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

Sergi Gonzàlez-Solís,Pablo Roig

doi:10.1140/epjc/s10052-019-6943-9

Abstract

We explore the potential of a combined analysis of the decays tau ^{-}rightarrow pi ^{-}pi ^{0}nu _{tau } and tau ^{-}rightarrow K^{-}K_{S}nu _{tau } in the determination of the rho (1450) and rho (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_{V}^{pi }|^{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 rho (1450) and rho (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 rho -pole position. On the other hand, we benefit from the recent experimental data for the transition tau ^{-}rightarrow K^{-}K_{S}nu _{tau } 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 higher-quality data on the K^{-}K_{S} decay channel will allow to compete with the |F_{V}^{pi }|^{2} ones and improve the determination of the rho (1450) and rho (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.

Highlights

Tau lepton decays into a neutrino and hadrons provide a privileged scenario to investigate the non-perturbative regime of QCD under rather clean conditions since half of the transition is purely electroweak and can be computed straightforwardly
We explore the potential of a combined analysis of the decays τ − → π −π 0ντ and τ − → K − K Sντ in the determination of the ρ(1450) and ρ(1700) resonance properties in the frame of resonance Chiral Theory supplemented by dispersion relations
As one approaches the resonance region E ∼ Mρ, Chiral Perturbation Theory (ChPT) ceases to provide a good description of the physics and the resonance fields shall be explicitly incorporated into the description as new degrees of freedom

Summary

Introduction

Tau lepton decays into a neutrino and hadrons provide a privileged scenario to investigate the non-perturbative regime of QCD under rather clean conditions since half of the transition is purely electroweak and can be computed straightforwardly. The strong dynamics is encoded within the hadronic matrix element which, in turn, is given in terms of form factors As it is well-known, Chiral Perturbation Theory (ChPT) [2,3] provides a successful description of these form factors valid at very low energies E

The pion vector form factor

Exponential Omnès representation

Dispersive representation

L r9 Fπ2

Conclusions