Radiative corrections to $\tau \to \pi (K) \nu_\tau [\gamma]$: a reliable new physics test

Abstract

The ratios $R_{\tau/P}\equiv \Gamma(\tau \to P \nu_\tau [\gamma]) / \Gamma(P \to\mu \nu_\mu[\gamma])$ ($P=\pi, K$) provide sensitive tests of lepton universality $\left|g_\tau/g_\mu\right|=1$ and are a useful tool for new physics searches. The radiative corrections to $R_{\tau/P}$ are computed following a large-$N_C$ expansion to deal with hadronic effects: Chiral Perturbation Theory is enlarged by including the lightest multiplets of spin-one heavy states such that the relevant Green functions are well-behaved at high energies. We find $\delta R_{\tau/\pi}=(0.18\pm 0.57 )\%$ and $\delta R_{\tau/K}=(0.97\pm 0.58 )\%$, which imply $\left|g_\tau/g_\mu\right|_\pi=0.9964\pm 0.0038$ and $\left|g_\tau/g_\mu\right|_K=0.9857\pm 0.0078$, compatible with and at $1.8\sigma$ of lepton universality, respectively. We test unitarity and bind non-standard effective interactions with the $\tau \to P \nu_\tau [\gamma]$ decays.