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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 arecalculated by using Chiral Perturbation Theory (ChPT), $\tau$ decays have beenstudied with an effective approach where ChPT is enlarged by including thelightest resonances and following the high-energy behavior dictated by QCD.These ratios have allowed us to test the lepton universality and the CKMunitarity and also to search for bounds on non-standard interactions. Ourresults, $\delta R_{\tau/\pi}=(0.18\pm 0.57 )\%$ and $\deltaR_{\tau/K}=(0.97\pm 0.58 )\%$, are consistent with the previous theoreticaldeterminations, but with much more robust assumptions, yielding a reliableuncertainty.

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