A Study of Lepton Flavor Violating $\mu N (e N) \to \tau X$ Reactions in Supersymmetric Models

We study a lepton flavor violating $\mu N \to \tau X$ reaction in deep inelastic scattering region in supersymmetric models. The contribution from the Higgs boson mediation could be important for this reaction. For that case, the cross section is constrained by the experimental limit of the pseudo-scalar coupling from $\tau \to \mu\eta$ decays. We find that at a muon energy ($E_{\mu}$) higher than 50 GeV, the predicted cross section increases significantly due to the contribution from sea $b$-quarks. As a result, with $10^{20}$ muons per year, at most a number of $\mathcal{O}(10^4)$ is expected for $\mu N \to \tau X$ events at $E_{\mu}$= 300 GeV, whereas $\mathcal{O}(10^2)$ events are given at $E_{\mu}= 50$ GeV. Furthermore, the $\mu N \to \tau X$ phenomenology, in particular that for the signal and backgrounds, is briefly discussed. Another promising possibility to search for the $e N \to \tau X$ reaction at an electron-positron linear collider is also discussed. Searches for these reactions would be competitive to studies of rare tau decays and have potential to improve sensitivities to lepton flavor violation significantly.