Study of dark matter physics in non-universal gaugino mass scenario

We study dark matter physics in the Minimal Supersymmetric Standard Model with non-universal gaugino masses at the unification scale. In this scenario, the specific ratio of wino and gluino masses realizes the electro-weak scale naturally and achieves 125 GeV Higgs boson mass. Then, relatively light higgsino is predicted and the lightest neutral particle, that is dominantly given by the neutral component of higgsino, is a good dark matter candidate. The direct detection of the dark matter is sensitive to not only a higgsino mass but also gaugino masses significantly. The upcoming XENON1T experiment excludes the parameter region where bino or gluino is lighter than about 2.5 TeV if the higgsino and the gaugino mass parameters have same signs. We see that the direct detection of dark matter gives stronger bound than the direct search at the LHC experiment when higgsino gives sizable contribution to the dark matter abundance.


Introduction
Supersymmetry (SUSY) is a promising candidate for physics beyond the Standard Model (SM). The supersymmetric extension predicts the superpartners of the SM particles, and the masses of the SUSY particles are expected to be at least TeV-scale, in order to explain the origin of the electroweak (EW) scale. 1 In the Minimal Supersymmetric Standard Model (MSSM), there is a supersymmetric mass parameter, what is called µ-parameter, for higgsino that is the superpartner of Higgs bosons. In order to realize the EW scale without fine-tuning, µ-parameter should be EW-scale. Besides, the lightest particle in the MSSM becomes stable because of R-parity, so that higgsino becomes a good dark matter (DM) candidate if there is no lighter SUSY particle. So far, a lot of efforts are devoted to the SUSY search in the collider experiments and the dark matter observations [3]. There are no decisive signals of the SUSY particles, but higgsino is still one of the possible and attractive DM candidates that reveal the origin of the EW scale.
In the MSSM, there are a lot of parameters, so that we can consider many possibilities of the mass spectrum for the SUSY particles. The direct searches for the SUSY particles as well as the 125 GeV Higgs boson mass measurement at the LHC [4], however, constrain the parameter space strictly. It is getting very difficult to construct SUSY models, as long as the explanation of the EW scale is not discarded. One possible setup to achieve both the 125 GeV Higgs boson mass and the explanation of the EW scale is known as the Non-Universal Gaugino Masses (NUGM) scenario [5,6]. In this scenario, a suitable ratio of the JHEP08(2017)072 wino mass to the gluino mass achieves the EW scale and the 125 GeV Higgs boson mass. Then, the µ-parameter is predicted to be close to the EW scale. The current status and the future prospect of the discovery of the SUSY particles at the LHC have been investigated in this scenario [7][8][9]. We find that the superpartners of top quark and gluon, what are called top squark and gluino, are promising particles to test this scenario. Expected reaches of these SUSY particles decaying to higgsinos are studied in refs. [10][11][12]. 2 Note that there are some models that lead such a ratio of the gauginos. One possibility is the mirage mediation [14][15][16], that is a mixture of the moduli mediation [17][18][19] and anomaly mediation [20,21]. The phenomenology of the mirage mediation is discussed before the Higgs boson discovery in refs. [22][23][24][25][26][27][28][29][30][31][32][33] and after that in refs. [34][35][36][37][38][39][40]. There are some works to realize the ratio of the gauginos in the GUT models [41] and superstring models [42].
In this kind of SUSY models, higgsino is light because of the explanation of the origin of the EW scale, and the SUSY particle is expected to be discovered in experiments. There are neutral and charged components in higgsino, and the neutral component mixes with bino and wino, and the charged component mixes with wino. 3 In our scenario, the gauginos are relatively heavy, so that all components of higgsino are light and almost degenerate; in fact, the mass difference is a few GeV [7,8]. Then, higgsino is hard to be detected at the LHC due to the certainly small mass differences. On the other hand, dark matter direct detection experiments can efficiently observe higgsinos, if the neutral component of higgsino slightly mixes with the gauginos and dominates over our universe. It is also interesting that the higgsino mass should be lighter than about 1 TeV, if higgsino is thermally produced. Then, our DM mass, that mainly comes from the neutral component of higgsino, is predicted to be between the EW scale and 1 TeV.
