Revisit to Non-decoupling MSSM

Dipole operator $\bar{s}\sigma_{\mu\nu}F^{\mu\nu}b$ requires the helicity flip in the involving quark states thus the breaking of chiral $U(3)_{Q}\times U(3)_{d}$. On the other hand, the $b$-quark mass generation is also a consequence of chiral $U(3)_{Q}\times U(3)_{d}$ symmetry breaking. Therefore, in many models, there might be strong correlation between the $b\to s\gamma$ and $b$ quark Yukawa coupling. We use non-decoupling MSSM model to illustrate this feature. 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 $b\to s \gamma$ 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 co upling. With combined flavor constraints $B\to X_{s}\gamma$ and $B_{s}\to \mu^{+}\mu^{-}$ and direct constraints on Higgs properties, we find best fit scenarios with light stop of $\cal O$(500 GeV), negative $A_{t}$ around -750 GeV and large $\mu$-term of 2-3 TeV. In addition, reduction in $b\bar{b}$ partial width may also result in large enhancement of $\tau\tau$ decay branching fraction. Large parameter region in the survival space under all bounds may be further constrained by $H\to \tau\tau$ if no excess of $\tau\tau$ is confirmed at LHC. We only identify a small parameter region with significant $H\to hh$ decay that is consistent with all bounds and reduced $\tau\tau$ decay branching fraction.


I. 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 → γγ) and four-lepton (gg → h → ZZ * → ℓ + i ℓ − i ℓ + j ℓ − j with i, j = e ± , µ ± ) modes [1]. Later both ATLAS and CMS collaboration also reported observations in the di-lepton (gg → h → W W * → ℓ + i ν i ℓ − jν j ) 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 measure- 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 supersymmetric 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][7][8][9][10][11][12][13][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 M h < m Z while the Higgs-like boson of 125 GeV can be identified as the heavier degree of freedom H. To reduce the ZZh coupling g ZZh = sin(β − α) which is the vacuum expectation value (vev) of h, simple realization is to let h be the H d -like boson since large m t naturally requires large v u . Given h is a mixture state as − sin α(Re H d ) + cos α(Re H u ), this scenario prefers sin α ≃ −1 and large tan β which suppresses the v d . In the limit of large tan β as sin β → 1, sin α → −1 gives the sin(β − α) approaches zero. On the other hand, within MSSM, at tree level, the Higgs mass matrix gives tan 2α tan 2β Taking M A → 0 and the β → π/2 as limit of large tan β, one can get α → −π/2 which results in By requiring M H 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 + → τ + ν requires the BR(t → bH + ) × BR(H + → τ + ν τ ) < 1 ∼ 5% for mass range M H ± 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 B u → τ ν τ and B → D ( * ) τ ν τ decays which receive charged Higgs contributions at the tree-level. The two most sensitive parameters involved in Higgs interaction are M A and tan β. As we argued, M A is taken to be not much heavier than m Z and LEP2 Zh search prefers a relatively large tan β. In addition, as we will show later, the recent search of t → bH + at the LHC restricts tan β ∼ 10 in non-decoupling region. For B u → τ ν τ 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 β is not small [18][19][20]: where the MSSM corrections to the down quark and lepton mass matrix have been neglected, which is safe for tan β ∼ 10. For M H + lies around 120 ∼ 150 GeV, the MSSM prediction would be about 20% ∼ 30% smaller than the SM result of (0.95 ± 0.27) × 10 −4 . While the experimental world average is (1.65 ± 0.34) × 10 −4 before 2012 [21], Belle updated their measurement at ICHEP2012 with much smaller value 0.72 +0.29 −0.27 × 10 −4 for hadronic tag of τ [22]. So in the nondecoupling limit, a light charged Higgs with tan β ∼ 10 is well consistent with the new Belle measurement. Similarly, the charged Higgs contribution to B → D ( * ) τ ν τ decays are not very significant in the interesting region of M H + and tan β. Therefore we will not discuss the bounds from B + → τ + ν and B → D ( * ) τ ν τ decays further in our study.
On the other hand, the penguin b → s processes are also sensitive to the charged Higgs effects.
Generally, b → sγ and B s → µ + µ − 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 paper, 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 µ → eγ at the MEG experiment will soon reach BR(µ → eγ) ≃ 1 × 10 −13 . The one loop contribution from charged state to µ → eγ is suppressed by small lepton masses and additional helicity-flip. The largest contribution in Higgs mediated µ → eγ 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 reach the sensitivity for tan β of 60 for M A of 100 GeV where the tan β 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 XENON100 is about 5 × 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/M 4 h,H . 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 O(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 1 If the DM is not dominated by the neutralino component, the bound can be evaded. 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 M H , di-photon, di-tau decay and the direct detection experiments of neutralino dark matter. We then conclude in the final section.

