Probing Non-holomorphic MSSM via precision constraints, dark matter and LHC data

In this analysis we explore the phenomenological constraints of models with non-holomorphic soft SUSY breaking terms in a beyond the MSSM scenario having identical particle content. The model referred as NHSSM shows various promising features like the possibility of a strong reduction in electroweak fine-tuning even for a scenario of a heavy higgsino type of LSP, a fact that is unavailable in pMSSM models. The other important aspect is satisfying the muon $g-2$ data even for a small $\tan\beta$ via a small value of coupling $A_\mu'$ associated with the tri-linear non-holomorphic soft term. Thus, a large SUSY contribution to muon $g-2$ is possible even for a significantly large smuon mass $m_{\tilde {\mu_1}}$. The Higgs mass radiative corrections are contributed by both the holomorphic and non-holomorphic trilinear soft parameters $A_t$ and $A_t'$, thus diluting the requirement to have a larger $A_t$ to satisfy the Higgs mass data. The model also provides with valid parameter space satisfying the constraint of $B \rightarrow X_s +\gamma$ for large values of $\tan\beta$, a scenario unfavourable in pMSSM.