In this paper, we study dark matter physics in the NUGM scenario. Direct detection experiments are sensitive to not only the higgsino mass itself, but also the gaugino masses, because the higgsino-gaugino mixing gives the most significant contribution to the detection rate. We also discuss the constraints from the LHC experiments, based on the results in refs. [7][8][9]. We explicitly show the exclusion limit and the future prospect on the plane of the higgsino and the gaugino masses. In the end, we find that this scenario can be fully covered by the future experiments, as far as the gluino mass is below 2.5 TeV in a certain parameter set. This paper is organized as follows. The NUGM scenario is reviewed in section 2, and we discuss dark matter physics in section 3. The results of numerical calculations are shown in section 4. Section 5 is devoted to conclusion.

Review of NUGM
The NUGM scenario is known as one of the attractive SUSY models to realize µ-parameter near the EW scale and the 125 GeV Higgs boson mass simultaneously. The µ-parameter JHEP08(2017)072 is related to the EW symmetry breaking scale through the minimization condition for the Higgs potential as where m Z is the Z-boson mass and m 2 Hu is the soft scalar mass squared for the up-type Higgs boson. This relation shows that |µ| 2 and |m 2 Hu | should be around the EW scale to avoid the fine-tuning between those parameters. The µ-parameter is an unique SUSYpreserving parameter in the MSSM. On the other hand, all other dimensional parameters softly break SUSY and would be originated from some mediation mechanisms of SUSY breaking: i.e., the soft SUSY breaking terms would have same origin. Let us assume that the all ratios of soft SUSY breaking parameters are fixed by some mediation mechanisms and the overall scale is given by M 0 . In this assumption, eq. (2.1) corresponds to the relation between µ and M 0 . In ref. [43], the parameter, ∆ x , to measure the sensitivity of the parameter x to the EW scale is introduced: Since m 2 Hu (m SUSY ) is expressed as a quadratic polynomial function of the boundary conditions, we can derive ∆ µ + ∆ M 0 = 1 at the tree-level and ∆ µ ∆ M 0 is satisfied. Thus the tuning of the µ-parameter represents the degree of tuning to realize the EW symmetry breaking in the model. From the relation eq. (2.1), the tuning measure of the µ-parameter can be written as ∆ µ = 2|µ| 2 /m 2 Z up to radiative corrections to the condition, so that small |µ| is simply required to avoid the fine-tuning in this assumption. The details of this kind of discussions in the NUGM scenario are shown in refs. [9,44]. We proceed to study collider and dark matter phenomenology with the NUGM in this assumption. For reference, ∆ µ = 10, 100, 250 correspond to µ ∼ 200, 650, 1000 GeV, respectively.
In this paper, we assume universal soft scalar mass m 0 and A-term A 0 , while the gaugino masses M 1,2,3 are non-universal at the gauge coupling unification scale ( 10 16 GeV). We assume the ratio of two Higgs vacuum expectation values (VEVs) tan β ≡ H u / H d = 10 throughout this paper. The soft mass squared m 2 Hu at m SUSY = 1 TeV relates to the boundary conditions at the unification scale as This relation shows that the contribution from the gluino mass is dominant among the renormalization group (RG) effects, but we find that the gluino mass contribution can be canceled by the RG effects from the other gaugino masses M 1,2 . In particular, the M We see that A t (m SUSY ) increases and m 2 t R (m SUSY ) decreases as the wino mass M 2 increases. Note that the latter effect is induced by the top Yukawa coupling. As a result, the ratio increases and the SM-like Higgs boson mass around 125 GeV can be achieved due to the relatively large wino.

Mass spectrum of NUGM
We see that the suitable wino-to-gluino mass ratio reduces the µ-parameter and also enhances the Higgs boson mass. Besides, some of sparticle masses are within reaches of the LHC experiment thanks to the sizable left-right mixing of the top squarks [7,8].
When the wino mass is large, left-handed sparticles become heavy due to the RG evolution. The right-handed slepton masses are determined by the bino mass, while the right-handed squark masses mainly depend on both the gluino and bino masses. The bino mass plays a crucial role in shifting the top squark mass, as well. This means that the bino mass have to be so heavy that the top squark mass is enough heavy to be consistent with the LHC results.
