Radiative Corrections to the Decay $τ\toπν_τ$

Abstract

We have calculated the radiative corrections to the decay $τ\to π(K) ν_τ$, taking to account internal bremsstrahlung and structure dependent radiation in the radiative decay and point meson, hadronic structure dependent and short distance contributions in the virtual corrections. We display the spectra of the photon energy and of the pion-photon invariant mass in the decay $τ\toπν_τγ$ and compare with the PHOTOS Monte-Carlo. Our result for the radiative correction to the ratio $Γ(τ\toπν_τ(γ))/ Γ(π\toμν_μ(γ))$ is $δR_{τ/π} = \left(0.16 \pm 0.14 \right) \%$ and for the ratio $Γ(τ\to Kν_τ(γ))/ Γ(K\toμν_μ(γ))$, we obtain $δR_{τ/K } = \left(0.90 \pm 0.22 \right) \%$.