Improved description of di-lepton production in $τ^-\toν_τP^-$ decays

Abstract

Recently, the Belle collaboration reported the first measurements of the τ − → ν τ π − e + e − branching fraction and the spectrum of the piondielectron system. This decay and the corresponding di-muon channel offer the possibility to extract information on the W πγ * vertex in a kinematical region relevant for the evaluations of the radiative corrections to τ − → ν τ π − and of the pion pole part of the hadronic light-by-light contribution to a µ . This is the motivation to seek for improvements on our previous evaluation of τ − → ν τ π − + − decays ( = e, µ). In this paper we ameliorate our calculation of the W P − 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 Belle to fix the remaining free ones. As a result, improved predictions for the branching ratios and hadronic/leptonic spectra are reported, in good agreement with observations. Analogous calculations for the strangeness-changing τ − → ν τ K − + − transitions are reported for the first time.

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

“…Let us start by considering the description of the real-photon corrections, for which, we follow refs. [25][26][27]. The matrix element can be split as…”

“…On the other hand, diagram (d) includes the vector and axial structure-dependent contributions given by M V + M A , which yield [25][26][27] 1…”

“…them from the Resonance Chiral Theory [19][20][21] computation in refs. [25][26][27], where the resonance couplings contributing -upon integrating vector and axial mesons out -up to the next-to-leading order chiral couplings in each parity sector were considered. Regarding the vector form factors, they are given by 2…”

“…Although we take as our main framework the more refined analysis of scenario (b), summarized in the tilded form factors of (2.27) and (2.28) [25][26][27], we have also calculated δ τ P vSD with scenario (a), summarized in the barred form factors of (2.21) [25][26][27]. We have taken as our first source of error in (4.11) one half of the deviation in δ τ P vSD between the two scenarios, resulting in ±0.22% and ±0.24% for the pion and kaon case, respectively.…”

Exclusive hadronic $τ$ decays, within $\&$ beyond the Standard Model

“…, which is obtained from lattice data [10]. Radiative corrections (including structuredependent effects) are essential in elucidating this [11][12][13]. LEP measurements of this one-meson tau decays branching ratios [14,15] and by BaBar of their normalization with respect to the lepton 1 See, respectively, Gabriel López Castro ( † ), Alberto Lusiani ( * ), Bachir Moussallam ( • ), Zhi-Hui Guo and Frederic Noël ( ), Álex Miranda ( % ), Fabian Krinner and Mikhail Mikhasenko ( △ ) talks and corresponding contributions to these proceedings.…”