Short and long distance effects in the decay τ → πν(γ)

Abstract

We calculate the radiative corrections to the decays τ → Mν τ and π → lν l , where the meson M is M = π or K and the lepton l is l = e or µ. We perform a complete calculation, which includes internal bremsstrahlung and structure dependent radiation in the radiative decays and point meson, hadronic structure dependent and short distance contributions in the virtual corrections. Our result for the radiative correction to the ratio Γ(τ → πν τ (γ))/Γ(π → µν µ (γ)) is δR τ /π = 0.16 +0.09 −0.14 %. For the ratio Γ(τ → Kν τ (γ))/Γ(K → µν µ (γ)), we obtain δR τ /K = 0.90 +0.17 −0.26 %. For completeness we have also calculated the ratio of the electronic and muonic decay modes of the pion.

The role of the S 3 GUT leptoquark in flavor universality and collider searches

“….0, (4.6) where the dominant error of the experimental ratio is due to the τ lifetime uncertainty, whereas on the theory side it is the radiative correction δR τ /K = (0.90 ± 0.22)% [63] which is the source of uncertainty. The constraint is expressed as:…”

Global constraints on a heavy neutrino

“…The radiative corrections δ π µ and δ K µ have been estimated in Ref. [26]. We estimate the prediction for Γ(τ → M ν)/Γ(M → eν) by multiplying the predicted value of Γ(τ → M ν)/Γ(M → µν) by the value of Γ(M → µν)/Γ(M → eν) calculated in Ref.…”

Spectral functions from hadronic T decays and QCD

“…As such it is expected to be weakly dependent on the specific hadronic final state, as verified in the τ −→ (π, K)ν τ channels [10]. Recently, detailed calculations have been performed for the ππ 0 channel [11] which also confirm the relative smallness of the longdistance contributions.…”

“…The evolution of the α s (m (10) where the last error stands for possible ambiguities in the evolution due to uncertainties in the matching scales of the quark thresholds [31]. The result (10) can be compared to the precise determination from the measurement of the Z width, as obtained in the global electroweak fit.…”