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The ATLAS and CMS collaborations have observed independently at the LargeHadron Collider (LHC) a new Higgs-like particle with a mass $M_h \sim$ 125 GeVand properties similar to that predicted by the Standard Model (SM). Althoughthe measurements indicate that this Higgs-like boson is compatible with the SMhypothesis, however due to large uncertainties in some of the Higgs detectionchannels, one still has the possibility of testing this object as being acandidate for some Beyond the SM (BSM) physics scenarios, for example, theMinimal Supersymmetric Standard Model (MSSM), in the CP-conserving version(CPC-MSSM). In this paper, we evaluate the modifications of these CPC-MSSMresults when CP-violating (CPV) phases are turned on explicitly, leading to theCP-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 lightestHiggs boson $h_1$, and the rates for the processes $gg \rightarrow h_1\rightarrow \gamma \gamma$, $gg \rightarrow h_1 \rightarrow ZZ^*\rightarrow4l$, $gg \rightarrow h_1 \rightarrow WW^*\rightarrow l \nu l \nu$, $pp\rightarrow V h_1 \rightarrow V b\bar b$ and $pp \rightarrow V h_1 \rightarrowV \tau^+\tau^-$, ($V \equiv W^\pm, Z$) at the LHC, considering the impact ofthe flavor constraints as well as the constraints coming from the ElectricDipole Moment (EDM) measurements. We find that the imaginary part of the topand bottom Yukawa couplings can take very small but non-zero values even aftersatisfying the recent updates from LHC. Our study shows that the CPV-MSSMprovides an equally potential solution (like its CP-conserving (CPC)counterpart) to the recent LHC Higgs data. Improvement in different Higgscoupling measurements is necessary in order to test the possibility of probingthe small dependence on these CPV phases in the Higgs sector of the MSSM.

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