The process $\mu \to \nu_{e}e\bar{\nu}_{\mu} $in the 2HDM with flavor changing neutral currents

We consider the process $\mu \to \nu_{e}e\bar{\nu}_{\mu}$in the framework of a two Higgs doublet model with flavor changing neutral currents (FCNC). Since FCNC generates in turn flavor changing charged currents in the lepton sector, this process appears at tree level mediated by a charged Higgs boson exchange. From the experimental upper limit for this decay, we obtain the bound $| \xi_{\mu e}/m_{H^{\pm}}| \leq 3.8\times 10^{-3}$ where$\xi_{\mu e}$refers to the mixing between the first and second lepton generations, and $m_{H^{\pm}}$denotes the mass of the charged Higgs boson. This bound is independent on the other free parameters of the model. In particular, for $m_{H^{\pm}}\simeq 100$GeV we get $| \xi_{e\mu}|$ $\lesssim 0.38$