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Physics Letters B

www.elsevier.com/locate/physletb

Neutralino dark matter in gauge mediation after run I of LHC and LUX

Ran Dinga, Liucheng Wangb *, Bin Zhua

a School of Physics, Nankai University, Tianjin 300071, PR China

b Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA

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ARTICLE INFO

Article history:

Received 1 April 2014

Received in revised form 25 April 2014

Accepted 4 May 2014

Available online 9 May 2014

Editor: J. Hisano

ABSTRACT

Neutralino can be the dark matter candidate in the gauge-mediated supersymmetry breaking models if the conformal sequestered mechanism is assumed in the hidden sector. In this paper, we study this mechanism by using the current experimental results after the run I of LHC and LUX. By adding new Yukawa couplings between the messenger fields and Higgs fields, we find that this mechanism can predict a neutralino dark matter with correct relic density and a Higgs boson with mass around 125 GeV. All our survived points have some common features. First, the Higgs sector falls into the decoupling limit. So the properties of the light Higgs boson are similar to the predictions of the Standard Model one. Second, the correct EWSB hints a relatively small ^-term, which makes the lightest neutralino lighter than the lightest stau. So a bino-higgsino dark matter with correct relic density can be achieved. And the relatively small ^-term results in a small fine-tuning. Finally, this bino-higgsino dark matter can pass all current bounds, including both spin-independent and spin-dependent direct searches. The spin-independent cross section of our points can be examined by further experiments.

© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3.

1. Introduction

It is now believed that the dominant matter in the universe should be non-baryonic dark matter (DM) instead of visible ones. And DM should not be composed of any known Standard Model (SM) particles. Extra symmetry is usually necessary to make DM stable on the cosmological time scale. In supersymmetric (SUSY) models, if the R-parity conservation is assumed, the lightest super-symmetric particle (LSP) is absolutely stable. The LSP should be a good DM candidate if it is electrically neutral. On the other hand, the measurement of relic density generally suggests that the DM mass is around several GeV to 10 TeV with a weak interaction. That is to say, the LSP is expected to be a weakly interacting massive particle (WIMP).

Unfortunately, gravitino with mass less than 1 GeV is usually the LSP in the gauge mediation supersymmetry breaking (GMSB) models. GMSB [1-9] is one of the promising mechanisms to describe the SUSY-breaking in the minimal supersymmetric Standard Model (MSSM) (for a modern review, see [10]). The effect of SUSY breaking is mainly transmitted to the MSSM sector through the gauge interaction, which makes GMSB models flavor-safe. The soft masses from gravity mediation are suppressed by Planck-scale and

* Corresponding author.

E-mail address: lcwang@udel.edu (L. Wang).

not generation-blind. So these Planck-scale induced soft masses are dangerous as they mediate flavor-changing effects. In order to escape from experimental constraints, these dangerous Planck-scale induced soft masses should be tiny. As the gravitino mass also arises from the Planck-scale induced operator, gravitino is always the LSP in GMSB models. Such a gravitino DM is hard to be detected and its relic density depends on the dynamics of inflation. Generally speaking, the lack of the predictability of gravitino DM is one of the drawbacks of GMSB models.

Instead of gravitino, the lightest neutralino can be the DM candidate in GMSB models if the hidden sector is strongly coupled [11-14]. The conformal sequestered hidden sector can raise the gravitino mass relative to the dangerous Planck-scale induced soft masses without introducing any flavor physics problems. As studied in [11-14], neutralino DM in the gauge mediation with sequestered SUSY breaking is typically purely bino-like and its mass is within the WIMP range. Since neutralino is the LSP, the lightest tau slepton (stau) should be heavier than the lightest neutralino. This is a strong constraint to those models, which requires the messenger scale Mmess typically around 1010 GeV. Compared to low-scale gauge mediation, stau will be heavier in such a high-scale gauge mediation, as the stau mass grows up when renor-malization group equations (RGEs) of MSSM are running from the input scale down to the electroweak scale.

