Lepton flavor violating $Z$-boson couplings from non-standard Higgs interactions

TL;DR

This paper investigates lepton flavor violating Z-boson couplings arising from non-standard Higgs interactions, calculating branching ratios for various tau decays and the Z to tau-mu decay, highlighting the significance of Z-mediated processes.

Contribution

It provides explicit formulae for effective LFV Z couplings from non-standard Higgs interactions and evaluates their impact on tau and Z decay processes.

Findings

Z-mediated LFV tau decays are generally not dominant for certain channels.

Branching fractions for $ au o au ext{hadron}$ decays are calculated.

Z to tau-mu decay branching ratio is estimated.

Abstract

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 non-diagonal Yukawa interactions with the muon and the tau lepton generated from physics beyond the Standard Model. We list the formulae of the couplings of the effective interactions among the $\tau$ lepton, the muon and the $Z$ boson. Using these formulae, 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 flipptings, it turns out that they are not very significant for $\tau\to3\mu$ 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.