Improved description of dilepton production in τ − → ντP− decays

Abstract

Recently, the Belle Collaboration reported the first measurements of the τ−→ντπ−e+e− branching fraction and the spectrum of the pion-dielectron system. In an analysis previous to Belle’s results, we evaluated this branching fraction which turned out to be compatible with that reported by Belle, although with a large uncertainty. This is the motivation to seek for improvement on our previous evaluation of τ−→ντπ−ℓ+ℓ− decays (ℓ=e, μ). In this paper we improve our calculation of the WP−γ∗ vertex by including flavor-symmetry breaking effects in the framework of the resonance chiral theory. We impose QCD short-distance behavior to constrain most parameters and data on the π−e+e− spectrum reported by the Belle Collaboration to fix the remaining free ones. As a result, improved predictions for the branching ratios and hadronic/leptonic spectra are reported, which are in good agreement with observations. Analogous calculations for the strangeness-changing τ−→ντK−ℓ+ℓ− transitions are reported for the first time. Albeit one expects the mπμ+μ− spectrum to be measured in Belle-II and the observables with ℓ=e can be improved, it is rather unlikely that the K channels can be measured due to the suppression factor |Vud/Vus|2=0.05.