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One-loop determination of $τ\to π(K) ν_τ[γ]$ branching ratios and new physics tests

We calculate the ratios $R_{τ/ P}\equiv Γ\left( τ\to P ν_τ[γ] \right) / Γ\left(P\to μν_μ[γ]\right)$ ($P=π,K$) at one loop following a large-$N_C$ expansion where Chiral Perturbation Theory is enlarged by including the lightest resonances and respecting the short-distance behavior dictated by QCD. We find $δR_{τ/π}=(0.18\pm 0.57 )\%$ and $δR_{τ/K}=(0.97\pm 0.58 )\%$, where the uncertainties are induced fundamentally by the counterterms. We test the lepton universality, obtaining $\left|g_τ/g_μ\right|_π=0.9964\pm 0.0038$ and $\left|g_τ/g_μ\right|_K=0.9857\pm 0.0078$, and analyze the CKM unitarity, getting results at $2.1σ$ and $1.5σ$ from unitarity via $|V_{us}/V_{ud}|$ and $|V_{us}|$, respectively. We also update the search for non-standard interactions in $τ$ decays. As a by-product, we report the theoretical radiative corrections to the $τ\to P ν_τ[γ]$ decay rates: $δ_{τπ} = -(0.24 \pm 0.56) \%$ and $δ_{τK} = -(0.15 \pm 0.57) \%$.} \maketitle