All above papers about neutralino DM in GMSB scenarios with sequestered SUSY breaking were done several years ago. After the

http://dx.doi.org/10.1016/j.physletb.2014.05.007

0370-2693/© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3.

run I of Large Hadron Collider (LHC) and Large Underground Xenon (LUX) DM experiment, these models are necessary to be revisited and carefully checked by current experimental constraints. Firstly, a SM-like Higgs boson with mass around 125 GeV has been confirmed at LHC [15,16]. A 125 GeV Higgs in decoupling MSSM scenario prefers either a heavy top squark (stop) or a large At-term [17-27], since both could contribute large loop corrections to the Higgs mass. Unfortunately, minimal GMSB models predict vanishing A-terms at the messenger scale, which presents another challenge for GMSB models. Secondly, no signals of SUSY particles have been detected at LHC. Together with a 125 GeV Higgs, it raises uncomfortable issues with naturalness which are widely discussed in [28-68]. Finally, the updated bounds of DM direct searches become severer than the bounds in previous studies. The current strictest bound is given by the LUX Collaboration [69], who is the first to break the 10—45 cm2 cross section barrier of DM spin-independent detection at some WIMP mass range. New LUX upper limits have already been used to constrain DM in SUSY models [70-74]. All in all, in this paper we would focus on these new constraints on GMSB models with sequestered SUSY breaking.

This paper is organized as follows. In Section 2, we give a brief review about the GMSB scenarios with sequestered SUSY breaking and how to get a neutralino DM in GMSB models. Section 3 is devoted to studying new constraints on those GMSB models and showing our results. We finally conclude with a summary in Section 4.

2. Gauge mediation with sequestered SUSY breaking

In this section, we give a brief review about the GMSB models with the sequestered SUSY breaking and how to get a neutralino DM. We start with the minimal GMSB model. As a singlet super-field S in the hidden sector breaks SUSY, the messenger superfields & couple to the hidden field S via a superpotential W = k S with k ~ 0(1)} In the view of a spurion field, S = (s) + Fs62 is assumed to parameterize the typical effect of SUSY breaking. As a low-energy effective field theory of SUSY, many higher-dimensional operators contribute to the Kahler potential after heavy fields are integrated out. Sfermions get soft masses through the following operators

Keff =

5'5 E,cf' + HE^'!'

'"mess

where Fj are superfields of sfermions in the visible sector. The messenger scale is Mmess = k (s) and MPL is the Planck scale. Since Mmess ^ MPL in GMSB models, the soft masses msoft mainly come from the first term of Eq. (1), which are proportional to NFs .

Here N is the effective number of the messenger fields. Because the gauge interaction is flavor-blind, Mmess-scale induced operators naturally escape from experimental constraints on the flavor violation. However, the Planck-scale induced operators are very dangerous since the Wilson coefficients bj,j are not diagonal under the flavor index j, j of the sfermions. Since bj,j are always expected to be O(1), the Planck-scale induced soft masses are

is°ft,

MM^ ~ m3/2. In order to avoid the flavor problems at elec-

troweak scale, mpf have to be less than 1 GeV. That is why grav-itino is always the LSP in GMSB models.

However, the dynamics of the hidden sector may be important to determine the MSSM spectrum if the SUSY breaking sector is strongly coupled [11-14,75-90]. One of the interesting mechanisms in the hidden sector is conformal sequestering, which can

raise the mass of the gravitino relative to the dangerous Planck-scale induced soft masses [11-14]. So the lightest neutralino can be the LSP and DM candidate.2 To illustrate these conformal sequestered models, we assume that a strongly coupled hidden sector is approximately in a conformal window [M1, M2], where M2 is the scale at which the conformality starts and M1 is the scale at which the conformality is broken. Namely, MEW < Mi < M2 < MPL. In the conformal window, the RGE runnings are dominated by the strongly coupled hidden sector. As long as the fixed point is stable, the coupling constants flow to their infrared fixed-point values by power laws. Below the conformal window, one has

/MA ^t s b0,- =1 ^M bj, j = Zst S (M1)bj, j.

Here ZSts(1p) comes from one particle irreducible (1PI) diagrams in the hidden sector deducting the wavefunction renormalization factors. ^sts is the anomalous dimension of StS. Explicit models in the hidden sector have been discussed in [12,81,86] to demonstrate this conformal mechanism. If ^ts > 0, ZStS (M1) can offer a power suppressed factor which is helpful to solve the flavor violation problem. Unfortunately, the exact value of ^ts cannot be calculated in a perturbative way. We simply assume that bj0, j is small enough to be consistent with the constraints on the flavor violation. So even if m3/2 ~ O(1 TeV), the dangerous Planck-scale

induced soft masses can be mPf ~ yb°m3/2 < 1 GeV. Gravitino will no longer be the LSP in GMSB models.

