Polarization effects in radiative decay of polarized $\tau$ lepton

TL;DR

This paper investigates how the polarization of a tau lepton affects the radiative decay process involving a pion and a photon, including polarization asymmetries and photon polarization, using chiral effective theory.

Contribution

It provides a detailed analysis of polarization effects in tau decay, incorporating both bremsstrahlung and structure-dependent amplitudes with numerical estimations.

Findings

Calculated asymmetry of decay width due to tau polarization

Determined photon Stokes parameters based on tau polarization

Estimated physical quantities for arbitrary tau polarization directions

Abstract

The polarization effects in the one-meson radiative decay of the polarized $\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, are investigated. The inner bremsstrahlung and structural amplitudes are taken into account. The asymmetry of the differential decay width caused by the $\tau$ lepton polarization and the Stokes parameters of the emitted photon itself, are calculated depending on the polarization of the decaying $\tau$ lepton. The numerical estimation of these physical quantities was done for arbitrary direction of the $\tau$ lepton polarization 3-vector in the rest frame. The vector and axial-vector form factors describing the structure-dependent part of the decay amplitude are determined using the chiral effective theory with resonances (R$\chi$T).