Exploring MSSM for Charge and Color Breaking and Other Constraints in the Context of Higgs@125 GeV

Exploring MSSM parameter space after the discovery of Higgs Boson with mass 125 GeV naturally demands large top-squark mixing or large trilinear coupling parameter $A_t$ in particular, so as to avoid excessively heavy squark, specially for the universal models like CMSSM. We study stability of electroweak symmetry breaking vacua in possible presence of deeper charge-color symmetry breaking minima within MSSM. Besides stable vacua, we consider scenarios characterized by the presence of global CCB minima, with SM like charge and color conserving vacuum, having stability over cosmologically large lifetime {(\it long-lived states)}. We allow vacuum expectation values for both stop as well as sbottom fields, since these belong to the third generation of sfermions with larger Yukawa couplings that have immediate effect on the tunneling time. Moreover, for large $\mu$ regions, radiative corrections to Higgs boson mass from bottom-squark loop is quite significant. Regions of MSSM parameters space become viable for large $A_t$ and large $\mu$ zones which are generically excluded via the traditional analytical CCB constraints. For a large value of $\tan\beta$, safe vacua associated with large values of $|\mu|$ and $|A_t|$ are predominantly long-lived and may be associated with relatively light stop masses. We also identify low $\mu$ regions associated with long-lived states. Both the above zones can be friendly to muon $g-2$ constraint. We also impose constraints from ${\rm Br}(B \rightarrow X_s \gamma)$ and ${\rm Br}(B_s \rightarrow \mu^+ \mu^-)$. We do the analysis for a moderate and a large $\tan\beta$. Results are compatible with dark matter related constraints, as expected.