Computing one-loop radiative corrections in τ → π(K)ν[γ] and testing new physics

Departamento de Matemáticas, Física y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, 46115 Alfara del Patriarca, València, Spain

^* e-mail: rosell@uchceu.es

Published online: 17 November 2022

Abstract

Without a doubt the ratios R_τ/p = Γ(τ → Pν_τ[γ])/Γ(P → μν_μ[γ]) (P = π, K) give a convenient scenario to test the lepton universality, the CKM unitarity and to search for non-standard interactions in τ decays. Moreover, the previous theoretical estimation of these observables is more than twenty-five years old and some assumptions of that estimation are unrealistic. Therefore, an update of R_τ/P was timely. The one-loop radiative corrections have been computed by considering an expansion of Chiral Perturbation Theory including the lightest spin-one resonances and respecting the short-distance behavior dictated by QCD. We have reported δR_τ/π = (0.18±0.57)% and δR_τ/K = (0.97±0.58)%, where the uncertainties have been induced fundamentally by the estimation of the counterterms. We have tested the lepton universality, the CKM unitarity and have searched for new physics in τ decays. As a by-product, we have also determined the theoretical radiative corrections to the τ → Pντ[γ] decay rates, δ_τπ = —(0.24 ± 0.56)% and δ_τK = —(0.15 ± 0.57)%.