Study of the lepton flavor-violating $Z'\to\tau\mu$ decay

TL;DR

This paper investigates the potential for lepton flavor-violating $Z'$ decays into tau and muon leptons within extended models, constraining couplings using experimental data, and estimating the decay's branching ratio.

Contribution

It provides a comprehensive calculation of the $Z' o au ext{mu}$ decay coupling and bounds it using muon magnetic moment and tau decay data across several models.

Findings

Re($ ext{Omega}_{L ext{mu} au} ext{Omega}^*_{R ext{mu} au}$) ~ 10^{-2} for a 2 TeV $Z'$

Most restrictive bounds from three-body tau decay, around 10^{-2} for $Z_ ext{chi}$ model

Branching ratio estimate for $Z' o au ext{mu}$ around 10^{-2} in least optimistic models

Abstract

The lepton flavor violating $Z^{\prime}\to\tau\mu$ decay is studied in the context of several extended models that predict the existence of the new gauge boson named $Z^\prime$. A calculation of the strength of the lepton flavor violating $Z^\prime\mu\tau$ coupling is presented by using the most general renormalizable Lagrangian that includes lepton flavor violation. We used the experimental value of the muon magnetic dipole moment to bound this coupling, from which the $\mathrm{Re}(\Omega_{L\mu\tau}\Omega^\ast_{R\mu\tau})$ parameter is constrained and it is found that $\mathrm{Re}(\Omega_{L\mu\tau}\Omega^\ast_{R\mu\tau})\sim 10^{-2}$ for a $Z^\prime$ boson mass of 2 TeV. Alongside, we employed the experimental restrictions over the $\tau\to\mu\gamma$ and $\tau\to\mu\mu^+\mu^-$ processes in the context of several models that predict the existence of the $Z^\prime$ gauge boson to bound the mentioned coupling. The most restrictive bounds come from the calculation of the three-body decay. For this case, it was found that the most restrictive result is provided by a vector-like coupling, denoted as $|\Omega_{\mu\tau}|^2$, for the $Z_\chi$ case, finding around $10^{-2}$ for a $Z^\prime$ boson mass of 2 TeV. We used this information to estimate the branching ratio for the $Z^\prime\to\tau\mu$ decay. According to the analyzed models the least optimistic result is provided by the Sequential $Z$ model, which is of the order of $10^{-2}$ for a $Z^\prime$ boson mass around 2 TeV.