II. GENERAL CONSTRAINTS AND THEIR IMPLICATIONS
In this section, we first scan the parameter space with focus on non-decoupling region with M A is at O(m Z ) 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 • Combined direct search bounds from HiggsBound3.8.0; Without loss of generality, we fix masses of the following sfermions as and the gauginos as As argued, our study focus on the flavor constraints of the non-decoupling MSSM and b → s transitions like B → X s γ and B s → µ + µ − 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 (Mt < 500 GeV), it is difficult to achieve enhanced di-photon. For comparison, we take the third generation up quark masses as MQ 3 = Mt = 500 GeV and a second group with 1 TeV .
We do the scan over four parameters 2 Discussed by many authors [4], light stau states may significantly enhance the di-photon rate of the perform the scan here. Figure 1 shows the scan results in 2D-plot of A t and µ. M A and tan β are also varied but aren't shown in the figures. GeV and an enhanced diphoton rate 1 < R γγ < 2. The points in blue region pass in addition the constraint of BR(B → X s γ), while the points in black region pass all the constraints, including further the restriction of BR(B s → µ + µ − ).
The scenario with heavy stop can survive the B → X s γ constraints. However, none of the scanned points can pass the B s → µ + µ − . In the case of light stop of 500 GeV, we find a small survival parameter region with negative A t around 750 GeV and large µ-term between 2 to 3 TeV.
In the following subsections, we discuss in details the physics implications of the scanned results.
A. b → sγ and B s → µ + µ − b → sγ and B s → µ + µ − turns out to be the most stringent flavor physics bounds in the nondecoupling limit. The helicity for the involved quark states must be flipped in b → sγ. Hence, 2 We confine ourselves to M A 150 GeV for larger splitting between h and H which can reduce the τ τ decay branching ratio. Details is discussed later. 3 In this scan, we take the pole mass of m t instead of the running m t mass. The survival parameter region after scan may be shifted by a few percent.  The squark contributions can be decomposed into chargino penguins, wino penguins and gluino penguins. Chargino penguins contain tan β-enhanced term which arises from v u insertion in Qd c H * u . The term explicitly breaks Peccei-Quinn symmetry as well as R-symmetry and is proportional to µA t . This contribution would destructively interfere with the SM and charged Higgs amplitudes in case of µA t < 0 [31,32]. In our study, gluino penguins are also important as they contain terms enhanced by µ tan β and terms chirally enhanced by mg/m b . Numerically, we use the FeynHiggs program to get the Non-MFV result of BR(B → X s γ). The experimental world average of this process is (3.43 ± 0.22) × 10 −4 [21], while the SM prediction up to NNLO perturbative QCD corrections is (3.15 ± 0.23) × 10 −4 [33]. However, B → X s γ decay is evaluated only at NLO in the FeynHiggs program, which produces the SM result as 3.8 × 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 → X s γ) M SSM < 5.5 × 10 −4 as the selection rule in the scan.
In the SM, BR(B s → µ + µ − ) is strongly helicity suppressed by the small muon mass as m 2 µ /m 2 Bs , which leads to a tiny branching ratio of (3.27 ± 0.23) × 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 β limit, as the leading contribution of Higgs penguin diagrams to the branching ratio are proportional to tan 6 β. In our study, tan β ∼ 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 tan 2 β at the amplitude level. Notice that B s → µ + µ − decay 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 × 10 −9 [35] 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(B s → µ + µ − ).
However, we notice that SUSY FLAVOR evaluates this branching ratio to be 4.8×10 −9 in the SM. This is about 50% larger than the SM prediction of (3.27 ± 0.23) × 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(B s → µ + µ − ) M SSM < 6 × 10 −9 in the scan.
In Fig. 1 Notice that BR(B → X s γ) is always larger than the SM prediction, which is mainly due to the enhancement of light charged Higgs. For BR(B s → µ + µ − ), it is always somewhat smaller than the SM prediction.

