A dispersive analysis of the pion vector form factor and $$\tau ^{-}\rightarrow K^{-}K_{S}\nu _{\tau }$$ decay

Abstract

We explore the potential of a combined analysis of the decays τ − → π − π 0 ν τ and τ − → K − K S ν τ in the determination of the ρ(1450) and ρ(1700) resonance properties in the frame of resonance Chiral Theory supplemented by dispersion relations. On the one hand, we take advantage of the very precise data on the modulus squared of the pion vector form factor |F π V | 2 obtained by Belle to carry out a very dedicated analysis of the region where these resonances come up into play. Our study provides an improved treatment of the systematic theoretical errors and, as a most important result, we conclude that they dominate over the fit uncertainties in the determination of the ρ(1450) and ρ(1700) pole parameters and tend to be larger than in other determinations quoted in the literature where these errors were ignored or underestimated. The results of our analysis are summarized in numerical tables for the form factor modulus and phase, including both statistical and systematic errors, that can be found as ancillary material of this paper. As a byproduct, we also determine the low-energy observables of the pion vector form factor and the ρ-pole position. On the other hand, we benefit from the recent experimental data for the transition τ − → K − K S ν τ released by BaBar to perform a first analysis of its decay spectrum and discuss the role of these resonances in this decay. We point out that higherquality data on the K − K S decay channel will allow compete with the |F π V | 2 ones and improve the determination of the ρ(1450) and ρ(1700) resonance parameters as a result of a combined analysis. We hope our study to be of interest for present and future experimental analysis of these decays.

Exclusive hadronic tau decays as probes of non-SM interactions

“…To describe the pion vector form factor we follow the representation outlined in Ref. [19], and briefly summarized below for the convenience of the reader, and write a thrice subtracted dispersion relation…”

“…(6), cut is a cut-off whose value is fixed from the requirement that the fitted parameters are compatible within errors with the case cut → ∞. The value of cut = 4 GeV 2 was found to satisfy this criterion [19], and variations of cut were used to estimate the associated systematic error. For the input phase ( ) we use [19] ( ) =…”

“…(17) of Ref. [19]. Finally, for the high-energy region, we guide smoothly the phase to at 2 ( ∞ ( )) to ensure the correct asymptotic 1∕ fall-off of the form factor [56] 5 .…”

“…Finally, for the high-energy region, we guide smoothly the phase to at 2 ( ∞ ( )) to ensure the correct asymptotic 1∕ fall-off of the form factor [56] 5 . Armed with this parametrization, in [19] we have analyzed the high-statistics Belle data [57] on the pion vector form factor. The outcome that better illustrates the resulting analysis, and that we use for this work, is displayed in Fig.…”

“…In this respect, dispersion relations are a powerful tool to direct oneself towards a modelindependent description of meson form factors. For exam-sgonzal@iu.edu (S. Gonzàlez-Solís); jmiranda@fis.cinvestav.mx (A. Miranda); jrendon@fis.cinvestav.mx (J. Rendón); proig@fis.cinvestav.mx (P. Roig) ORCID(s): 0000-0003-1947-5420 (S. Gonzàlez-Solís); 0000-0002-6612-7157 (P. Roig) ple, the analyses of the decays − 0 [16,17,18,19] and − [20,21,22,23,24], carried out by exploiting the synergy between Resonance Chiral Theory [25] and dispersion theory, are found to be in a nice agreement with the rich data provided by the experiments. Accord with experimental measurements is also found for the − [19] and − [24,26] decay modes, although higher-quality data on these processes is required to constrain the corresponding theories or models, while the predictions for the isospinviolating − (′) channels [27,28] respect the current experimental upper bounds.…”