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.