Another important point derived from the relatively heavy bino and wino is that the mass differences among the components of higgsino become small. The mass differences are induced by the mixing with higgsino and gauginos, so that these are suppressed by the bino and wino masses as explicitly shown in next section. The mass differences among the components of higgsino are typically 2 GeV as shown in ref. [7]. This small mass difference makes it difficult to detect higgsino directly at the LHC, because their daughter particles are too soft to be distinguished from backgrounds and their lifetimes are too short to be recognized as charged tracks unlike the case that wino is the lightest SUSY particle (LSP) [45]. 4 This feature also indicates that we can treat all of the particles from higgsino as invisible particles at the LHC.
Let us summarize the important features of our mass spectrum discussed below: • All gauginos are O(1) TeV.
• The higgsino mass is between the EW scale and 1 TeV, and the mass differences are O(1) GeV.
• Right-handed top squark is relatively light.

LHC bounds
In our scenario, the top squark and the gluino are the good candidates to be detected at the LHC. The current exclusion limit and the future prospect have been studied in refs. [7][8][9].
In the NUGM scenario, a top squark decays ast 1 → tχ 0 1,2 /bχ ± 1 where each branching fraction is 50% as long as the mass difference between the top squark and each of the higgsino-like particles is significantly larger than the top quark mass. Note that the neutralinos consist of higgsino that slightly mixes with wino and bino in our scenario. The relevant top squark searches at the LHC are discussed in ref. [48] and ref. [49]. The former analysis aims to a pair of bottom squarks that decay asb 1b1 → bχ 0 bχ 0 . This gives same signal ast 1t1 → bχ ± bχ ± in the NUGM scenario. The latter analysis aims to hadronically decaying top squarks,t 1t1 → tχ 0 tχ 0 → bjjχ 0 bjjχ 0 . In ref. [49], the signal regions require more than 4 jets, where 2 of these should be b-tagged. Such signal regions will be sensitive to eventst 1t1 → t(→ bjj)χ 0 bχ ± in the NUGM scenario, although this analysis is not completely optimized. This decay pattern is realized in almost half of the events with the pair produced top squarks if the mass difference between the top squark and higgsino is enough large. Thus this channel that targets to the hadronically decaying top squark is sensitive to the large mass difference region, while the former channel that targets to bottom squarks decaying to a bottom quark and a neutralino is sensitive to the mass degenerate region. Referring the analysis in ref. [9], top squark lighter than 800 GeV is excluded if µ 200 GeV is satisfied, and top squark lighter than 600 GeV is excluded in the range with 200 GeV µ 270 GeV. There is no exclusion limit for top squarks if µ is greater than 270 GeV.
In present scenario, a gluino decays asg → tt 1 → t + tχ 0 /bχ ± . Hence, the signal from the gluino pair production is expected to have 4 b-tagged jets, jets/leptons coming from 2-4 W-bosons and large missing energies in the final state. The analysis in ref. [50] aims to this type of signals, and we refer the exclusion limit obtained in ref. [9]. Gluino lighter than 1.8 TeV is excluded if the µ-parameter is less than 800 GeV. The bound is relaxed if the mass difference is smaller than about 300 GeV.
Note that there is another channel,g → gχ 0 , that is induced by the top squark loop. If the mass difference between gluino and higgsino is near or less than the top quark mass, this decay channel becomes important. We need to consider the limits based on data such as ref. [51], but it is beyond the scope of this paper.
Let us comment on the case with light bino. If gluino is enough heavy, bino can be as light as higgsino and top squark can also decay to bino. The decay is, however, usually suppressed unless bino is significantly lighter than higgsino because the coupling of bino with top squark is much weaker than the one of higgsinos because of the top Yukawa coupling. Such a light bino is less attractive from the experimental point of view. If the bino mass is light, gluino has to be much heavier than the experimental reach in order to shift the top squark mass. Then, the light bino case would be unfavorable from the naturalness point of view. Furthermore, it is known that bino LSP tends to overclose the universe and some dilution mechanisms are necessary.

