The standard model predicts that the Higgs boson couples to the fermions in the mass eigenstates. We consider the effects of lepton flavor violating (LFV) $Z$ boson couplings in the case where the Higgs boson has flavor nondiagonal Yukawa interactions with the muon and the tau lepton generated from physics beyond the standard model. We list the formulas of the couplings of the effective interactions among the $\tau$ lepton, the muon and the $Z$ boson. Using these formulas, we calculate the branching fractions of various leptonic and hadronic LFV $\tau$ decays, and the LFV $Z$ boson decay: $Z\to \tau \mu$. Although the $Z$-boson contributions to LFV tau decays cannot be ignored in terms of the counting of operator dimensions or chirality flippings, it turns out that they are not very significant for $\tau \to 3\mu$ and $\tau \to \mu \rho$ decays. We also calculate the branching fractions of the processes, $\tau \to \mu \pi$, $\tau \to \mu {\eta }^{(\prime )}$ and $\tau \to \mu a_1$, which are dominated by the $Z$-boson exchanges due to the spin and the parity of the hadrons.

• Received 15 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.075021