Contents lists available at SciVerse ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Revisit to non-decoupling MSSM

Jiwei Ke, Hui Luo, Ming-xing Luo, Kai Wang *, Liucheng Wang, Guohuai Zhu

Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China

ARTICLE INFO

Article history:

Received 23 November 2012 Received in revised form 22 April 2013 Accepted 26 April 2013 Available online 30 April 2013 Editor: M. cvetic

ABSTRACT

Dipole operator sa/v F/xvb requires the helicity flip in the involving quark states thus the breaking of chiral U(3)q x U(3)d. On the other hand, the b quark mass generation is also a consequence of chiral U (3) q x U (3)d symmetry breaking. Therefore, in many models, there might be strong correlation between the b ^ sy and b quark Yukawa coupling. In this Letter, we use non-decoupling MSSM model to illustrate this feature. In the scenario, the light Higgs boson may evade the direct search experiments at LEPII or Tevatron while the 125 GeV Higgs-like boson is identified as the heavy Higgs boson in the spectrum. A light charged Higgs is close to the heavy Higgs boson which is of 125 GeV and its contribution to b ^ sy requires large supersymmetric correction with large PQ and R-symmetry breaking. The large supersymmetric contribution at the same time significantly modifies the b quark Yukawa coupling. With combined flavor constraints B ^ Xsy and Bs ^ //+/- and direct constraints on Higgs properties, we find best fit scenarios with light stop of 0(500 GeV), negative At around -750 GeV and large /-term of 2-3 TeV. In addition, reduction in bb partial width may also result in large enhancement of tt decay branching fraction. Large parameter region in the survival space under all bounds may be further constrained by H ^ tt if no excess of tt is confirmed at LHC. We only identify a small parameter region with significant H ^ hh decay that is consistent with all bounds and reduced tt decay branching fraction. In the end, if current dark matter mostly consists of neutralino, direct detection experiments like XEN0N100 also puts stringent bound over this scenario with light Higgs bosons. The light stops which are required by flavor constraints can further enhance the scattering cross section.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

A Higgs-like boson of 125 GeV has been discovered at the Large Hadron Collider (LHC) at CERN via two cleanest channels, the di-photon (gg ^ h ^ yy) and four-lepton (gg ^ h ^ ZZ* ^ £+£—£+£— with i, j = e±,/±) modes [1]. Later both ATLAS and CMS Collaborations also reported observations in the di-lepton (gg ^ h ^ WW* ^ £+vi£-vj) channels with the mass range consistent with the four-lepton measurement [2]. However, the confirmation of whether it is the Higgs boson of the standard model (SM) will require comprehensive and precise measurements of Higgs properties. The deviation of the Higgs couplings from the SM ones may imply the existence of the beyond SM physics, in particular, the excess in the di-photon channel with 0obs./0sM ~ 1.5-2.0 at both ATLAS and CMS. In all extension theories, additional charged and neutral scalars are inevitable. Therefore, searches of other Higgs-like states also provide direct test to models beyond SM physics. The LHC and Tevatron Collaborations [3] have put stringent bounds over the SM Higgs, particularly

* Corresponding author.

E-mail address: wangkai1@zju.edu.cn (K. Wang).

0370-2693/$ - see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016Zj.physletb.2013.04.056

heavy Higgs decaying into pure leptonic final states via WW and ZZ. For instance, CMS Collaboration has excluded the SM Higgs of 110-121.5 GeV and 128-600 GeV at 95% C.L. The LEPII experiments also exclude the SM Higgs with mass lower than 114 GeV via e+e- ^ Zh channel. These bounds at the same time apply to various models with Higgs extension.

For two decades, weak scale supersymmetry has been the most elegant candidate to cancel the quadratic divergence if the Higgs boson is indeed a fundamental scalar. Within the supersymmet-ric framework, there exist several scenarios where the di-photon decay branching fraction is enhanced, for instance, models with light stau [4] or light stop [5]. Another particularly interesting region of non-decoupling limit in minimal supersymmetric standard model (MSSM) has been discussed by various authors [6-14]. It was observed that there might exist even lighter Higgs h which evades the search at LEP [6] due to suppressed ZZh coupling and thus production of Zh. The light Higgs h can then have Mh < mZ while the Higgs-like boson of 125 GeV can be identified as the heavier degree of freedom H. To reduce the ZZh coupling gZZh = sin(^ — a) which is the vacuum expectation value (vev) of h, simple realization is to let h be the Hd-like boson since large mt naturally requires large vu. Given h is a mixture state as — sin a(Re Hd) + cos a(Re Hu), this scenario prefers sin a ~ — 1 and

large tan p which suppresses the Vd. In the limit of large tan p as sin p ^ 1, sin a 1 gives the sin(p — a) approaches zero. On the other hand, within MSSM, at tree level, the Higgs mass matrix gives

tan 2a tan

M2a + m2Z

MA — m2z'

Taking MA ^ 0 and the p ^ n/2 as limit of large tan p, one can get a ^ — it/2 which results in sin(p — a) ^ 0 and reproduce the previous requirement. For MA > 200 GeV, the gZZh goes to the SM value. However, since the charged Higgs state H± are at the similar scale as MH as M2H± = M2A + mW at tree level, small MA leads to lighter H± which suffers from direct search bounds of light charged Higgs. Drell-Yan production of charged Higgs pair at LEP e+e— ^ H+ H— put strict bounds as MH± > 80-100 GeV depends on its decay [15]. Combining all the constraints, one expect an intermediate MA region around mz scale to be consistent with the LEPII Zbb search and charged Higgs search at LEP, Tevatron and LHC. In the limit of MA ^ mZ, h and H masses at tree level are degenerate which is known as non-decoupling limit.

