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Exploring MSSM parameter space after the discovery of Higgs Boson with mass125 GeV naturally demands large top-squark mixing or large trilinear couplingparameter $A_t$ in particular, so as to avoid excessively heavy squark,specially for the universal models like CMSSM. We study stability ofelectroweak symmetry breaking vacua in possible presence of deeper charge-colorsymmetry breaking minima within MSSM. Besides stable vacua, we considerscenarios characterized by the presence of global CCB minima, with SM likecharge and color conserving vacuum, having stability over cosmologically largelifetime {(\it long-lived states)}. We allow vacuum expectation values for bothstop as well as sbottom fields, since these belong to the third generation ofsfermions with larger Yukawa couplings that have immediate effect on thetunneling time. Moreover, for large $\mu$ regions, radiative corrections toHiggs boson mass from bottom-squark loop is quite significant. Regions of MSSMparameters space become viable for large $A_t$ and large $\mu$ zones which aregenerically excluded via the traditional analytical CCB constraints. For alarge value of $\tan\beta$, safe vacua associated with large values of $|\mu|$and $|A_t|$ are predominantly long-lived and may be associated with relativelylight stop masses. We also identify low $\mu$ regions associated withlong-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 amoderate and a large $\tan\beta$. Results are compatible with dark matterrelated constraints, as expected.

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