Lepton flavor violation in the left-handed slepton production at future lepton colliders

The Super-Kamiokande atmospheric neutrino data suggest the existence of a large lepton-flavor violating (LFV) interaction in the higher energy scale. If the minimal supersymmetric standard model is extended to have right-handed neutrinos, the left-handed sleptons in the second and third generations are expected to have LFV masses in the minimal supergravity scenario. In this article we study the LFV signals in the left-handed slepton production at ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ colliders and ${e}^{+}{e}^{\ensuremath{-}}$ linear colliders (LC's), ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{(e}^{+}{e}^{\ensuremath{-}})\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\mu}+4 \mathrm{jets}+E/$ and ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{(e}^{+}{e}^{\ensuremath{-}})\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\mu}l+2 \mathrm{jets}+E/$. The main background comes from decay of a tau lepton into a muon in the lepton-flavor conserving slepton pair production. They are significantly reduced by the energy and the impact parameter cuts for the muon. At ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ colliders (LC's) it may be possible to reach the mixing angle $\mathrm{sin}2{\ensuremath{\theta}}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}}\ensuremath{\gtrsim}0.1(0.5)$ and the mass difference $\ensuremath{\Delta}{m}_{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\nu}}}\ensuremath{\gtrsim}0.1(0.4)$ GeV for sneutrinos in the second and third generations at the statistical significance of $3\ensuremath{\sigma}$. Such a small mass difference and a mixing angle may be induced radiatively even if the Yukawa coupling constant for the tau neutrino is of the order of 0.1.