By requiring MH to be at 125 GeV, the first consequence of these non-decoupling scenarios is that the charged Higgs is around similar scale. Charged scalar below top quark mass receives stringent bound from the ATLAS search of t ^ bH+ with H + ^ t + v requires the BR(t ^ bH+) x BR(H + ^ t +vt) < 1-5% for mass range MH± in between 90 and 160 GeV [16]. In the conventional Two-Higgs-Doublet models (2HDM) such a light charged Higgs suffer severe constraints due to flavor violation processes [17]. For example, one might be concerned by Bu ^ Tvt and B ^ D(*)tvt decays which receive charged Higgs contributions at the tree level. The two most sensitive parameters involved in Higgs interaction are MA and tan p. As we argued, MA is taken to be not much heavier than mZ and LEP2 Zh search prefers a relatively large tan p. In addition, as we will show later, the recent search of t ^ bH+ at the LHC restricts tan p ~ 10 in non-decoupling region. For Bu ^ tvt decay, the W±-mediated SM contribution is helicity suppressed. Therefore, even though the charged scalar is somewhat heavier, its contribution could be comparable to the SM part if tan p is not small [18-20]:

T + v) MSSM

t+v)sm

tan2 p

where the MSSM corrections to the down quark and lepton mass matrix have been neglected, which is safe for tan p ~ 10. For MH+ lies around 120-150 GeV, the MSSM prediction would be about 20-30% smaller than the SM result of (0.95 ± 0.27) x 10—4. While the experimental world average is (1.65 ± 0.34) x 10—4 before 2012 [21], Belle updated their measurement at ICHEP2012 with much smaller value

0.72+0.27 x 10—4 for hadronic tag of t .So in

the non-decoupling limit, a light charged Higgs with tan p ~ 10 is well consistent with the new Belle measurement. Similarly, the charged Higgs contribution to B ^ D (*)tvt decays are not very significant in the interesting region of MH+ and tan p. Therefore we will not discuss the bounds from B + ^ t +v and B ^ D(*)tvt decays further in our study.

On the other hand, the penguin b ^ s processes are also sensitive to the charged Higgs effects. Generally, b ^ sy and Bs ^ ¡i+are two most stringent constraints. But choosing appropriate MSSM parameters, supersymmetric contributions may cancel part of the SM and charged Higgs amplitudes [23]. For example, b ^ s transition mediated by the scalar top quark (stop) loop in MSSM may cancel the top quark loop in SM and 2HDM in some parameter region. One can thus expect that light stop in MSSM

may significantly reduce the flavor violation [24]. In this Letter, we start with this argument and study whether scenarios with light stop can resolve the tension in flavor physics due to the light charged Higgs H ±.

Search of ¡i ^ ey at the MEG experiment will soon reach BR(^ ^ ey ) — 1 x 10—13. The one loop contribution from charged state to i ^ ey is suppressed by small lepton masses and additional helicity flip. The largest contribution in Higgs mediated l ^ ey is usually the Barr-Zee two-loop effects involving the charged scalar coupling to a top-bottom loop. However, [25] shown that the charged Higgs contribution only reaches the sensitivity for tan p of 60 for MA of 100 GeV where the tan p is much larger than what is considered in non-decoupling scenarios.

With conserved R -parity, the thermal relic abundance of the lightest neutralino (LSP) can often be identified with dark matter (DM), consistent with the current cosmological observations. In recent years, direct detection of weakly interacting (WIMP) DM particle through the DM scattering with nuclei has excluded large parameter space of supersymmetric DM and put stringent bound on many models. The latest bound from XEN0N100 is about 5 x 10—9 pb for DM mass around 200 GeV [26]. Neutral Higgs states h, H can also mediate the scattering between DM and nuclei which is of 1/M4H. Then the second consequence of non-decoupling scenarios is that the spin-independent scattering is significantly enhanced by the interaction through neutral Higgs H, A of 0(100 GeV) [27]. Therefore, models with only neutralino DM in the non-decoupling MSSM suffer stringent constraints from direct detection experiments. In addition, light stop which may significantly improve the flavor physics behavior of non-decoupling MSSM as argued above, would further enhance the scattering of DM and nuclei and put stronger bound on non-decoupling scenarios with only neutralino DM.1

In the next section, we discuss some general constraints on the non-decoupling scenarios and the scan results. Then we discuss in details the physics interpretation of the scan results, in particular, light stop contribution to cancel light charged Higgs and its implication to MH, di-photon, di-tau decay and the direct detection experiments of neutralino dark matter. We then conclude in the final section.