Neutralino sector
In our study, we assume that the signs of all the gaugino masses are positive and the sign of the µ-parameter is either negative or positive. After the EW symmetry breaking, gauginos and higgsino are mixed each other. The neutralino mass matrix in a basis of where c β = cos β, s β = sin β, c W = sin θ W and s W = sin θ W are defined and θ W is the Weinberg angle. This matrix is diagonalized by an unitary matrix N as The masses, mχ 1 , mχ 2 , mχ 3 and mχ 4 approach to M 1 , M 2 , µ, and −µ in the limit that m Z is vanishing, respectively. The mass eigenstateχ 3 (χ 4 ) becomes the lightest one if the µ-parameter is positive (negative) and |µ| < M 1 , M 2 . The neutralino-neutralino-Higgs coupling, L (1/2)λ hnn hχ nχn , is given by where t W , s α and c α are short for tan θ W , sin α and cos α, respectively. α is a mixing angle of the Higgs boson. The mixing matrix is given by where m Z |M 1,2 ± µ| is assumed.

Thermal relic abundance
It is known that the thermal relic density of the purely higgsino LSP saturates the universe when the higgsino mass is about 1 TeV [52,53]. If we assume that there is no dilution effect after the thermal production of the LSP, the higgsino-like LSP heavier than 1 TeV overcloses the universe and is cosmologically excluded unless the higgsino and another sparticle, such as a top squark, are so degenerate that co-annihilation processes between them reduce the relic density.

JHEP08(2017)072
Let us comment on possibilities that gauginos contribute to dark matter considerably. In our scenario, the wino mass should be as large as the gluino mass at the TeV scale and it hardly contributes to the dark matter. The bino mass can be as light as the higgsino mass if the gluino mass is enough large to keep the top squark mass. It was interesting that the welltempered bino-higgsino LSP explains the observed abundance in the thermal scenario [54], but most of parameter space has been already excluded by the direct detections as will be discussed later. 5 In our scenario, the relic DM abundance thermally produced may not be sufficient to satisfy the observed DM abundance in our universe. When we denote the relic abundance of the LSP as Ω χ h 2 , we can simply consider two possibilities to saturate the observed value, Ω obs h 2 = 0.1188 ± 0.0001 [56]: where Ω th is the thermal relic density of the LSP. Detection rates for the LSP at dark matter detections are suppressed by a fraction ξ ≡ Ω χ /Ω obs = Ω th /Ω obs ≡ ξ th .
(B) Ω χ h 2 = Ω obs h 2 is always satisfied, assuming non-thermal production of LSP works. Detection rates for the LSP are simply determined by cross sections for relevant processes and the suppression factor is unity: ξ ≡ Ω χ /Ω obs = 1.
In the case (A), the LSP may not saturate our universe, depending on the parameter region. Then, we need other DM candidates such as axion to achieve the observed relic abundance of the DM. We also assume that the thermal relic density of the LSP is not changed by introducing other DM candidates to the MSSM. The direct detection rate is suppressed by ξ th and the indirect detection rate is suppressed by ξ 2 th . The difference of the scalings comes from the fact that the relevant process is scattering of the LSP against nucleons in the direct detection, while it is coannihilation of two LSPs into SM particles in the indirect detection.
In the case (B), we simply assume that the LSP dominates our universe and satisfies ξ = 1. We do not explicitly calculate the relic abundance, but several mechanisms for the non-thermal productions have been proposed so far. For instance, it is known that the decays of long-lived heavy particles, such as gravitino, saxion and moduli field, can significantly produce the LSP after the LSP is frozen out from the thermal bath [57][58][59][60].
Throughout this paper, we focus on the region where ξ th ≤ 1 corresponding to µ 1.0 TeV. We note that region with ξ th ≥ 1 is not truly excluded in the case (B), but such region is less attractive because the degree of tuning of the µ-parameter to realize the EW scale is severer than ∆ µ 250 corresponding to 0.4 % tuning.
Let us discuss spin-independent cross section of neutralino scattering with nucleons. Note that the limits on the gaugino masses from the spin-independent cross section are stronger than those from the spin-dependent cross section in most cases.
