A new theoretical determination of $R_{\tau /P}$ $(P=\pi ,K)$

Abstract

We have determined $R_{\tau /P}\equiv \Gamma (\tau \to P{\nu }_{\tau }[\gamma ])/\Gamma (P\to \mu {\nu }_{\mu }[\gamma ])$ ($P=\pi ,K$). Whereas $P$ decays are calculated by using Chiral Perturbation Theory (ChPT), $\tau$ decays have been studied with an effective approach where ChPT is enlarged by including the lightest resonances and following the high-energy behavior dictated by QCD. These ratios have allowed us to test the lepton universality and the CKM unitarity and also to search for bounds on non-standard interactions. Our results, $\delta R_{\tau /\pi }=(0.18\pm 0.57)\%$ and $\delta R_{\tau /K}=(0.97\pm 0.58)\%$, are consistent with the previous theoretical determinations, but with much more robust assumptions, yielding a reliable uncertainty.

Comments: Talk given at the 19th International Conference on Hadron Spectroscopy and Structure in memoriam Simon Eidelman (HADRON2021), 26-31 July (2021), Mexico City (Mexico). 5 pages, 1 figure, 1 table