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.

Comments: 5 pages, minor rewording. Accepted for publication as a Letter in Physical Review D