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

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 $\delta_{\tau K} = -(0.15 \pm 0.57) \%$