2. General constraints and their implications

In this section, we first scan the parameter space with focus on non-decoupling region with MA is at 0(mZ) then discuss in details the physics interpretation of scan results.

Latest data from the LHC require the resonance to be at 125 GeV with di-photon decay enhanced with respect to the SM prediction. We therefore impose the selection rules as

• Mh : 125 ± 2 GeV;

Rvv = o.

YY IrrYY-

— Irr'

RYY = "obs/0SM

• Combined direct search bounds from HiggsBound3.8.0;

• BR(B ^ Xsy) < 5.5 x 10—4;

• BR(Bs ^ ) < 6 x 10—9.

Without loss of generality, we fix masses of the following sfermions as

MQ = Mu12 = M~, = ML = Me12 3 = 1 TeV, (3)

Q. 12 u 1,2 <11,2,3 L 1,2,3 e1,2,3 ' v '

and the gauginos as

1 If the DM is not dominated by the neutralino component, the bound can be evaded.

3.0 2.5 2.0

1.0 0.5

M-tL =

M~tR = 1000 GeV

Ma : 95 GeV— 150 GeV tan/8:1 — 30

-1 0 *f(TeV)

3.0 r 2.52.0-

a. ■ 1.00.5-

M-tL = M-tR = 500 Ge\

: 95 GeV— 150 GeV taiv8:1 -- 30

-1 0 1

•Af(TeV)

Fig. 1. Scan results in [At, /] plane. The heavy (light) stop scenario with Mq3 = M{ = 1 (0.5) TeV is shown in the left (right) plot. The red region pass the direct search bounds from HiggsBounds with a heavy CP-even Higgs MH = 125 ± 2 GeV and an enhanced di-photon rate 1 < Ryy < 2. The blue region pass in addition the constraint of BR(B ^ Xsy), while the black region pass all the constraints, including further the restriction of BR(Bs ^ /+/-). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

Ml = 200 GeV, M2 = 400 GeV, M3 = 1200 GeV. (4) Higgs M h = 125 ± 2 GeV and an enhanced di-photon rate 1 <

As argued, our study focus on the flavor constraints of the non-decoupling MSSM and b ^ s transitions like B ^ Xsy and Bs ^ /+provide the most severe constraints. Light stop usually helps to cancel the charged Higgs contribution in b ^ s transition. On the other hand, for light stop below 500 GeV, we find that the gluon fusion production of H is suppressed significantly with respect to the SM value due to the cancellation between top squark and top quark in the loop. Thus, for light stop (M~t < 500 GeV), it is difficult to achieve enhanced di-photon. For comparison, we take the third generation up quark masses as

M^3 = Mt = 500 GeV and a second group with 1 TeV. (5)

We do the scan over four parameters2

MA: 95-150 GeV, tan p: 1-30, /: 200 GeV-3 TeV,

Au = Ad = A£:- 3-3 TeV. (6)

Discussed by many authors [4], light stau states may significantly enhance the di-photon rate of the Higgs-like boson decay which are observed by both ATLAS and CMS Collaborations. On the other hand, we don't require much stronger di-photon bound as Ryy to be the experimental preferred central value of 1.5. Stau states are irrelevant to the flavor constraints from b ^ s transition but only give minor change to the Higgs boson mass. Therefore, we don't take light stau in the study.

We use FeynHiggs 2.9.2 [28]3 with HiggsBounds 3.8.0 [29] and SUSY_Flavor 2.01 [30] to perform the scan here. Fig. 1 shows the scan results in 2D-plot of At and /. MA and tanp are also varied but aren't shown in the figures. Fig. 1(a) is the heavy stop scenario with M^3 = M~t = 1 TeV and (b) is the light stop scenario with Mq = Mt = 500 GeV. Points in red region pass the direct search bounds from HiggsBounds with a heavy CP-even

2 We confine ourselves to MA < 150 GeV for larger splitting between h and H which can reduce the tt decay branching ratio. Details is discussed later.

3 In this scan, we take the pole mass of mt instead of the running mt mass. The

survival parameter region after scan may be shifted by a few percent.

Rrr < 2. The points in blue region pass in addition the constraint of BR(B ^ Xsy), while the points in black region pass all the constraints, including further the restriction of BR(Bs ^ fi+

The scenario with heavy stop can survive the B ^ Xsy constraints. However, none of the scanned points can pass the Bs ^ ¡i+. In the case of light stop of 500 GeV, we find a small survival parameter region with negative At around 750 GeV and large /-term between 2 and 3 TeV. In the following subsections, we discuss in details the physics implications of the scanned results.

