$\tau^-\to\pi^-\gamma\nu_\tau$ as a source of background on the Lepton Flavour Violating decay $\tau^-\to\mu^-\gamma$

TL;DR

This paper calculates the decay $ au^- o ext{pi}^- ext{gamma} u_ au$ using Resonance Chiral Theory, predicts its branching ratio, and assesses its impact as a background in lepton flavor violation searches, highlighting discrepancies in simulation tools.

Contribution

It provides a parameter-free prediction of the $ au^- o ext{pi}^- ext{gamma} u_ au$ decay and evaluates its role as a background in LFV $ au$ decays, using high-energy QCD constraints.

Findings

Branching ratio around 0.1% for photon energy cut at 100 MeV.

PHOTOS simulation agrees at low energies but not at high energies.

The decay can mimic LFV signals at high photon energies.

Abstract

We calculate the decay of $\tau^-\to\pi^-\gamma\nu_\tau$ in the framework of Resonance Chiral Theory ($R\chi T$). By demanding the high energy constraints from QCD on the related form factors, we could predict the various physical observables of $\tau^-\to\pi^-\gamma\nu_\tau$ without any free parameter. Our results show that for a realistic cut on the photon energy (around $100$ MeV) this mode gives a branching ratio of roughly $0.1%$ that should have already been detected at the heavy-flavour factories. Another interesting subject we have studied based on our calculation of the decay $\tau^-\to\pi^-\gamma\nu_\tau$ is the experimental background estimation of the lepton flavour violation process $\tau^- \to \mu^- \gamma$. We point out that although the description of radiation that PHOTOS provides -which has been used by BaBar and Belle collaborations to estimate this source of background- is in excellent agreement with the theoretical expectations in the low energy region in $\tau^-\to\pi^-\gamma\nu_\tau$ decay, this is not the case in the high energy region, precisely where it is easier that this decay mimics the process $\tau^-\to\mu^-\gamma$.