Effect of FCNC mediated Z boson on lepton flavor violating decays

Abstract

We study the three body lepton flavor violating (LFV) decays μ ⁻→e ⁻ e ⁺ e ⁻, $\tau^{-} \to l_{i}^{-} l_{j}^{+} l_{j}^{-}$ and the semileptonic decay τ→μφ in the flavor changing neutral current (FCNC) mediated Z boson model. We also calculate the branching ratios for LFV leptonic B decays, B _d,s →μe, B _d,s →τe, B _d,s →τμ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on μ ⁻→e ⁻ e ⁺ e ⁻ and τ ⁻→μ ⁻ μ ⁺ μ ⁻. We find that the branching ratios for τ→eee and τ→μφ processes could be as large as ${\sim}{\mathcal{O}}(10^{-8})$ and $\mathrm{Br}(B_{d,s} \to \tau \mu,~ \tau e) \sim {\mathcal{O}}(10^{-10})$. For other LFV B decays the branching ratios are found to be too small to be observed in the near future.