2.1. b ^ sy and Bs ^ ¡i+

b ^ sy and Bs ^ ¡x+ turn out to be the most stringent flavor physics bounds in the non-decoupling limit. The helicity for the involved quark states must be flipped in b ^ sy. Hence, both chiral symmetry U(3)q x U(3)d and electroweak symmetry SU(2)l x U(1)Y must be broken. The SM b ^ s transition is mediated by the charged weak boson W— and only left-handed quarks are involved in the weak interaction. Consequently, b ^ sy is suppressed by mass insertion of bottom quark mass mb in the SM. In MSSM, the charged Higgs H—-top quark loop contribution to b ^ sy is also suppressed by mb insertion, and has the same sign as the SM amplitude. Besides the above contributions, squarks can also generate b ^ sy in MSSM which may not flip the helicity of the involved quark states, for instance, loops with right-handed stop-Higgsino (tR — Hu ) or left-handed stop-Wino (tL — W). Therefore the squark contributions, in particular the top squark ones, are not necessarily suppressed by mb, which is helpful to cancel the SM and charged Higgs amplitudes with appropriate MSSM parameters. Consequently, scalar top quark with small M~t, say ~ 500 GeV, could significantly reduce b ^ s transition.

The squark contributions can be decomposed into chargino penguins, wino penguins and gluino penguins. Chargino penguins contain tan p-enhanced term which arises from Vu insertion in Qdc(H*). The term explicitly breaks Peccei-Quinn symmetry as well as R-symmetry and is proportional to /At. This contribution would destructively interfere with the SM and charged Higgs amplitudes in case of /At < 0 [31,32]. In our study, gluino penguins are also important as they contain terms enhanced by / tan p and terms chirally enhanced by mg/mb. Numerically, we use the FeynHiggs program to get the non-MFV result of BR(B ^ Xsy). The experimental world average of this process is (3.43 ± 0.22) x 10—4

[21], while the SM prediction up to NNLO perturbative QCD corrections is (3.15 ± 0.23) x 10—4 [33]. However, B ^ Xsy decay is evaluated only at NLO in the FeynHiggs program, which produces the SM result as 3.8 x 10—4. This is about 30% larger than the NNLO SM prediction. Taking this and the theoretical and experimental uncertainties into account, we require loosely BR(B ^ XsY)mssm < 5.5 x 10—4 as the selection rule in the scan.

In the SM, BR(Bs ^ fi+¡—) is strongly helicity suppressed by the small muon mass as m^/mB^, which leads to a tiny branching ratio of (3.27 ± 0.23) x 10—9 [34]. However, it is well known that the MSSM contributions to this decay could be enhanced several orders of magnitude larger than the SM prediction in large tan fi limit, as the leading contribution of Higgs penguin diagrams to the branching ratio are proportional to tan6 fi. In our study, tan fi ~ 10 is not very large, so all the 1-loop diagrams have to be considered, including the charged Higgs diagrams which is enhanced up to tan2 fi at the amplitude level. Notice that Bs ^ de-

cay is even more sensitive to the MSSM parameters in the non-decoupling limit as the neutral Higgs bosons are all light. Experimentally, a combined search of ATLAS, CMS and LHCb has set the upper limit of 4.2 x 10—9 for time integrated branching ratio. As pointed out in [36,37], this upper limit should be reduced by about 10% when compared with the theoretical calculation. Numerically, we use the SUSY_FLAVOR program [30] to get the complete NLO result of BR(Bs ^ ). However, we notice

that SUSY_FLAVOR evaluates this branching ratio to be 4.8 x 10—9 in the SM. This is about 50% larger than the SM prediction of (3.27 ± 0.23) x 10—9 in [34], probably mainly due to different choice of hadronic parameters. Taking this into account, we set the corresponding selection rule to be BR(Bs ^ ¡—)MSSM < 6 x 10—9 in the scan.

In Fig. 1, the black region which satisfy all the constraints give 104BR(B ^ XsY)mssm in the region [4.9, 5.3] and 109BR(BS ^ )MSSM in the region [2.3, 4.3]. Notice that BR(B ^ Xsy) is always larger than the SM prediction, which is mainly due to the enhancement of light charged Higgs. For BR(Bs ^ ), it is al-

ways somewhat smaller than the SM prediction.

2.2. Higgs mass and its decay properties

We discuss the mass spectrum of the Higgs bosons in non-decoupling MSSM and its decay properties in this section. More general discussion can be found in [38]. In particular, we focus on the parameter region that minimizes the flavor violation in b ^ s transition. Combined constraints from B ^ Xs y and Bs ^ , we take light stop of M~t ~ 500 GeV with negative

At of 0(-750 GeV) and large ¡-term of 2-3 TeV. MSSM contains two SU(2)l doublets Hu and Hd with the ratio of their vevs tan fi = vu /vd. To evade LEPII bounds, non-decoupling limit corresponds to a region of much lighter Hd state with small vev in the spectrum. After spontaneously electroweak symmetry breaking, MSSM gives rise to five physical states of Higgs bosons, the two CP-even scalar h, H with one CP odd scalar state A and charged scalars H±. The two CP-even scalar bosons h, H arise from mixing of the real gauge eigenstates (Re Hd, Re Hu),

h\_ / — sin a cos a\ /Re H J = y cos a sin a J y Re Hu J '

After diagonalizing the general mass matrix of neutral Higgs

M2 = (^

\M221 m222 the masses of two CP-even Higgs are

M2 = M11 sin2 a + M22 cos2 a — M\2 sin 2a

MH = M2n cos2 a + M22 sin2 a + M22 sin 2a.

