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

arXiv commentTalk given at the 10th International Workshop on QCD: Theory and Experiment (QCD@work 2022), 27-30 June (2022), Lecce (Italy). 7 pages, 2 tables

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