Predictions for lepton flavor violation inZdecays in supersymmetry with left-right symmetry

Abstract

Recent experimental results on neutrino oscillations and the muon anomalous magnetic moment, combined with radiative lepton decays, set strict limits on fractional slepton and sneutrino flavor violating mixings. We study the effect of these mixings on Z lepton flavor violating decays and the implications for the observability of these decays in view of the new GigaZ option at the ${e}^{+}{e}^{\ensuremath{-}}$ collider, expected to reach a sensitivity of up to ${10}^{\ensuremath{-}8}$ for branching rates. The largest branching ratio predicted is of order ${10}^{\ensuremath{-}11}--{10}^{\ensuremath{-}12}$ for the decays $\stackrel{\ensuremath{\rightarrow}}{Z}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}},$ therefore precluding observation of a signal at DESY TESLA. The branching ratios for $\stackrel{\ensuremath{\rightarrow}}{Z}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{e}^{\ensuremath{\mp}}$ and $\stackrel{\ensuremath{\rightarrow}}{Z}{e}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}}$ are expected to be even smaller.