Dispersive representation of the pion vector form factor in τ→ππν τ decays

Abstract

We propose a dispersive representation of the charged pion vector form factor that is consistent with chiral symmetry and fulfills the constraints imposed by analyticity and unitarity. Unknown parameters are fitted to the very precise data on τ − → π − π 0 ντ decays obtained by Belle, leading to a good description of the corresponding spectral function up to a ππ squared invariant mass s ≃ 1.5 GeV 2 . We determine the ρ(770) mass and width pole parameters and obtain the values of low energy observables. The significance of isospin breaking corrections is also discussed. For larger values of s, this representation is complemented with a phenomenological description to allow its implementation in the new TAUOLA hadronic currents.

Resonance chiral Lagrangian currents and experimental data forτ−→π−π−π+ντNugent1, Przedziński2, Roig3 et al. 2013Phys. Rev. DSelf Cite932990View full textAdd to dashboardCite

“…In the case of the ð1450Þ resonance, the comparison of our results in Table VI with those in Ref. [27] show agreement for the width but some tension on the mass that is 20 MeV smaller in Table VI. It is important to note here, that there are observed resonances, f 2 ð1270Þ and f 0 ð1370Þ, which were reported CLEO [24,32] and are suggested by the fit to the BABAR data.…”

“…In particular there is very nice agreement in the literature for the ð770Þ pole parameters: M pole ¼ 761 AE 3 MeV and À pole ¼ 145 AE 4 MeV using different types of data and methods (see [27] and references therein for details). Our value in Table VI…”

“…Similar discussion for the two-pion and K decay modes can be found in Refs. [27,44]. 25 When looking at the right-hand plot in Fig.…”

“…Although we currently restrict ourselves to the lowest axial-vector resonance, a 1 ð1260Þ, in future analysis of multidimensional distributions we are going to include the a 1 ð1640Þ in the same way as it was done for the 0 ð1450Þ to test our hypothesis. 27 We prefer not to do this at the moment because the improvement of the fit on the peak and tail regions in the three-meson invariant mass distribution will come again together with an increase of the fit instability and a growth of the correlations between the (larger number of ) fit parameters. Lacking the complete multidimensional distributions it is advisable to proceed this way at present.…”

“…Precision studies of the two-pion vector form factor (see e.g. [27] and references therein), more specifically, a P-wave two-pion state, did not require to include the Coulomb interaction between the pion pair to describe the data accurately. We will consequently neglect P-wave Coulomb interaction among the final-state pions and stick to formula (12) to evaluate the effect of electromagnetic interactions among the pions and set (8) on rhs of (12).…”