B. 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 → X s γ and B s → µ + µ − , we take light stop of Mt ∼ 500 GeV with negative After diagonalizing the general mass matrix of neutral Higgs To illustrate the feature, we take the limit of sin(β − α) → 0 which is the vanishing limit of g ZZh to completely suppress the Zh production at LEPII. As a result of sin α → −1 and sin β → 1, we Radiative corrections to the elements in mass matrix Eq. 9 are given in [39]. We list the most relevant M 22 in Eq. 11 where g 3 is the QCD running coupling constant, y t and y b are the top and bottom Yukawa couplings. M SU SY is the arithmetic mean of top squark masses Mt. A t is the SUSY breaking A-term associated with top squark and µ is the Higgsino mass parameter. t is defined as ln(M 2 SU SY /m 2 t ) andã The particular choices of A t and Mt 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]. Since H is mostly H u with large tan β, the v u 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 diphoton decay is dominated by the W -boson contribution, the di-photon decay partial width is not Therefore, light stau states in the spectrum can improve the di-photon behavior R γγ and reduce the tension in increasing ZZ * or W W * .
Discussed in [10], in the non-decoupling limit when H → bb still dominates the H decay, H → τ + τ − can be significantly enhanced.
where ǫ = 1 + tan α/ tan β with α < 0, ∆ b is from the radiative correction in bottom Yukawa, r gg is the ratio in gluon fusion production of H which is order 1 in relatively large tan β and Mt > 500 GeV. With the radiative correction, Hbb coupling is Similar to the story of µA t in b → s transition, ∆ b also breaks Peccei-Quinn symmetry and Rsymmetry at the same time. In this case, ∆ b contains two R-symmetry breaking pieces as gluino mass Mg and A-term contribution. Our choice of µA t < 0 results in cancellation between the two contribution but the enhancement to R τ τ is still significant. Our results also confirm the finding in [10] with many points of enhanced H → τ τ decay. Figure 3 shows the correlation between BR(H → τ + τ − ) and BR(H → bb) in the survival points. On the other hand, we also find many points with R τ τ < 1. One particularly interesting feature around non-decoupling limit is that or 2b2τ channels. The phenomenology of such channels have been widely studied in the context of NMSSM with h → AA search [40]. Studies of h → AA in NMSSM shows that for M h ∼ 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 τ τ < 1 bare the same feature as BR(H → hh) ∼ 50%. Among these points, predictions on W W * 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 → τ τ at ATLAS is still with large error bar and consistent with these large numbers of 2 σ τ τ SM . However, CMS collaboration has reported their latest data that exclude the SM τ τ rate by 1 σ [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 M A can be extended to O(200 GeV) in our study and the flavor bounds are less constrained for larger M A . However, the larger M A region corresponds to the enhanced R τ τ region. Only smaller M A generates larger splitting between H and h which reduces R τ τ . Therefore, we only focus on the region M A 150 GeV.
Besides the direct search via τ τ , LHC has put much stronger bounds on t → bH + with H + → τ + ν τ 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 M H ± by assuming BR(H + → τ + ν τ ) = 100% in Fig.4. It clearly shows that all the parameter points that

C. σ χN
Finally we discuss the last constraint for non-decoupling MSSM. Latest direct dark matter detection experiments XENON100 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 axialvector (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 H → τ τ if no excess of τ τ is confirmed at LHC. We only identify a small parameter region with significant H → hh decay that is consistent with all bounds and reduced τ τ 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
When completing our work, 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 R τ τ due to H → hh decay.