  The ATLAS and CMS collaborations discovered a new boson particle. If the new
boson is the Higgs boson, the diphoton signal strength is 1.5 - 1.8 times
larger than the Standard Model (SM) prediction, while the WW and ZZ signal
strengths are in agreement with the SM one. In the Minimal Supersymmetric
Standard Model (MSSM), overall consistency can be achieved by a light stau and
the large left-right mixing of staus. However, a light stau and large
left-right mixing of staus may suffer from vacuum instability. We first apply
the vacuum meta-stability condition to the Higgs to diphoton decay rate in the
MSSM. We show that the vacuum meta-stablity severely constrains the enhancement
to the Higgs to diphoton rate. For example, when the lighter stau mass is 100
GeV, the upper bound on the enhancement to the Higgs to diphoton rate becomes
25%.
