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

TL;DR

This paper calculates radiative corrections to tau decays into pions and kaons to test lepton universality and search for new physics, using a large-N_C expansion and chiral perturbation theory with heavy states.

Contribution

It introduces a reliable method for computing radiative corrections to tau decay ratios, improving tests of lepton universality and constraining new physics.

Findings

Radiative corrections are quantified with uncertainties.

Results support lepton universality within experimental errors.

Constraints on non-standard interactions are derived.

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.