Radiative corrections to $τ\to π(K) ν_τ[γ]$: a reliable new physics test

Abstract

The ratios $R_{τ/P}\equiv Γ(τ\to P ν_τ[γ]) / Γ(P \toμν_μ[γ])$ ($P=π, K$) provide sensitive tests of lepton universality $\left|g_τ/g_μ\right|=1$ and are a useful tool for new physics searches. The radiative corrections to $R_{τ/P}$ 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 $δR_{τ/π}=(0.18\pm 0.57 )\%$ and $δR_{τ/K}=(0.97\pm 0.58 )\%$, which imply $\left|g_τ/g_μ\right|_π=0.9964\pm 0.0038$ and $\left|g_τ/g_μ\right|_K=0.9857\pm 0.0078$, compatible with and at $1.8σ$ of lepton universality, respectively. We test unitarity and bind non-standard effective interactions with the $τ\to P ν_τ[γ]$ decays.