At tree-level, spin-independent scatterings are induced by the t-channel Higgs boson exchange and the s-channel squark exchange. Since only one top squark is light in the NUGM scenario, the latter contribution is negligibly small. The mixing between gauginos and higgsino are important in the Higgs boson exchange, because the LSP-LSP-Higgs coupling in the mass eigenstate basis is originated from the gaugino-higgsino-Higgs couplings in the gauge eigenstate basis. In the limit of m Z |M 1,2 ± µ|, the mixing effects are suppressed by m Z /|M 1,2 ± µ| as shown in eqs. (3.6) and (3.7).
It has been shown that there is a parameter set to lead vanishing gaugino-higgsino mixing, what is called the blind spot [72]. As we see eqs. (3.3), (3.4) and (3.5), the mixing is proportional to M 1,2 + µ sin 2β, so that the mixing vanishes when the relative signs of M 1,2 and µ are opposite, and |M 1,2 | |µ| and tan β 1 are satisfied. Thus the blind spot appears only in the gaugino-like LSP scenario.
Note that the mixing is suppressed when the LSP is higgsino-like and signs of µ and M 1,2 are opposite, as we can see from eqs. (3.6) and (3.7). Since the mixing is proportional to 1±sin 2β, smaller tan β induces larger enhancement (suppression) for the same (opposite) sign. We need tan β 10 in order to realize the SM-like Higgs boson mass unless the sparticle masses are much heavier than 1 TeV, so that such effect is at most 20%-level. Thus we conclude that the gaugino-higgsino mixing is sizable and the factor, 1 ± sin 2β, leads significant difference between the positive and the negative µ-parameter cases in the DM scattering cross section.
The spin-independent cross section per nucleon at the tree-level can be written as 8) where m N is the nucleon mass and m N f N Tq = N |m qq q|N . In the decoupling limit m A m Z that is a good approximation for our case, using eqs. (3.6) and (3.7), the LSP-LSP-Higgs coupling λ hχχ is derived from eq. (3.3): where ± corresponds to a sign of the µ-parameter. We list the explicit values of masses and observables at the sample points in table 1. In our numerical analysis, We use softsusy-3.5.1 [88] to calculate the RG effects and the mass spectrum of sparticles and Higgs bosons. Their width and branching ratios are calculated by SDECAY and HDECAY [89][90][91]. Note that the dark matter observables are calculated by micrOmega-4.2.5 [73][74][75]. We can see that the A-term is same order as other input JHEP08 (2017) parameters, but the Higgs boson mass is about 125 GeV owing to the suitable wino-togluino mass ratio. The top squark mass is about 1.5 TeV and the gluino mass is 2-3 TeV, so that they could be in the reach of the HL-LHC. The bino and wino masses are between 2 TeV and 5 TeV and they are far beyond the experimental reach of the LHC experiment.
From the naturalness point of view, we are especially interested in the low-scale µ scenarios. When |µ| = 250(1000) GeV in the samples (a), (b), (c) and (d), the thermal relic abundance is ∼ 0.01(0.1). The self-annihilation rate of the neutralinos in the zerovelocity limit, denoted by σv 0 , is O(0.1 − 1.0) × 10 −25 [cm 3 /s] and they are dominantly annihilating in pairs into weak gauge bosons. These processes are induced by the t-channel neutralino or chargino exchange, and then the rate is determined by the higgsino mass itself. These are important for the indirect detections as discussed below.

JHEP08(2017)072
We also show the spin-dependent and spin-independent LSP-proton cross sections, σ SD , σ SI , calculated by using micrOMEGA-4.2.5 [73][74][75]. σ h SI is obtained from eqs. (3.8) and (3.9), where f p Tq are taken same as the values adopted in micrOMEGA [76]. We can see the SI cross section is well described by the tree-level Higgs-exchanging process, but there are small deviations from the results of micrOMEGA.
