Effect of FCNC mediated Z boson on lepton flavor violating decays

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.