  Current Higgs data at the Large Hadron Collider is compatible with a SM
signal at the 2$\sigma$ level, but the central value of the signal strength in
the diphoton channel is enhanced with respect to the SM expectation. If the
enhancement resides in the diphoton partial decay width, the data could be
accommodated in the Minimally Supersymmetric Standard Model (MSSM) with highly
mixed light staus. We revisit the issue of vacuum instability induced by large
mixing in the stau sector, including effects of a radiatively-corrected tau
Yukawa coupling. Further, we emphasize the importance of taking into account
the $\tan\beta$ dependence in the stability bound. While the metastability of
the Universe constrains the possible enhancement in the Higgs to diphoton decay
width in the light stau scenario, an increase of the order of 50% can be
achieved in the region of large $\tan\beta$. Larger enhancements may be
obtained, but would require values of $\tan\beta$ associated with
non-perturbative values of the tau Yukawa coupling at scales below the GUT
scale, thereby implying the presence of new physics beyond the MSSM.

High Energy Physics - Phenomenology;High Energy Physics - Experiment