Besides the large anomalous dimension of St S, the hidden sector with sequestered SUSY breaking would also provide a significant wavefunction renormalization factor ZS(p.), which makes Leff = Jd48ZS(p)StS canonically normalized. ZS(p) can be absorbed into the redefinitions of the couplings. For example, the coupling k in the superpotential W = k S becomes very small below the conformal window as

K ° =

k = Zs 2 (M1)K.

Here yS is the anomalous dimension of S at the conformal fixed point. Since S is a singlet, yS = 3R(S)/2 — 1 with R(S) being the R charge of S. The unitarity bound of the superconformal algebra requires R(S) > 2/3, which leads to yS > 1 [91]. So the wavefunction renormalization always offers a power suppressed factor to k . Below the conformal window, the superpotential is W = k0S&&>.

Finally we pay attention to the first term of Eq. (1), which is mediated by the gauge interaction. Since the superpotential W = k0 Scontributes to the coefficient cj, cj must receive the yS effect from anomalous dimension of S. It is interesting to discuss whether this term will further get a large correction from the anomalous dimension of StS:

Case I. The messenger scale Mmess is below the conformal window, namely MEW < Mmess < M1 < M2 < MPL. After the messengers fields are integrated out, the hidden sector is out of the con-formal window. Thus the coefficients cj do not receive the effect from the anomalous dimension ^ts [12,13]. Below the messenger scale, RGE runnings, which are dominated by the traditional MSSM ones, allow us to predict the entire MSSM spectrum at the elec-troweak scale. In this case, the p/Bp -problem can be solved by introducing some Planck-scale induced operators [12].

Case II. The messenger scale Mmess is within the conformal window, namely MEW < M1 < Mmess < M2 < MPL. After the messengers fields are integrated out, the hidden sector is still strongly

1 Because of 0(1), k is neglected in many papers for simplify.

2 Interestingly, the same mechanism can be used to solve the p/Bp-problem in

GMSB models [80,81,84,88,89] or to construct focus point SUSY [90].

100 120 140 160 180 200 220 240 Л (103GeV)

100 120 140 160 180 200 220 240

Л (103GeV)

Fig. 1. Contour plots of mh (left) and mt1 /m-0 (right) in the Mmess vs. A plane with tanp = 10.

coupled. Even the visible sector and hidden sector are coupled through higher-dimensional operators, the coefficient c could be renormalized dominantly by the hidden sector. From the scale Mmess to the scale M1, c will further receive a damping factor. Below the scale M1, all coefficients run to the electroweak scale according to the usual MSSM RGEs. So in this case the soft masses of sfermions will be further suppressed by the large anomalous dimension of StS [11,14]. In order to make neutralino the LSP, the lightest stau should be heavier than the lightest neutralino. This constraint in Case II is stronger than that in Case I, since the stau mass in Case II will be further suppressed. After the run I of LHC, a Higgs boson with mass around 125 GeV has been found but no SUSY particles have been detected. The stop sector should provide a large loop contribution to raise Higgs mass. Even assuming a non-vanishing At -term at the messenger scale, stop mass would be heavier than 500 GeV to get a 125 GeV Higgs [92]. For the Case II, due to the suppression coming from the anomalous dimension of St S, it is hard to obtain such heavy sfermions. A heavy stop may be realized if RGEs are assumed to run for a long time. But this requirement asks for a high scale M1, which would weaken the suppression of the dangerous Plank-scale induced operators. Thus, the Case II is not suggested by the current LHC data. In the next section, we will discuss more phenomenologies of the Case I.

3. Mass spectrum and neutralino dark matter

In this section, we discuss MSSM mass spectrum and neutralino DM in GMSB models with sequestered SUSY breaking. The grav-itino mass is fixed to be 1 TeV. We first study minimal GMSB model with A = 0 at the input scale. Then we move forward to an extension with non-vanishing A-terms at the messenger scale.

3.1. Minimal GMSB model with sequestered SUSY breaking

In this model, the superpotential is W = к S Ф[ Фi.

Here the messengers Фj, Фj fill out either antisymmetric tensor 10 + 10 or fundamental 5 + 5 representation of SU(5). Below the conformal window, the conformal sequestered hidden sector will lead to a very small coupling к0 in the superpotential, which can

be absorbed into the definition of mass parameter Л as Л = M FS .

This small coupling k0 guarantees A ~ 0(105 GeV) even when the gravitino mass is fixed to be 1 TeV. For the discussion of phenomenologies, there are six input parameters as

{tan в, sign(^), Mmess^,n5, П10}.

