the center of mass energy of 14TeV when 10fb−1data is accumulated[50].

14

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Once the signal of the pure gravity mediation model is discovered, the next

important task will be the mass determinations of gauginos. When the gluino is

about 1TeV and 100fb−1data is accumulated at the LHC experiment with the

center of mass energy of 14TeV, the mass difference between gluino and wino can be

determined with the accuracy of 5%, which is obtained by observing the endpoint of

two-jets invariant mass distribution at ”four jets + missing energy” events[50]. The

mass difference will be determined more accurately with the use of a novel method

recently proposed in Ref.[51], where the endpoint of so-called MT2distribution[52]

is shown to be stable against the contamination of initial state radiations. On the

other hand, the gluino mass may be determined by observing the cross section of

the gluino pair production if the acceptance of the LHC experiment for this mode is

well understood. The wino mass is expected to be determined by observing the MT2

endpoint, because the endpoint has a kink structure at the wino mass as a function

of the test mass defining MT2[51]. It has been also shown that the wino mass is

determined by using the charged track of˜ W±, because its decay length is estimated

to be O(10)cm[53]. It may be even possible to measure the lifetime of˜ W±using

this method. The mass difference between bino and wino is determined only when

the branching fraction Br(˜ g → q¯ q˜B) × Br(˜B → l¯l˜ W0) is large enough[50].

Finally, we comment on collider signals of the pure gauge mediation model when

the gluino is heavier than a few TeV and is not accessible at the current and near

future LHC experiments. In such cases, we have to rely on the direct production

(Drell-Yan process) of charged winos associated with a quark (gluon). Associated

quark (gluon) is necessary as a trigger for recording data[18, 35]. Its cross section

is rapidly decreased with increasing the wino mass. Since the mass of the wino is

at most 1TeV for the successful leptogenesis, the high luminosity LHC experiment

(HL-LHC)[54] may help us to discover the signal. On the other hand, if the multi-

TeV linear colliders such as ILC [55] or CLIC [56] are available, we can investigate

the properties of neutral and charged wino in details. Since the analysis strategy

for the mode e+e−→˜ W+˜ W−→˜ W0˜ W0π+π−is very similar to that for the golden

mode of dark matter detections, e+e−→ ˜ χ+˜ χ−→ ˜ χ0˜ χ0W+W−with χ0and χ±

being the dark matter and its charged partner[57], we can easily find the signal of

the pure gravity mediation model if π-mesons are efficiently detected.

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4 Conclusion

The pure gravity mediation model is the bare bones model of the supersymmetric

Standard Model. Despite its simpleness, the model is quite successful for m3/2=

O(10 − 102)TeV; the model has a good candidate of dark matter, the gauge cou-

pling constants unify at the GUT scale very precisely, the Higgs boson mass around

125GeV can be easily accounted. In this sense, the model is superior even to the

Standard Model. The consistency with the thermal leptogenesis is also an significant

support of the model.

In this paper, we discussed details of the gaugino mass spectrum in the pure

gravity mediation model. There, we showed that the wino mass obtains comparable

contributions both from the anomaly-mediation and the Higgsino threshold effects.

As a result, the ratio between the wino LSP and the gluino masses can be as large

as around one third, which enhances the detectability of the model at the LHC

experiments. In fact, we showed that the gluino can be within the reach of the LHC

experiments even for the wino mass which satisfies the cosmological and astrophysical

constraints, mwino? 300GeV. This is a sharp contrast to the cases of the anomaly

mediated gaugino spectrum where the gluino mass is about eight to nigh times

larger than the wino mass. Utilizing this property, we discussed the strategies of the

discovery and the measurement of the model at the LHC experiments via the gluino

production.

In this paper, we also discussed the prospects of the wino dark matter detection

via the cosmic ray observations. As a result, we found that the wino dark matter

scenario which is consistent with the thermal leptogenesis can be fully surveyed by

observing the cosmic ray anti-proton flux at the AMS-02 experiment. Therefore,

the most motivated parameter region of the pure gravity mediation model which is

consistent with the thermal leptogenesis can be tested over the next ten years or so.

Acknowledgments

This work is supported by Grant-in-Aid for Scientific research from the Ministry of

Education, Science, Sports, and Culture (MEXT), Japan, No. 22244021 (S.M. and

T.T.Y.) and No. 23740169 (S.M.), and also by World Premier International Research

Center Initiative (WPI Initiative), MEXT, Japan.

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