One-loop determination of τ → π(K)ν τ [γ] branching ratios and new physics tests

Abstract

Abstract We calculate the ratios R τ/P ≡ Γ (τ → Pν 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. As a by-product, we report the theoretical radiative corrections to the τ → Pν τ [γ] decay rates: δ τπ = −(0.24 ± 0.56)% and δ τK = −(0.15 ± 0.57)%.

Keywords

• Chiral Lagrangians
• Effective Field Theories
• Kaon Physics
• 1/N Expansion