Lepton flavor violating Higgs boson decay H --> mu tau at muon colliders

We consider an effective nondiagonal coupling $H\bar{\mu}\tau$ and present the analysis of the Higgs boson mediated lepton-flavor violating (LFV) reaction $\mu^-\mu^+ --> \mu \tau$. For a Higgs boson mass around 115 GeV and convenient values of the strength of the coupling $H\bar{\mu}\tau$, which are within the bounds obtained from the experimental limits on the LFV decays $\tau-->\eta\mu$ and $\tau-->\mu\gamma$, we found that there would be up to a few hundreds of $\mu \tau$ events per year at a muon collider running with an integrated luminosity of $1 fb^{-1}$. We paid special attention on the background for this LFV reaction, which arises from the standard model process $\mu^-\mu^+ --> \mu\tau\bar{\nu}_{\mu}\nu_{\tau}$, and discuss how it can be separated from the main signal.