A 125 GeV SM-like Higgs in the MSSM and the $\gamma \gamma$ rate

We consider the possibility of a Standard Model (SM)-like Higgs in the context of the Minimal Supersymmetric Standard Model (MSSM), with a mass of about 125 GeV and with a production times decay rate into two photons which is similar or somewhat larger than the SM one. The relatively large value of the SM-like Higgs mass demands stops in the several hundred GeV mass range with somewhat large mixing, or a large hierarchy between the two stop masses in the case that one of the two stops is light. We find that, in general, if the heaviest stop mass is smaller than a few TeV, the rate of gluon fusion production of Higgs bosons decaying into two photons tends to be somewhat suppressed with respect to the SM one in this region of parameters. However, we show that an enhancement of the photon decay rate may be obtained for light third generation sleptons with large mixing, which can be naturally obtained for large values of $\tan\beta$ and sizable values of the Higgsino mass parameter.