To perform a comprehensive analysis of our models, including spectrum calculation and DM studies, we use the code toolbox1.2.2 [93], which is compiled with SARAH3.3.0, SPheno3.2.2 and mi-crOMEGAs2.4.5. The code SARAH [94-96] is used to create a SPheno version of our models with the soft masses at the messenger scale. The mass spectrum at electroweak scale is calculated by the code SPheno [97,98] with MSSM RGEs and the DM information is obtained by the code micrOMEGAs [99].3 In our studies, sign(^) = +1, n5 = 1 and n10 = 1 are fixed. We first scan the parameters A and Mmess by assuming tan p = 10. Contour plots of mh in the Mmess vs. A plane are shown in the left of Fig. 1. For a fixed mass parameter A, the Higgs boson would be heavier if the messenger scale is higher. Though At = 0 at the messenger scale, the yt M3 term in the RGE ensures that At will not vanish at the electroweak scale. RGE runnings also lift the stop mass. A high-scale gauge mediation helps to obtain sufficiently large absolute value of At -term and heavy stops at the electroweak scale, which are preferred by a 125 GeV Higgs boson. In the right of Fig. 1, we show the ratio of the lightest stau mass to the lightest neu-tralino mass in the Mmess vs. A plane. In most of the parameter space, the LSP is the lightest stau particle. A neutralino LSP can only be achieved when the messenger scale Mmess is higher than 4 x 1011 GeV.

In Fig. 2, A = 1.6 x 105 GeV is fixed in order to be consistent with a 125 GeV Higgs boson. In the left, we show how the lightest stau mass mT1 and the lightest neutralino mass m^0 depend on

the messenger scale Mmess. In this case is purely bino-like and its mass is not sensitive to the messenger scale Mmess. Due to RGE running, mT1 becomes heavier for a higher messenger scale Mmess. When Mmess is larger than 3.6 x 1011 GeV, the LSP is and this model has a good DM candidate with mass around 870 GeV. In the right, the DM relic density Qh2 has been calculated by the code micrOMEGAs. When the LSP is x?, its relic density is always

3 We calculate the mass of the Higgs boson at two-loop level. Recently, some three-loop corrections have been discussed in [100,101].

4 x 10" 5 x 10" Mmess(GeV)

^ ,, 0.61—^ 6 x 1011 2 x 1011

3 x 1011 4 x 10" 5 x 10" Mmess(GeV)

6 x 10"

Fig. 2. (Color online.) A = 1.6 x 105 GeV and tanß = 10. Left: m-ri (green solid line) and m^o (red dashed line) depend on the messenger scale Mmess. Right: The relic density üh2 depends on the messenger scale Mmess.

o ►J

123 124 i T \ \ -

\ \ \ \ - \ \ \ \ \ \ \

\ \ \ 125 126 127 128

\ \ ' \ \

121 I

100 120 140 160 180 200 220 240

A (103GeV)

100 120 140 160 180 200 220 240

A (103GeV)

Fig. 3. Contour plots of mh (left) and mi1 /m^0 (right) in the Mmess vs. A plane with tan p = 10 and Xu = 1. In the whole blank area of right figure, mi1 /m^0 > 1. Since m^ /m^a is very sensitive to the choice of A and Mmess in this area, the exact values are difficult to be shown in this contour.

larger than 0.6, which is not consistent with the WMAP experimental result Qh2 = 0.1138 ± 0.0045 [102]. In this case, ^ and jf10 are degenerate and the coannihilation effect has been involved to make predictions of relic density. Since the LSP is around 870 GeV, all other SUSY particles should be heavier than 870 GeV. Because the exchanged SUSY particles are so heavy, the cross section (aan v) is not large enough even including the coannihilation effect. That is why we get too large DM relic density in this model. We have varied the value of tan p in this model. But the main features of Fig. 1 and Fig. 2 do not change. DM candidate is purely bino-like with a relatively large mass. It is well-known that the observed relic abundance requires the mass of purely bino-like DM to be less than 200 GeV for thermal production [103]. Even including coannihilation effects, purely bino-like DM cannot be too heavy [104]. So generally speaking, the neutralino DM with correct relic density is hard to be achieved in this model.

