Charge and Color Breaking Constraints in MSSM after the Higgs Discovery at LHC

We revisit the constraints on the parameter space of the Minimal Supersymmetric Standard Model (MSSM), from charge and color breaking minima in the light of information on the Higgs from the LHC so far. We study the behavior of the scalar potential keeping two light sfermion fields along with the Higgs in the pMSSM framework and analyze the stability of the vacuum. We find that for lightest stop $\lesssim 1$ TeV and small $\mu \lesssim 500$ GeV, the absolute stability of the potential can be attained only for $|X_{t}| \lesssim \sqrt{ 6 m_{\tilde{t}_1} m_{\tilde{t}_2}}$. The bounds become stronger for larger values of the $\mu$ parameter. Note that this is approximately the value of $X_t$ which maximizes the Higgs mass. Our bounds on the low scale MSSM parameters are more stringent than those reported earlier in literature. We reanalyze the stau sector as well, keeping both staus. We study the connections between the observed Higgs rates and vacuum (meta)stability. We show how a precision study of the ratio of signal strengths, ($\mu_{\gamma\gamma}/\mu_{ZZ}$) can shed further light.