To illustrate the feature, we take the limit of sin(f — a) ^ 0 which is the vanishing limit of gZZh to completely suppress the Zh production at LEPII. As a result of sin a ^ —1 and sin f ^ 1, we have

Mh ~ M11, M h ~ M22.

Radiative corrections to the elements in mass matrix Eq. 9 are given in [39]. We list the most relevant M22 in Eq. 11

M H ~ m2

~ M2 cos2 f + m2Z sin2 f ( 1 — y2t

+g12-2 p\t

M SUSY

V2 yt 2 f

b sin2 f 1

1 + ^ (1.5 y2 + 0.5 y2 — 8 g32)

1 + ^ (3 y2 + yb — 16g3)

Mt M SUSY

1 + ^(9 y2 —5 y2 —16 g3)

where g3 is the QCD running coupling constant, yt and yb are the top and bottom Yukawa couplings. MSUSY is the arithmetic mean of top squark masses M-t. At is the SUSY breaking A-term associated with top squark and i is the Higgsino mass parameter. t is defined

as ln(M2USY/mj) and

a = At — fi/ tan f.

In Eq. (11), only the leading terms in powers of yb and tan fi have been retained. Even though the Eq. (11) is only valid in the limit of small splittings between the running stop masses, it shows the qualitative feature for how couplings to stop and sbottom modify the Higgs masses. MA is cos fi dependent which is suppressed in the limit of large tan fi. Therefore, the MH is not very sensitive to MA and with tan fi ~ 10, varying MA by 100 GeV results in 10 GeV difference in MH. Unlike the m™x scenario with a = V6MSUSY which is usually used in many studies, minimization of the flavor violating b ^ s transition leads to our best fit parameter region around

At ~ —750 GeV, Mt ~ 500 GeV, i ~ 2000-3000 GeV.

The particular choices of At and Mtt significantly modifies the Higgs boson masses through radiative corrections. In our studies, we use the FeynHiggs program to compute the mass spectrum of Higgs in which full radiative corrections of Higgs masses have been implemented [28]. Fig. 2 shows how the Mh,H,H± vary with respect to MA for one of our benchmark points tan fi = 11, Mtt = 500 GeV, At = —740 GeV and i = 2300 GeV. For a large range of MA, MH is around 125 GeV. Non-decoupling limit of nearly degenerate h, H lies near MA ~ 160 GeV.

Since H is mostly Hu with large tan fi, the vu dominates the electroweak symmetry breaking v. The couplings between H and W + W— and top quark t are similar to their SM values. Since the di-photon decay is dominated by the W -boson contribution, the di-photon decay partial width is not changed significantly from the SM FSM(H ^ yY). However, di-photon decay branching fraction BR(H ^ YY) may still be enhanced due to decrease of H

in (0 a

MEl = MEr = 500 GeV H = 2300RGeV At = -740 GeV tan/?=ll

140 160 180 200 220 240

M>i(GeV)

Fig. 2. Mh,H,H± vary with respect to MA for Mt tan p = 11,,// = 2300 GeV.

: 500 GeV, At = -740 GeV,

total width. At 125 GeV, H ^ bb and H ^ WW*, H ^ ZZ* dominate the H decay. Since H is mostly Hu-like, H coupling to b is naturally suppressed. Given vu ~ v, gHZZ and gHWW are not significantly changed from the SM g^MZ and ghWW. The partial widths of H ^ WW* and H ^ ZZ* are indifferent from the SM values. With the reduction in H ^ bb, the increase of H ^ WW* and H ^ ZZ* are inevitable. Therefore, light stau states in the spectrum can improve the di-photon behavior RYY and reduce the tension in increasing ZZ* or WW*.

Discussed in [10], in the non-decoupling limit when H ^ bb still dominates the H decay, H ^ t +t - can be significantly enhanced.

Rtt~ r

1 + Ab

1 + Ab (1 - e)

where e = 1 + tan a/ tan p with a < 0, Ab is from the radiative correction in bottom Yukawa, rgg is the ratio in gluon fusion production of H which is order 1 in relatively large tan p and Mt > 500 GeV. With the radiative correction, Hbb coupling is

gHbb =

1 + Ab

tan a tan p

Similar to the story of //At in b ^ s transition, Ab also breaks Peccei-Quinn symmetry and R-symmetry at the same time. In this case, Ab contains two R -symmetry breaking pieces as gluino mass Mg and A-term contribution. Our choice of /At < 0 results in cancellation between the two contribution but the enhancement to R TT is still significant. Our results also confirm the finding in [10] with many points of enhanced H ^ tt decay. Fig. 3 shows the correlation between BR(H ^ t+t-) and BR(H ^ bb) in the survival points. On the other hand, we also find many points with Rtt < 1. One particularly interesting feature around non-decoupling limit is that H ^ hh decay may open up and take significant portion of the H decay. In large parameter region, H ^ hh decay partial width may completely dominate the decay of H once it opens up. Discussed in [41], the tree level H ^ hh decay and one loop contributions may have different signs and severely cancel each other.4 There then exists a very fine tuned parameter region that the r(H ^ hh) is at similar order as other decay and only takes about 50%of H decay. If H ^ hh decay occurs, h can further decay into bb or tt, the search of H then fall

4 The result is based on full one loop calculation in [41] and stability of the result may require higher order calculation.