A dominant source for the deviation come from the QCD corrections to the heavy quark matrix elements [77], which enhance the cross section about 10% against the tree-level contribution. Besides, the top squarks could give contribution to the cross section, when a mass difference m 2 t 1 − m 2 χ is small. However, it is known that the leading contribution, which is suppressed by (m 2 is proportional to the size of non-trivial mixing of the top squarks [78]. The top squark is almost right-handed in our scenario and thus such contribution can not be sizable. We take the top squark corrections derived in ref. [78] into account, and confirm that these are about 1% against the tree-level countribution at the sample (d) and fewer for the other sample points. We have checked that our results agree with the results of micrOMEGA exhibited in table 1 within several %-level after including these effects. There are potentially sizable corrections from neutralino/Z-boson and chargino/W-boson mediated loop diagrams, where the neutralino and chargino are higgsino-like, but these are almost canceled out among them as shown in ref. [79].

Indirect detection
Let us comment on indirect detections for the dark matter. A pair of neutralinos decay to W + W − or ZZ with the zero-velocity cross section: that is O(10 −25 )[cm 3 /s] as shown in table 1.
One of the most promising observables may be the neutrino flux from the sun. The capture rate of neutralino by the sun is determined by the interaction between neutralino and nucleons. Since the spin-dependent cross section is much larger than the spin-independent one, the observations would give significant bounds on the spin-dependent cross section. The weak bosons produced by the annihilation of dark matter decay to neutrinos. The observed limit of neutrinos given by the IceCube is 3.76×10 −5 pb when the dark matter mass is 500 GeV and they decay to W-bosons exclusively [80]. This limit is comparable to the expected limit at the XENON1T [61]. We will see that exclusion limits for the parameter space from the XENON1T are much weaker than limits from the spin-independent cross section, so that the current limit from IceCube experiment can not be important one.
Cosmic ray observations such as photons, positrons and anti-protons could be powerful tools to detect dark matter. These limits of the annihilation cross section of DM reach to O(10 −25 )[cm 3 /s] and the parameter region discussed in present paper is competing with these bounds. We consider the recent experimental results obtained by the Fermi-LAT [81] and AMS-02 [82]. The former observes gamma rays coming from the dwarf spheroidal satellite galaxies (dSphs) of the Milky Way and the latter observes anti-protons coming from dark matter annihilations in the Milky Way. We refer the exclusion limit from the AMS-02 experiment obtained in the analysis [83]. 6 The Fermi-LAT experiment also JHEP08(2017)072 observes gamma-rays coming from the galactic center and this potentially gives significant constraints on the dark matter annihilation rate. However, the results are highly dependent on dark matter density profiles [85], so that we do not discuss about this in present paper. Figure 1 shows the upper limits on the annihilation cross section from the recent results of the Fermi-LAT (black line) and the AMS-02 (green line). The uncertainty of the limit from the AMS-02 is shown by the green band, because the limit from the AMS-02 experiment still has large uncertainty. The dots are predictions from the NUGM scenario and obtained by the parameter scanning to draw figures in next section. We plot the points with M 1 ≥ 2.5 TeV at the unification scale. The blue dots indicate the lightest neutralino mass and the annihilation rate itself and are predicted in the case (B) where ξ = 1, but it is multiplied by ξ 2 th ≡ (Ω th /Ω obs ) 2 for the red dots corresponding to the case (A). Since the higgsino-like dark matter dominantly annihilate to W-bosons or Z-bosons by the t-channel exchange of the higgsino-like chargino or neutralino, the annihilation rate is mostly determined by the higgsino mass itself and almost independent of other parameters. We see that the Fermi-LAT result excludes the neutralino lighter than about 300 GeV and the AMS-02 excludes the neutralino lighter than about 800 −300 +200 GeV if the LSP saturates the dark matter and ξ = 1. On the other hand, the indirect detections do not give limits if the annihilation rate is suppressed by the factor ξ 2 th . Exclusion limits on the higgsino dark matter produced from some non-thermal processes at the Fermi-LAT and the future planned CTA experiments [86] have been discussed in ref. [87].
In the case (B), where ξ = 1, the higgsino lighter than about 500 GeV has been excluded even in the loosest case within the uncertainty. This means that the degree of tuning of the µ-parameter is worse than a few %-level. Note that this limit is independent of other parameters as long as the higgsino is the dominant component of the LSP. For this reason, we will not draw the limits from the indirect detections on figures in the next section. The conservative limit for the higgsino mass is about 500 GeV if ξ = 1, while there is no bound for the higgsino mass if ξ = ξ th .

