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

Abstract

We calculate the ratios R τ /P ≡ Γ (τ → P ν τ [γ]) /Γ (P → µν µ [γ]) (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±0.57)% and δR τ /K = (0.97±0.58)%, where the uncertainties are induced fundamentally by the counterterms. We test the lepton universality, obtaining |g τ /g µ | π = 0.9964±0.0038 and |g τ /g µ | K = 0.9857±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: ∆ τ π = −(0.15 ± 0.72) • 10 −2 and ∆ τ K = −(0.36 ± 1.18) • 10 −2 . As a by-product, we report the theoretical radiative corrections in τ → P ν τ [γ] decays: δ τ π = −(0.24 ± 0.56)% and δ τ K = −(0.15 ± 0.57)%.