The ATLAS and CMS Collaborations have observed independently at the LHC a new Higgs-like particle with a mass $M_h\sim 125\mathrm{GeV}$ 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, 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 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 effect 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 $gg\to h_1\to \gamma \gamma$, $gg\to h_1\to Z{Z}^{*}\to 4l$, $gg\to h_1\to W{W}^{*}\to l\nu l\nu$, $pp\to V{h}_1\to Vb\overline{b}$ and $pp\to V{h}_1\to V{\tau }^{+}{\tau }^{-}$, ($V\equiv W^{\pm },Z$) at the LHC, considering the impact of the flavor constraints as well as the constraints coming from the electric dipole moment measurements. We find that it is possible to have a Higgs mass of about 125 GeV with relatively small $\tan \beta$, large $A_t$ and a light top squark, which is consistent with the current SUSY particle searches at the LHC. We obtain that the imaginary part of the top and bottom Yukawa couplings can take very small but nonzero values even after satisfying the recent updates from both the ATLAS and CMS Collaborations within $1–2\sigma$ uncertainties which might be an interesting signature to look for at the future run of the LHC. Our study shows that the CPV-MSSM provides an equally possible solution (like its $CP$-conserving counterpart) to the recent LHC Higgs data, in fact offering very little in the way of distinction between these two SUSY models (CPC-MSSM and CPV-MSSM) at the 7 and 8 TeV runs of the LHC. 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.

• Received 27 September 2013

DOI:https://doi.org/10.1103/PhysRevD.90.055005