Numerical results
Based on the above discussion, we summarize the experimental bounds and show the allowed region. Figure 2 shows the allowed region for the dark matter observables, the top squark mass and exclusion limits from the collider experiments. We assume m 0 = 1 TeV, M 3 = 1.5 TeV at the unification scale and A 0 , M 2 are chosen to realize the SM-like Higgs boson mass and the µ-parameter at each point. We take the ratio of the Higgs VEVs as tan β = 10.
The red lines represent the thermal relic density of the neutralino, where the solid (dashed) lines correspond to ξ th ≡ Ω th /Ω obs = 0.5 (0.1). Ω χ h 2 = Ω obs h 2 = 0.1188 ± 0.0001 [56] is achieved in the red bands around |µ| 1 TeV. The thermal relic density of the dark matter exceeds the observed value, Ω χ h 2 > Ω obs h 2 , in the light gray region. If we allow only O(10) % fine-tuning for the EW scale, |µ| should be O(100) GeV, as discussed in section 2.1. In such region, ξ th = O(0.1) in the case (A) and some mechanisms to compensate the DM relic density are required.
Note that the gray region at |µ| ≤ 90 GeV is excluded by the LEP experiment [92]. Although the charged and neutral components of higgsino are certainly degenerate, they can be probed by the mono-photon channel. The background color represent the mass of the lightest top squark. The purple line around M 1 2.0 TeV and µ −100 GeV is the expected exclusion limits for the spin-dependent cross section from the XENON1T experiment [61]. Next, let us discuss the exclusion lines from the spin-independent direct detection. The spin-independent cross section exceeds the current limit given by the LUX experiment [65] in the blue band, assuming that ξ ≡ Ω χ /Ω obs = 1 is satisfied on all parameter points. The blue shaded region covered by the solid blue line is the expected limit from the XENON1T experiment in this case. The exclusion limit from the spin-independent cross section becomes stronger as the µ-parameter decreases. The reason is that the experimental limits for the cross section becomes tighter for lighter dark matter masses as long as the dark matter mass is heavier than about 40 GeV. The light bino mass region is easier to be excluded due to the large bino-higgsino mixing, especially the well-tempered region has already excluded by the current LUX limit as well known. The spin-independent cross section is significantly large for the positive µ-parameter compared with the case of the negative µ-parameter. This is because the cross section is proportional to (1 + sign(µ) sin 2β) 2 as can be read from eq. (3.9).
Note that the exclusion limits on the µ-M 1 plane are severer than the ones derived in ref. [72]. The difference comes from the fact that wino does not decouple completely in the NUGM scenario. The gray lines represent the ratio of wino to gluino mass r 2 ≡ M 2 /M 3 at the unification scale. In order to keep the µ-parameter smaller than 1 TeV motivated by the naturalness problem, the wino mass at the unification scale has to be 3-4 times larger than the gluino mass. The higher wino-to-gluino ratio is required for the lower typical sparticle scale which is defined as the geometric mean of the top squark masses. In this case, (M 2 , M 3 ) are about (4 TeV, 1.5 TeV) at the unification scale and it enhances the spin-independent cross section.
Note that the cross section of the spin-independent direct detection is always larger than 0.25 × 10 −10 pb in all figures in this paper. Then, we expect that the future experiments, the XENON1T [70] and the LZ [71], could cover our parameter region as far as ξ = 1 is satisfied. On the other hand, the current limit from the spin-dependent cross section is fully covered by the spin-independent one.
When we assume that Ω χ is only thermally produced, the bound from the direct detection should include the suppression from ξ th = Ω th /Ω obs . Taking into account the suppression, the limit would be relaxed as the µ-parameter decreases in the case (A) because of ξ th < 1. The region below the white dashed line is excluded by the LUX in this case. The dashed blue line corresponds to the future prospect of the XENON1T experiment JHEP08(2017)072 when the spin-independent direct detection rate is suppressed from ξ th . We see that the exclusion limit is significantly relaxed by this suppression. Figure 3 shows the allowed region for µ and M 1 at M 3 = 1.0 TeV. The different value of M 3 influences to the direct detection rate and the top squark mass. Top squark becomes the lightest SUSY particle in the dark gray region, and the top squark search at the LHC excludes the brown region. The LHC bounds are projected from the analysis in ref. [9]. The bino mass has to be so large that top squark mass is larger than the higgsino mass.