,4 0.6 0.8 1.0

Fig. 3. BR(H ^ t+t-) in correlation with BR(H ^ bb). 0.020

ATLAS Observed CLs Data2011 7TeV 4.6 fb"1

130 140 150 160 M„*( GeV)

Fig. 4. BR(t ^ bH+) vs MH± by assuming BR(H + ^ t+ vt) = 100%. Red dots are parameter points that pass all our selection and constraints. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

into the 4b, 4t or 2b2T channels. The phenomenology of such channels has been widely studied in the context of NMSSM with h ^ AA search [40]. Studies of h ^ AA in NMSSM show that for Mh ~ 120 GeV, it requires the 14 TeV LHC with at least 100 fb-1 of data to claim discovery. Therefore, we argue the H ^ hh decay is not constrained by any current direct search experimental data from LHC. In Fig. 3, all the points R TT < 1 bare the same feature as BR(H ^ hh) ~ 50%. Among these points, predictions on WW* and ZZ* are also slightly higher than the SM values but mostly within 1.5 which is consistent with the experimental data. The current search of H ^ tt at ATLAS is still with large error bar and consistent with these large numbers of 2 aTM However, CMS Collaboration has reported their latest data that exclude the SM tt rate by 1 a [42]. If one takes this seriously, most of our final survival parameter region will be cut away and only a few points that with significant H ^ hh decay can survive. In addition, the H ^ bb are highly suppressed in these points and the predictions of these points agree with ATLAS central values of R in all channels very well. In principle, the choice of MA can be extended to 0(200 GeV) in our study and the flavor bounds are less constrained for larger MA. However, the larger MA region corresponds to the enhanced R TT region. Only smaller MA generates larger splitting between H and h which reduces R TT. Therefore, we only focus on the region MA < 150 GeV.

\ Mr = Mr = 500 GeV

v L t:R

f 10"8 XENON100(2012)"--^., ® - 'i—^

M£l = MEe = 1000 GeV

-ml.......

130 140

150 160 Afj(GeV)

170 180

Fig. 5. Spin-independent scattering between neutralino dark matter and the nuclei computed for XENONIOO by varying MA. Red dashed line is in the case of light stop of 500 GeV and the blue dotted line corresponds to the stop mass of 1 TeV. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this Letter.)

Besides the direct search via tt, LHC has put much stronger bounds on t ^ bH+ with H + ^ t+ vt comparing with Tevatron. The previous Tevatron upper bound of BR(t ^ bH+) is 5% while the latest ATLAS results become 1-5%. We plot the BR(t ^ bH+) with respect to MH± by assuming BR(H + ^ t +vt) = 100% in Fig. 4. It clearly shows that all the parameter points that pass our selections are below the search of light charged Higgs boson via top decay t ^ bH+ with H + ^ t+vt .

2.3. Oj n

Finally we discuss the last constraint for non-decoupling MSSM. Latest direct dark matter detection experiments XEN0N100 have reached the level of sensitivity needed to detect neutralino dark matter over a substantial range of supersymmetric parameter space. These experiments attempt to detect weakly interacting (WIMP) dark matter particles through their elastic scattering with nuclei. Neutralinos can scatter with nuclei through both scalar (spin-independent) and axial-vector (spin-dependent) interactions. The experimental sensitivity to scalar couplings benefits from coherent scattering, which leads to cross sections and rates proportional to the square of the atomic mass of the target nuclei which is exactly being used for direct detection experiments. Consequently the spin-independent interactions are far more important than the spin-dependent in these experiments. In MSSM, the spin-independent interactions are mediated by the light Higgs bosons with cross section proportional to

tan2 fi

IMf ■

Fig. 5 has shown the spin-independent scattering between neutralino dark matter and the nuclei computed for XEN0N100 setup by varying MA for pure-bino of 200 GeV to illustrate the enhancement feature due to light Higgs bosons and light top squarks. The calculation is done using micrOMEGAs 2.4 [43]. It clearly shows the enhancement of such interaction in small MA. In addition, squark can induce neutralino-gluon scattering which can further enhance the scattering cross section [44]. The two lines for different stop mass choices of 500 GeV and 1 TeV also indicate the enhancement of light stop in the neutralino-nuclei scattering. For most of our points with 500 GeV stop and MA < 170 GeV, XEN0N100 bounds have put stringent constraints over the scenario. On the

other hand, it is not clearly whether the current dark matter completely consists of supersymmetric neutralino. The bounds can also be easily evaded by adding new component of dark matter from non-supersymmetric origin.

