Improved Calculation of Radiative Corrections to τ → π π ν τ Decays

A reliable calculation of radiative corrections to τ→ππν_{τ} decays is an important prerequisite for using hadronic τ decays for a data-driven evaluation of the hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon, a_{μ}^{HVP,LO}[ππ,τ]. In this Letter, we present an improved model-independent analysis of these radiative corrections, including, for the first time, effects beyond pointlike 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 ρ(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 τ→ππν_{τ} spectra and discuss the consequences for isospin-breaking corrections in the evaluation of a_{μ}^{HVP,LO}[ππ,τ].