Effect of FCNC mediated Z boson on lepton flavor violating decays

Abstract

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