Stau with Large Mass Difference and Enhancement of the Higgs to Diphoton Decay Rate in the MSSM

The ATLAS and the CMS collaborations have presented results which show an excess of the Higgs to diphoton decay channel. In the Minimal Supersymmetric Standard Model (MSSM), this situation can be achieved by a light stau and a large left-right mixing of the staus. However, this parameter region is severely constrained by vacuum stability. In order to relax the vacuum meta-stability condition, we focus on the parameter region where the mass difference between the two staus is large. This region has not been considered yet. In this paper, we show that staus with a large mass difference can relax the vacuum meta-stability condition sufficiently even if the lighter stau mass is kept light. We find that when the mass difference of two staus is large, the enhancement of the Higgs to diphoton decay rate becomes small in spite of a relaxation of the vacuum meta-stability condition. Because of this feature, an O(70)% enhancement of the Higgs to diphoton decay rate is difficult to achieve in the light stau scenario in the MSSM.