Exploring Charge and Color Breaking vacuum in Non-Holomorphic MSSM

Non-Holomorphic MSSM (NHSSM) shows various promising features that are not easily obtained in MSSM. However, the additional Non-Holomorphic (NH) trilinear interactions that attribute to the interesting phenomenological features, also modify the effective scalar potential of the model significantly. We derive analytic constraints involving trilinear parameters $A_t'$ and $A_b'$ that exclude global charge and color breaking minima (CCB). Since the analytic constraints are obtained considering specific directions in the multi-dimensional field space, we further probe the applicability of these constraints by exhaustive scan over NH parameter space with two different regimes of $\tan\beta$ and delineate the nature of metastability by considering vacuum expectation values for third generation squarks. We adhere to a natural scenario by fixing Higgsino mass parameter ($\mu$) to a low value and estimate the allowed ranges of NH trilinear parameters by considering vacuum stability and observed properties of Higgs as the determining criteria.