Computing one-loop radiative corrections in $\tau \to \pi (K) \nu [\gamma]$ and testing new physics

TL;DR

This paper updates theoretical calculations of radiative corrections in tau decays to pions and kaons, testing lepton universality and CKM unitarity with improved precision and considering potential new physics effects.

Contribution

The authors computed one-loop radiative corrections using an advanced Chiral Perturbation Theory approach including resonances, providing updated and more realistic estimates for tau decay ratios.

Findings

Radiative correction for tau to pion decay: (0.18±0.57)%

Radiative correction for tau to kaon decay: (0.97±0.58)%

Confirmed consistency with lepton universality and CKM unitarity

Abstract

Without a doubt the ratios $R_{\tau / P}\equiv \Gamma \left( \tau \to P \nu_{\tau}[\gamma] \right) / \Gamma \left(P\to \mu \nu_{\mu}[\gamma]\right)$ ($P=\pi,K$) give a convenient scenario to test the lepton universality, the CKM unitarity and to search for non-standard interactions in $\tau$ decays. Moreover, the previous theoretical estimation of these observables is more than twenty-five years old and some assumptions of that estimation are unrealistic. Therefore, an update of $R_{\tau / P}$ was timely. The one-loop radiative corrections have been computed by considering an expansion of Chiral Perturbation Theory including the lightest spin-one resonances and respecting the short-distance behavior dictated by QCD. We have reported $\delta R_{\tau/\pi}=(0.18\pm 0.57 )\%$ and $\delta R_{\tau/K}=(0.97\pm 0.58 )\%$, where the uncertainties have been induced fundamentally by the estimation of the counterterms. We have tested the lepton universality, the CKM unitarity and have searched for new physics in $\tau$ decays. As a by-product, we have also determined the theoretical radiative corrections to the $\tau \to P \nu_{\tau}[\gamma]$ decay rates, $\delta_{\tau \pi} = -(0.24 \pm 0.56) \%$ and $\delta_{\tau K} = -(0.15 \pm 0.57) \%$