Can $μ$--$e$ Conversion in Nuclei be a Good Probe for Lepton-Number Violating Higgs Couplings ?

Motivated by the improving sensitivity, $R$, of experiments on $\mu~Ti \rightarrow e~Ti$ and the enhanced Higgs nucleon interaction, we study this lepton number violating process induced by Higgs exchange. Taking the possible sensitivity, $R \simeq 10^{-16}$, we obtain the constraint on the Higgs-muon-electron vertex, $\kappa_{\mu e}$, to be less than $2.4\times10^{-7}$ if the masses of the Higgs scalar and $W$ gauge boson are the same. $\kappa_{\mu e}$ is also calculated for some models.