$\tau^{-}\to \ell_i^{-} \ell_i^{+} \ell_j^{-} \bar{\nu}_{j} \nu_{\tau}$ decays with a magnetic dipole term

TL;DR

This paper calculates tau decay amplitudes within the Standard Model and explores how effective magnetic dipole interactions could allow experimental limits to be set on the tau's anomalous magnetic moment.

Contribution

It introduces a dimension-five effective vertex to evaluate the potential for constraining the tau's magnetic dipole moment through decay measurements.

Findings

Calculated decay amplitudes using massive helicity formalism.

Assessed the impact of magnetic dipole terms on decay branching ratios.

Proposed experimental bounds on $a_\tau$ based on current and future measurements.

Abstract

Using the massive helicity formalism we calculate the five-body average square amplitude of the decays $\tau^{-}\to \ell_i^{-} \ell_i^{+} \ell_j^{-} \bar{\nu}_{j} \nu_{\tau}$ $(\ell=e,\,\mu)$ within the Standard Model (SM), we then introduce a dimension-five effective vertex $\Gamma^{\tau\tau \gamma}$ in order to determine the feasibility of imposing limits on the tau anomalous magnetic dipole moment ($a_\tau$) via the current or future experimental measurements of the branching ratio for the decay $\tau^{-}\to e^{-} e^{+} e^{-} \bar{\nu}_{e} \nu_{\tau}$.