3. Conclusions

In this Letter, we discuss the non-decoupling MSSM scenario where a light Higgs boson can evade the direct search experiments at LEP or Tevatron and the 125 GeV Higgs-like boson is explained as the heavy Higgs boson in the spectrum. The light Higgs boson may evade the direct search experiments at LEPII or Tevatron while the 125 GeV Higgs-like boson is identified as the heavy Higgs boson in the spectrum. Two direct consequences of the scenario are the flavor violation induced by the light charged scalar and the spin-independent scattering between neutralino and nuclei in dark matter direct detection experiments. With combined flavor constraints B ^ Xsy and Bs ^ ¡x+ and direct constraints on Higgs properties, we find best fit scenarios with light stop of 0(500 GeV), negative At around -750 GeV and large ^,-term of 2-3 TeV. However, large parameter region in the survival space under all bounds may be further constrained by H ^ tt if no excess of tt is confirmed at LHC. We only identify a small parameter region with significant H ^ hh decay that is consistent with all bounds and reduced tt decay. In addition, if current dark matter mostly consists of neutralino, direct detection experiments like XENON100 also puts stringent bound over this scenario with light Higgs bosons. The light stops which are required by flavor constraints can further enhance the scattering cross section.

Note added in proof

When completing our work, arXiv:1211.1955 [hep-ph] [45] has appeared. The paper also studied similar region of non-decoupling MSSM and the results are in agreement with ours. We also include study on its enhancement of spin-independent neutralino-nuclei scattering. In addition, we find new parameter region which corresponds to reduce Rtt due to H ^ hh decay.

Acknowledgements

ML is supported by the National Science Foundation of China (11135006) and National Basic Research Program of China (2010CB833000). KW is supported in part, by the Zhejiang University Fundamental Research Funds for the Central Universities (2011QNA3017) and the National Science Foundation of China (11245002, 11275168). GZ is supported in part, by the National Science Foundation of China (11075139, 11135006) and Program for New Century Excellent Talents in University.

References

[1] G. Aad, et al., ATLAS Collaboration, Phys. Lett. B 716 (2012) 1, arXiv:1207.7214 [hep-ex];

S. Chatrchyan, et al., CMS Collaboration, Phys. Lett. B 716 (2012) 30, arXiv: 1207.7235 [hep-ex].

[2] ATLAS Collaboration, ATLAS-C0NF-2012-098.

[3] CDF Collaboration, arXiv:1207.0449 [hep-ex];

V.M. Abazov, et al., D0 Collaboration, arXiv:1207.0422 [hep-ex].

[4] M. Carena, S. Gori, N.R. Shah, C.E.M. Wagner, JHEP 1203 (2012) 014, arXiv: 1112.3336 [hep-ph];

M. Carena, S. Gori, N.R. Shah, C.E.M. Wagner, L.-T. Wang, JHEP 1207 (2012) 175, arXiv:1205.5842 [hep-ph];

J. Ke, M.-X. Luo, L.-Y. Shan, K. Wang, L. Wang, arXiv:1207.0990 [hep-ph].

[5] M.R. Buckley, D. Hooper, arXiv:1207.1445 [hep-ph].

[6] A. Belyaev, Q.-H. Cao, D. Nomura, K. Tobe, C.-P. Yuan, Phys. Rev. Lett. 100 (2008) 061801, arXiv:hep-ph/0609079.

[7] S. Heinemeyer, O. Stal, G. Weiglein, Phys. Lett. B 710 (2012) 201, arXiv: 1112.3026 [hep-ph].

[8] A. Bottino, N. Fornengo, S. Scopel, Phys. Rev. D 85 (2012) 095013, arXiv: 1112.5666 [hep-ph].

[9] N.D. Christensen, T. Han, S. Su, Phys. Rev. D 85 (2012) 115018, arXiv:1203.3207 [hep-ph].

10] K. Hagiwara, J.S. Lee, J. Nakamura, arXiv:1207.0802 [hep-ph].

11] R. Benbrik, M.G. Bock, S. Heinemeyer, O. Stal, G. Weiglein, L. Zeune, arXiv: 1207.1096 [hep-ph].

12] A. Arbey, M. Battaglia, A. Djouadi, F. Mahmoudi, JHEP 1209 (2012) 107, arXiv:1207.1348 [hep-ph].

13] G. Belanger, U. Ellwanger, J.F. Gunion, Y. Jiang, S. Kraml, J.H. Schwarz, arXiv:1210.1976 [hep-ph].

14] M. Drees, arXiv:1210.6507 [hep-ph].

15] LEP Higgs Working Group for Higgs boson searches, ALEPH Collaboration, DELPHI Collaboration, L3 Collaboration, OPAL Collaboration, arXiv:hep-ex/0107031.

16] G. Aad, et al., ATLAS Collaboration, JHEP 1206 (2012) 039, arXiv:1204.2760 [hep-ex].

17] U. Haisch, F. Mahmoudi, arXiv:1210.7806 [hep-ph].

18] W.-S. Hou, Phys. Rev. D 48 (1993) 2342.

19] A.G. Akeroyd, S. Recksiegel, J. Phys. G 29 (2003) 2311, arXiv:hep-ph/0306037.

