Lepton flavor violation in a supersymmetric grand unified theory model with nonuniversal sfermion masses

Abstract

We analyze lepton flavor violating $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ and $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ processes in a supersymmetric grand unified theory model in which sfermions have a special mass spectrum. It is assumed that only third generation sfermions which are contained in $\mathbf{10}(\mathrm{Q},{\mathrm{U}}^{\mathrm{c}},{\mathrm{E}}^{\mathrm{c}})$ of SU(5) can have a different mass from the others. This mass spectrum is derived from the ${\mathrm{E}}_{6}$ grand unified theory model with horizontal symmetries. It is shown that branching ratios of $\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma}$ and $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ depend strongly on a right-handed stau mass. The weak scale stability requires a light stau, so large decay rates can be expected in this scenario. When the stau mass is around 150 GeV and $\mathrm{tan}\ensuremath{\beta}\ensuremath{\sim}10$, the branching ratios can be larger than $\mathrm{Br}(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\gamma})\ensuremath{\simeq}{10}^{\ensuremath{-}8}$ and $\mathrm{Br}(\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma})\ensuremath{\simeq}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$, which are within reach of future experiments. In addition, this model has an interesting feature that the final state charged lepton tends to have right-handed chirality.