Phenomenology of $\tau^- \rightarrow \pi^- \nu_{\tau} \gamma$ using LCSR

TL;DR

This paper investigates the radiative decay of tau leptons into pions, neutrinos, and photons, calculating form factors using Light Cone Sum Rules to understand the decay dynamics and compare with experimental data.

Contribution

The study introduces a Light Cone Sum Rules approach to compute timelike form factors for tau decay, accounting for real hadronic resonance production and providing analytical expressions.

Findings

Form factors are calculated for the decay process.

The decay width and invariant mass spectrum are presented.

The structure dependent parameter matches experimental values.

Abstract

We present the study of radiative tau decay ($\tau^- \rightarrow \pi^- \nu_\tau \gamma$), computing the structure dependent contribution using Light Cone Sum Rules. This decay includes the same form factors as the radiative pion decay with the crucial difference that the momentum transfer squared, $t$, between the pion-photon system is positive, which makes these form factors timelike and also as $t$ can now take values upto $m_\tau^2$ , it can produce real hadronic resonances. The analytical form for these form factors has been calculated using light cone sum rules method and the invariant mass-spectrum in the $\pi-\gamma$ system and the decay width are presented. The structure dependent parameter, $\gamma$, the ratio of the axial to vector form factor is found to be in good agreement with the experimental determination.