About The Polarized $\tau$ Lepton Radiative Decay

TL;DR

This paper analyzes the polarization effects in the radiative decay of polarized tau leptons, providing analytical formulas for the decay distributions and demonstrating the dominance of structure-dependent contributions at higher photon energy cuts.

Contribution

It offers new analytical expressions for polarization-dependent decay distributions in tau radiative decays, applicable to both pion and kaon channels, using chiral effective theory with resonances.

Findings

Inner bremsstrahlung decreases with higher photon energy cuts.

Structure-dependent contributions dominate at higher photon energies.

Analytical formulas are valid for both pion and kaon decay channels.

Abstract

The polarization effects in the one-meson radiative decay of the polarized $\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, have been investigated. We present the analytical results for the $t-$distribution of the partial differential widths, which responsible for different polarization phenomena, in the case of the photon energy cut: $\omega>X$. These quantities depend on the invariant mass squared $t$ of the pseudoscalar meson and photon and the photon energy cut $X.$ Our analytical formulae, in terms of the weak vector and axial-vector form factors, describing the structure-dependent part of the decay amplitude, are valid also for the decay $\tau^{\pm}\to K^{\pm}\,\nu_\tau\,\gamma$ after trivial substitutions of the corresponding constants. We demonstrate the essential decrease of the inner bremsstrahlung contribution in comparison with the structural one with increase of the photon cut energy. In numerical calculations the vector and axial-vector form factors are determined using the chiral effective theory with resonances (R$\chi$T).