Improved calculation of radiative corrections to $\tau\to\pi\pi\nu_\tau$ decays

TL;DR

This paper improves the calculation of radiative corrections to tau decays into pions, incorporating structure-dependent effects and resonance enhancements, which are crucial for precise muon magnetic moment evaluations.

Contribution

It introduces a model-independent, dispersive approach to include structure-dependent effects beyond point-like pions in radiative correction calculations for tau decays.

Findings

Significant changes in corrections near the rho resonance.

Strategies for matching to chiral perturbation theory.

Dispersive fits to tau decay spectra and implications for muon g-2.

Abstract

A reliable calculation of radiative corrections to $\tau\to\pi\pi\nu_\tau$ decays is an important prerequisite for using hadronic $\tau$ decays for a data-driven evaluation of the hadronic-vacuum-polarization contribution to the anomalous magnetic moment of the muon, $a_\mu^\text{HVP, LO}[\pi\pi,\tau]$. In this Letter, we present an improved model-independent analysis of these radiative corrections, including, for the first time, effects beyond point-like pions in the evaluation of the loop diagrams. These structure-dependent corrections, implemented via a dispersive representation of the pion form factor, lead to significant changes compared to previous calculations due to enhancements near the $\rho(770)$ resonance. We also devise strategies for the matching to chiral perturbation theory and a stable implementation of the real corrections down to the two-pion threshold, which shows that some higher-order isospin-breaking corrections need to be kept due to a strong threshold enhancement. Finally, we perform dispersive fits to the currently available $\tau\to\pi\pi\nu_\tau$ spectra and discuss the consequences for isospin-breaking corrections in the evaluation of $a_\mu^\text{HVP, LO}[\pi\pi,\tau]$.