3.2. An extension model with non-vanishing A-terms

Minimal GMSB model can be extended with non-vanishing A-terms at the messenger scale. In [90,92,105-109], new Yukawa couplings between the Higgs sector and messengers are introduced to generate one-loop A-terms at Mmess scale without flavor problems. So in this subsection, we add a new term in the superpotential as

Here we introduce a new singlet &S as another messenger field.

are all the fields taking the (1, 2, —1/2) representation in the 5 + 5 messenger fields. Eq. (6) would lead to a non-vanishing At at the messenger scale. Since the singlet S is the only SUSY-breaking source, the A/m2H -problem is not large [106]. Here we do not introduce new Yukawa couplings between Hd and the messenger fields. So there is no p/Bp-problem. In this GMSB model with sequestered SUSY breaking, the p -term can be generated by some Planck-scale induced operators [12]. Compared to the mass spectrum in minimal GMSB model, Eq. (6) results in extra contributions of At, mHu, m2Q and m^ at the input scale as [106]

At = 16n2A'

_ n5>4h( y

= 48n2 h( Mm

_A N2.2

, (3+ns)A.u-(3g2/5+3g2)A2 n 2 + 256n4 n5A '

IsW = XUHU 0i .

m2 _ n5y2K yt 2 mQ = 256n4 y '

m2 _ n5y2A y 2 mU = 128n4 y .

Here the function h(x) & 1 + 4x2/5. If the messenger scale Mmess ~ 0(105 GeV), the first term of m2H in Eq. (7) is important to realize the electroweak symmetry breaking (EWSB). When the messenger scale Mmess is large, this term can be neglected due to the Mmess-suppression. Instead, the top Yukawa yt contribution in the

Mmess(GeV)

Mmess(GeV)

Fig.4. (Color online.) A = 1.5 x 105 GeV, tanp = 10 and Xu = 1. Left: mT1 (green solid line) and m^0 (red dashed line) depend on the messenger scale Mmess. Right: the relic density Qh2 depends on the messenger scale Mmess.

WIMP Mass (GeV)

WIMP Mass (GeV)

Fig. 5. (Color online.) Our DM points are shown in the red region. For the spin-independent cross section, plot ctSI vs. m^0 is shown in the left, with the current bounds from LUX [69] (solid black line), XEN0N100 [110] (solid blue line) and future reaches of LUX(2014/2015) [111] (dashed black line), XEN0N10T [112] (dashed blue line). For the spin-dependent cross section, plot ctSD vs. m-0 is shown in the right, with the current bounds from SuperK [113] (solid black line), IceCube [114] (solid blue line) and XEN0N100 [115] (solid cyan line). 1

RGEs could cause m2H to run negative at the electroweak scale, helping to achieve EWSB.

So in this model, there are seven input parameters as

{tan ß, sign(^), Mmess,A,Xu, n5, nW}

Xu is not suppressed by the sequestered SUSY breaking sector since it is not directly coupled to the hidden sector S. Thus Xu ~ O(1). Contour plots of mh and m^ /m^ 0 in the Mmess vs. A plane are shown in Fig. 3 when tan p = 10 and Xu = 1 are assumed. By comparing the left figures between Fig. 1 and Fig. 3, the Higgs boson with mass around 125 GeV is easier to be obtained with non-vanishing A-term. In the right of Fig. 3, we show the ratio of the lightest stau mass to the lightest neutralino mass in the Mmess vs. A plane. A neutralino LSP as well as a 125 GeV Higgs can

be achieved in a large parameter space with 106 GeV < Mmess < 107 GeV, as shown in the blank area in the right of Fig. 3. We should like to focus on neutralino DM in this parameter area.

In Fig. 4, Л = 1.5 x 105 GeV is fixed in order to be consistent with a 125 GeV Higgs boson. In the left, we show how the lightest stau mass mTl and the lightest neutralino mass m~ 0 depend

on the messenger scale in the range 106 GeV < Mmess < 107 GeV. In this range, mT1 is almost independent of the messenger scale and x? is actually a mixture of bino and higgsino. m~ 0 is sensitive

to the messenger scale because mx0 is dominated by the value

of ^,-term, which depends on Mmess. The exact value of ^,-term is determined by the correct EWSB. Due to the Xu corrections of mHu in Eq. (7), EWSB in this model is quite different from that in the minimal GMSB model. In the range 106 GeV < Mmess <

107 GeV, EWSB can be realized by two reasons. One is the negative A/Mmess-suppressed contribution of m2H at input scale and the other is the top Yukawa contribution in RGE running. In the range 1.5 x 106 GeV < Mmess < 8 x 106 GeV, the correct EWSB hints that /-term is less than 500 GeV, which makes j^0 lighter than T1. As it is a bino-higgsino DM, the corresponding DM relic density Qh2 has been shown in the right of Fig. 4. We can have a neutralino DM which is consistent with the WMAP experimental relic density result Qh2 = 0.1138 ± 0.0045 [102]. Though we fix A = 1.5 x 105 GeV in the above discussion, our conclusion is general. A relatively small /-term can be obtained in this model, which makes j^0 the LSP. So a bino-higgsino DM with correct relic density can be achieved. On the other hand, EWSB with a large tan p leads to the following constraint at the electroweak scale,

m\ ~-2(M2 + mHu).

