$\mu -e$ Conversion With Four Generations

We study $\mu -e$ conversion with sequential four generations. A large mass for the fourth generation neutrino can enhance the conversion rate by orders of magnitude. We compare constraints obtained from $\mu -e$ conversion using experimental bounds on various nuclei with those from $\mu \to e\gamma$ and $\mu \to e\bar{e}e$. We find that the current bound from $\mu -e$ conversion with Au puts the most stringent constraint in this model. The relevant flavor changing parameter ${\lambda }_{\mu e}=V_{\mu 4}^{\ast }{V}_{e4}^{}$ is constrained to be less than $1.6\times {10}^{-5}$ for the fourth generation neutrino mass larger than 100 GeV. Implications for future $\mu -e$ conversion, $\mu \to e\gamma$ and $\mu \to e\bar{e}e$ experiments are discussed.