$\tau^- \to \pi^- \eta \nu_\tau$ decay induced by QED one-loop effects

TL;DR

This paper investigates the isospin-breaking effects from one-loop QED corrections on the rare $ au^- o ext{pi}^- ext{eta} u_ au$ decay, highlighting their significance for precision tests of the Standard Model and new physics searches.

Contribution

It provides the first estimate of QED one-loop effects on the decay, showing they can significantly alter Standard Model predictions and must be considered in experimental analyses.

Findings

QED effects shift decay rate predictions by about 12%.

Effects on $ au^- o ext{pi}^- ext{eta'} u_ au$ can be as large as 78%.

These effects are crucial for accurate theory-experiment comparisons.

Abstract

The $\tau^- \to \pi^-\eta\nu_{\tau}$ decay is forbidden in the Standard Model in the limit of exact $G$-parity, it becomes a rare decay due to isospin symmetry breaking and it is very sensitive to the effects of effective scalar interactions. Since the parameters driving isospin breaking, $(m_d-m_u)/(m_s-\bar{m})$ and $\alpha$, are of the same order, one may expect their $G$-parity breaking effects in this decay can be of similar magnitudes. In this work, we evaluate the effects of isospin-breaking amplitudes originated from a virtual photon at one-loop in a resonance dominance model to describe photon-hadron interactions. We find that these effects can shift the leading SM predictions based on the $u-d$ quark mass difference by roughly $12\%$, and should be taken into consideration in a precision comparison of theory and experiment in order to draw meaningful conclusions on New Physics. The effects in the rate of the analogous $\tau^- \to \pi^-\eta'\nu_{\tau}$ decay can be larger ($\sim$ $78\%$), under the approximations assumed in this model.