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Pure Gravity Mediation with m_{3/2} = 10-100TeV

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.


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 Bterm, 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, m 3/2 . 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 m 3/2 = 10-100 TeV. 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, GeV, 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. 1 In 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 1 See also Ref. [14] for the Polonyi problem in dynamical supersymmetry breaking models. 2 In fact, the gauge coupling constants unify at around 10 16 GeV at a few percent level even for 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. In this letter, we discuss phenomenological, cosmological and astrophysical aspects of the pure gravity mediation model. In particular, in this paper, we concentrate 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 section 2, we review the model with pure gravity mediation. There, we discuss the details of the gaugino spectrum. In section 3, we discuss the phenomenological, cosmological and astrophysical aspects on the model. The final section is devoted to our conclusions.
2 Pure gravity mediation model

Mass 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 Kähler potential, all the soft squared masses of the scalar bosons are a rather large µ-term of 10-100 TeV. It should be noted that the scale of the coupling unification is slightly lower than the conventional SSM for m 3/2 = 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, τ p 10 35 yrs, which is within the reach of the Hyper-Kamiokande Experiment [15].
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 Kähler potential, Here, X denotes a chiral SUSY breaking field in a (dynamical) SUSY breaking sector, M P L is the reduced Planck scale, and c and c are coefficients of O(1). Through the above Kähler potential, the µ-and the B-parameters [3,18] where F X is 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(m 3/2 ). 3 For the gaugino masses, on the other hand, tree-level contributions in the supergravity 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, M SUSY = O(m 3/2 ), are given by [4,10] M 1 = 33 5 Here, the subscripts M a , (a = 1, 2, 3) correspond to the gauge groups of the Standard Model U (1) Y , SU (2) L and SU (3), respectively. In the above expressions, the terms proportional to m 3/2 denote the anomaly mediated contributions and the terms proportional to L denote the Higgsino threshold contributions. The parameter L is given by where m A denotes the mass of the heavy Higgs bosons, and tan β is the ratio of the vacuum expectation values of the up-type Higgs boson H u and the down-type Higgs boson H d . 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. M SUSY 10 4−6 GeV. Thus, the anomalymediated 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.

Details on gaugino masses
As discussed above, the pure gravity mediation model predicts that the sfermions, 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) L gauge 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, with small dependences on the heavy scalar threshold scale, M SUSY . Thus, for the wino mass m wino = 300 GeV, for example, the gluino mass is heavier than 2 TeV 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 = sin βH u −cos βH * d remains very light for successful electroweak symmetry breaking. In terms of the Higgs mass parameters, the above fine-tuning condition requires, while the Higgs mixing angle is related to the Higgs mass parameters by,  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 tan β = 1, 3, 10 and 30 (Fig. 2). Here, we have assumed that µ H and B range from m 3/2 /3 to 3m 3/2 , respectively. 6 The figure also shows that |L/m 3/2 | 0.5 − 2 for tan β = O(1). Therefore, in the pure gravity mediation model, we expect L/m 3/2 = 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 5 Hereafter, we use a phase convention where Bµ H is real and positive. 6 More precisely, we assumed that log 10 µ H /m 3/2 and log 10 B/m 3/2 obey the normal distribution with the mean value 0 and the standard deviation 0.5×log 10   for the degenerated neutralino-chargino obtained gz by LEPII experiment [27]. The orange shaded region shows the experimental constrain on the gauginos, m gluino 750 GeV for m LSP 200 GeV reported by the ATLAS collaboration [28]. By remembering that L/m 3/2 2.5 is less likely in the pure gravity mediation, the figure shows that the gluino mass bound requires m 3/2 30 TeV. 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 expected 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, λ = 1 4 at the heavy scalar scale. The threshold corrections at the heavy scalar scale are also taken into account. We also take into account the weak scale threshold corrections 8 Fig. 2 shows that L/m 3/2 2.5 is possible for tan β 1. As we will see from Fig. 5, however, the lightest Higgs boson mass of our main concern (124 GeV< m h < 126 GeV) requires m 3/2 100 TeV for tan β 1. Thus, the conclusion m 3/2 30 GeV is not changed. 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

Signals 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 14 TeV.

Cosmological 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) L partner, the charged wino, is slightly heavier than the neutral one by 155-170 MeV because of contributions from oneloop 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 m wino 2.7 TeV. 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 2.7 TeV [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; m wino 1 TeV [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 −25 cm 3 /s when m wino 1 TeV, it may affect several 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 m wino 200 GeV 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 m wino 200 GeV, which is comparable to that from BBN.

Dark matter detections
Since the µ-parameter is of the order of 10-100 TeV in the pure gravity mediation model, the effect of the mixing between wino and higgsino components on the lightest supersymmetric particle (dark matter) is negligibly small. The scattering cross section between the dark matter and a nucleon is then estimated to be 10 −47 cm 2 [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 Supersymmetry 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 experiments 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 prediction 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 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 300 GeV.
Another interesting indirect detection is the PAMELA experiment observing the cosmic-rayp (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 thep flux depends on howp 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 m wino 230 GeV in spite of the uncertainties. On the other hand, the observation of the cosmic-rayp 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 thep 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-rayp 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 m wino by observing thep spectrum.  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 thep 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 −48 cm 2 in the pure gravity mediation model [38].

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 m wino 300 GeV. On the other hand, all the sfermions as well as the higgsinos are of the order of 10-100 TeV 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 → gχ 0 ) 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 → qq +χ 0 /χ ± i ). The chargino, which is nothing but the charged wino, decays into a neutral wino (dark matter) by emitting a soft 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 →W 0 h), or a charged/neutral wino + two leptons (B →W ll ), 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 m bino m gluino /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 decayg → qq χ with q(q ) being a quark except the top quark andχ 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 (m gluino , m wino )-plane, which is obtained by the LHC experiment with the center of mass energy of 7 TeV and 1.04 fb −1 data, is depicted with assuming that m wino ∼ m bino and 100 % branching fraction of the decayg → qq 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 1.2 TeV can be discovered at the LHC experiment with the center of mass energy of 14 TeV when 10 fb −1 data is accumulated [50].
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 1 TeV and 100 fb −1 data is accumulated at the LHC experiment with the center of mass energy of 14 TeV, 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 M T 2 distribution [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 M T 2 endpoint, because the endpoint has a kink structure at the wino mass as a function of the test mass defining M T 2 [51]. It has been also shown that the wino mass is determined by using the charged track ofW ± , because its decay length is estimated to be O(10) cm [53]. It may be even possible to measure the lifetime ofW ± using this method. The mass difference between bino and wino is determined only when the branching fraction Br(g → qqB) × Br(B → llW 0 ) 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 1 TeV 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 − →W 0W 0 π + π − is very similar to that for the golden mode of dark matter detections, e + e − →χ +χ− →χ 0χ0 W + W − with χ 0 and 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.
The pure gravity mediation model is the bare bones model of the supersymmetric Standard Model. Despite its simpleness, the model is quite successful for m 3/2 = O(10 − 10 2 ) TeV; the model has a good candidate of dark matter, the gauge coupling constants unify at the GUT scale very precisely, the Higgs boson mass around 125 GeV 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, m wino 300 GeV. 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.