The 125 GeV Higgs signal at the LHC in the CP Violating MSSM

The ATLAS and CMS collaborations have observed independently at the Large Hadron Collider (LHC) a new Higgs-like particle with a mass $M_h \sim$ 125 GeV and properties similar to that predicted by the Standard Model (SM). Although the measurements indicate that this Higgs-like boson is compatible with the SM hypothesis, however due to large uncertainties in some of the Higgs detection channels, one still has the possibility of testing this object as being a candidate for some Beyond the SM (BSM) physics scenarios, for example, the Minimal Supersymmetric Standard Model (MSSM), in the CP-conserving version (CPC-MSSM). In this paper, we evaluate the modifications of these CPC-MSSM results when CP-violating (CPV) phases are turned on explicitly, leading to the CP-violating MSSM (CPV-MSSM). We investigate the role of the CPV phases in (some of) the soft Supersymmetry (SUSY) terms on both the mass of the lightest Higgs boson $h_1$, and the rates for the processes $gg \rightarrow h_1 \rightarrow \gamma \gamma$, $gg \rightarrow h_1 \rightarrow ZZ^*\rightarrow 4l$, $gg \rightarrow h_1 \rightarrow WW^*\rightarrow l \nu l \nu$, $pp \rightarrow V h_1 \rightarrow V b\bar b$ and $pp \rightarrow V h_1 \rightarrow V \tau^+\tau^-$, ($V \equiv W^\pm, Z$) at the LHC, considering the impact of the flavor constraints as well as the constraints coming from the Electric Dipole Moment (EDM) measurements. We find that the imaginary part of the top and bottom Yukawa couplings can take very small but non-zero values even after satisfying the recent updates from LHC. Our study shows that the CPV-MSSM provides an equally potential solution (like its CP-conserving (CPC) counterpart) to the recent LHC Higgs data. Improvement in different Higgs coupling measurements is necessary in order to test the possibility of probing the small dependence on these CPV phases in the Higgs sector of the MSSM.