Since the value of ^,-term is relatively small in this model, the cancellation between /x and mHu is correspondingly relatively small. There is a small fine-tuning to get the Z boson mass.

Finally, we take into account the updated bounds of DM direct searches. The current strictest bound of spin-independent cross section is recently given by the LUX Collaboration [69], who is the first to break the 10-45 cm2 cross section barrier of DM spin-independent detection. We also consider the existing upper limits of spin-dependent cross section. For this study, we scan the parameters in the Mmess vs. A plane and collect the points which have a Higgs boson with mass 123 GeV < mh < 127 GeV and a bino-higgsino DM with relic density 0.1 < Qh2 < 0.12. The results of DM direct searches are shown in Fig. 5. The left figure

Fig. 6. Mass spectrum of a benchmark point. In this case a bino-higgsino DM with right relic density is predicted.

is devoted to the spin-independent cross section. Our DM points are below the current experimental bounds, such as LUX [69] and XEN0N100 [110]. Interestingly, based on the proposals of future experiments, our DM points can be examined by future DM direct searches, such as LUX in 2015 [111] and XEN0N10T [112]. For the spin-dependent cross section, the results are shown in the right figure. Our DM points are far below the existing experimental bounds. For both spin-independent detection and spin-dependent detection, the cross section will become relatively small if DM is relatively heavy. That is because all other SUSY particles should be heavier than the LSP. DM with a relatively large mass will force overall sparticles to be relatively heavy.

4. Conclusion

In this paper, we have studied the neutralino DM in gauge mediation using the data after the run I of LHC and LUX. Neutralino can be the DM candidate in GMSB models if the conformal sequestered mechanism is introduced in the hidden sector. So the gravitino mass m3/2 can be fixed to 1 TeV without introducing any flavor violation problem. For the minimal GMSB model with sequestered SUSY breaking, the DM candidate can be a purely bino-like neutralino. In this case it is hard to achieve the correct relic density due to its relatively large mass. So we move forward to extending the minimal GMSB model by adding new Yukawa couplings between the messenger fields and the Higgs field Hu. In this extension, this sequestered mechanism can predict a good DM candidate as well as a 125 GeV Higgs boson. As an example, the mass spectrum of one benchmark point is shown in Fig. 6, which

is corresponding to m~0 = 688.4 GeV and Qh2 = 0.108. The initial

parameters are sign(p) =+1, n5 = 1, n10 = 1, tan p = 10, Xu = 1, A = 2 x 105 GeV and Mmess = 1.46 x 106 GeV. Thus for this case, the coupling is

Ш3/2 Mpl

■O (10

This k0 can be simply realized, for example, by assuming M1 = 2 x 106 GeV, M2 = 2 x 1016 GeV and ys = 2. ys = 2 can be achieved if the hidden sector is SP(3) x SP(1)2 model. All our survived points have some common features. Firstly, the light Higgs boson h is around 125 GeV and other Higgs bosons are heavy. So the Higgs sector falls into the decoupling MSSM limit. The properties of the light Higgs boson h are similar to the predictions of

the SM Higgs boson. Secondly, the correct EWSB hints a relatively small p-term, which makes the lightest neutralino lighter than the lightest stau. So a bino-higgsino DM with correct relic density can be achieved. The relatively small p-term results in a small fine-tuning of obtaining the Z boson mass. Finally, this bino-higgsino DM can pass all the existing bounds of both spin-independent and spin-dependent searches. Interestingly, the spin-independent cross section of our DM points can be examined by further dark matter experiments, such as LUX in 2015 and XENONIOT.

Acknowledgements

We would like to thank Qaisar Shafi, Ilia Gogoladze, Kai Wang, David Shih, Florian Staub and Jared Evans for very valuable discussions or comments. L.W. is supported by the DOE Grant No. DE-FG02-12ER41808.

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