20] G. Isidori, P. Paradisi, Phys. Lett. B 639 (2006) 499, arXiv:hep-ph/0605012.

21] Y. Amhis, et al., Heavy Flavor Averaging Group Collaboration, arXiv:1207.1158 [hep-ex], and online update at http://www.slac.stanford.edu/xorg/hfag.

22] M. Nakao, talk presented at 36th International Conference on High Energy Physics, Melbourne, 4-11 July, 2012.

23] J.-J. Cao, Z.-X. Heng, J.M. Yang, Y.-M. Zhang, J.-Y. Zhu, JHEP 1203 (2012) 086, arXiv:1202.5821 [hep-ph].

24] M.A. Ajaib, I. Gogoladze, Q. Shafi, arXiv:1207.7068 [hep-ph].

25] J. Hisano, S. Sugiyama, M. Yamanaka, M.J.S. Yang, Phys. Lett. B 694 (2011) 380, arXiv:1005.3648 [hep-ph].

26] E. Aprile, et al., XEN0N100 Collaboration, Phys. Rev. Lett. 109 (2012) 181301, arXiv:1207.5988 [astro-ph.CO].

27] M.S. Carena, D. Hooper, A. Vallinotto, Phys. Rev. D 75 (2007) 055010, arXiv:hep-ph/0611065.

28] M. Frank, T. Hahn, S. Heinemeyer, W. Hollik, H. Rzehak, G. Weiglein, JHEP 0702 (2007) 047, arXiv:hep-ph/0611326;

G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich, G. Weiglein, Eur. Phys. J. C 28 (2003) 133, arXiv:hep-ph/0212020;

S. Heinemeyer, W. Hollik, G. Weiglein, Eur. Phys. J. C 9 (1999) 343, arXiv:hep-ph/9812472;

S. Heinemeyer, W. Hollik, G. Weiglein, Comput. Phys. Commun. 124 (2000) 76, arXiv:hep-ph/9812320.

[29] P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K.E. Williams, Comput. Phys. Commun. 181 (2010) 138, arXiv:0811.4169 [hep-ph];

P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K.E. Williams, Comput. Phys. Commun. 182 (2011) 2605, arXiv:1102.1898 [hep-ph].

[30] A. Crivellin, J. Rosiek, P.H. Chankowski, A. Dedes, S. Jaeger, P. Tanedo, arXiv: 1203.5023 [hep-ph].

[31] R. Barbieri, G.F. Giudice, Phys. Lett. B 309 (1993) 86, arXiv:hep-ph/9303270.

[32] M.S. Carena, M. Olechowski, S. Pokorski, C.E.M. Wagner, Nucl. Phys. B 426 (1994) 269, arXiv:hep-ph/9402253.

[33] M. Misiak, H.M. Asatrian, K. Bieri, M. Czakon, A. Czarnecki, T. Ewerth, A. Ferroglia, P. Gambino, et al., Phys. Rev. Lett. 98 (2007) 022002, arXiv:hep-ph/0609232.

[34] A.J. Buras, J. Girrbach, D. Guadagnoli, G. Isidori, arXiv:1208.0934 [hep-ph].

[35] CMS Collaboration, CMS-PAS-BPH-12-009.

[36] K. De Bruyn, R. Fleischer, R. Knegjens, P. Koppenburg, M. Merk, N. Tuning, Phys. Rev. D 86 (2012) 014027, arXiv:1204.1735 [hep-ph].

[37] K. De Bruyn, R. Fleischer, R. Knegjens, P. Koppenburg, M. Merk, A. Pellegrino, N. Tuning, Phys. Rev. Lett. 109 (2012) 041801, arXiv:1204.1737 [hep-ph].

[38] A. Djouadi, Phys. Rept. 459 (2008) 1, arXiv:hep-ph/0503173.

[39] M.S. Carena, J.R. Espinosa, M. Quiros, C.E.M. Wagner, Phys. Lett. B 355 (1995) 209, arXiv:hep-ph/9504316.

[40] M. Carena, T. Han, G.-Y. Huang, C.E.M. Wagner, JHEP 0804 (2008) 092, arXiv: 0712.2466 [hep-ph].

[41] K.E. Williams, H. Rzehak, G. Weiglein, Eur. Phys. J. C 71 (2011) 1669, arXiv:1103.1335 [hep-ph];

K.E. Williams, G. Weiglein, Phys. Lett. B 660 (2008) 217, arXiv:0710.5320 [hep-ph].

[42] CMS PAS HIG-12-018.

[43] G. Bélanger, F. Boudjema, P. Brun, A. Pukhov, S. Rosier-Lees, P. Salati, A. Se-menov, Comput. Phys. Commun. 182 (2011) 842, arXiv:1004.1092 [hep-ph].

[44] M. Drees, M.M. Nojiri, Phys. Rev. D 47 (1993) 4226, arXiv:hep-ph/9210272.

[45] P. Bechtle, S. Heinemeyer, O. Stal, T. Stefaniak, G. Weiglein, L. Zeune, arXiv: 1211.1955 [hep-ph].