The lighter gluino mass leads the lighter wino mass and the spin-independent cross section is enhanced by the wino-higgsino mixing. We see that the XENON1T experiment covers the whole region with µ > 0 in the case (B) that ξ = 1 is assumed on all parameter points. Figures 4 and 5 show the allowed region for µ and M 3 where M 1 is 5.0 TeV and 10.0 TeV at the unification scale, respectively. Other parameters are set to be the same as in figures 2 and 3. The constraint from the gluino search at the LHC is also applied to these figures and it excludes the dark brown region. The gluino mass lower bound is around 800 GeV, so that there was no exclusion bounds in figures 2 and 3. We can see that experimental reaches from direct detections for the gluino mass can be much severer than those from the LHC experiment, assuming ξ = 1, and µ > 0 or µ 0.
The wino-higgsino mixing is reduced as gluino becomes heavy. The mixing, however, is not vanishing in our model-dependent analysis. We see that the gaugino-higgsino mixing predicts the spin-independent cross section larger than 2.5 × 10 −11 pb everywhere in all of the four figures. Thus the parameter region is on the neutrino floor [93] and the region in our analysis would be fully covered by the future planned observations such as the XENON-nT, LZD, PandaX-4T and so on.

Conclusion
In this paper, we study the dark matter physics in the Non-Universal Gaugino Mass scenario. The NUGM scenario is one of the possible setups of the MSSM to achieve the 125 GeV Higgs boson mass and the µ-parameter below 1 TeV, that naturally explain the origin of the EW scale. Since one top squark is relatively light in our scenario, the authors in refs. [7,8] study the current status and the future prospect on the direct search for top squark and gluino at the LHC.
Although the higgsino mass is the most important from the naturalness point of view, higgsino can not be probed by the LHC due to their suitable mass difference ∼ 2 GeV. On the other hand, the higgsino mass is critically important for dark matter physics and can be tested by the dark matter observations. The higgsino mass can not be larger than 1 TeV in order not to overclose the universe if we assume that there is no dilution effect after the LSP is frozen out. Furthermore, the degree of tuning the µ-parameter is severer than ∼ 0.4% if the higgsino is heavier than 1 TeV.
Indirect detections for dark matter gives the limits on the higgsino mass independent of other parameters. If the LSP saturates our universe, the AMS-02 experiment have already excluded the higgsino lighter than about 500 GeV even in the most conservative case. This JHEP08(2017)072 limit is tighter than the limits from direct detections especially for negative µ-parameter and very heavy gauginos. On the other hand, there is no limit of the parameter space if the LSP relic density is determined by the thermal production mechanism.
Direct detections for dark matter are powerful tool to probe the neutralino sector of the MSSM. Even the bino and the wino masses are 3-4 TeV, the spin-independent cross section between higgsino and nucleon is in the observational reach. Therefore, the wider parameter space can be covered by the direct detection than the gluino search at the LHC, when the wino-to-gluino mass ratio is fixed to realize the small µ-parameter and the higgsino-like LSP dominates the relic density of dark matter.
If the neutralino density is determined by the standard thermal process, the direct detection is sensitive to the parameter region where the higgsino mass is around 1 TeV, while the top squark and the gluino searches at the LHC are generally sensitive to lighter higgsino. Thus the direct detection complement the direct search at the LHC.
The universal gaugino masses are clearly disfavored by the recent dark matter observations. The LSP is either bino or higgsino in this case, but the bino LSP easily overclose the universe. Even if the higgsino LSP is realized in some ways such as considered in refs. [94,95], light bino and wino are severely constrained by the direct detections. The direct detection constraints push up the gluino mass far above the experimental reach and such a heavy gluino indicates all other sparticles are also hopeless to be discovered except in some special cases. Thus the non-universal gaugino masses with relatively heavy bino and wino masses seems to be more interesting than the universal gaugino masses.