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.