K pi vector form factor, dispersive constraints and tau -> nu_tau K pi decays

TL;DR

This paper models the K pi vector form factor using dispersive constraints to analyze tau decay data, extracting resonance parameters and form factor shape parameters with high precision.

Contribution

It introduces a dispersive approach with multiple subtractions to accurately describe tau decay data and extract resonance and form factor parameters.

Findings

Resonance parameters of K*(892) are determined as M=892.0±0.9 MeV, Γ=46.2±0.4 MeV.

The slope and curvature of the vector form factor are measured as λ_+'=(24.7±0.8)×10^{-3} and λ_+''=(12.0±0.2)×10^{-4}.

A good fit to Belle data is achieved using a three-times subtracted dispersion relation.

Abstract

Recent experimental data for the differential decay distribution of the decay $\tau^-\to\nu_\tau K_S\pi^-$ by the Belle collaboration are described by a theoretical model which is composed of the contributing vector and scalar form factors $F_+^{K\pi}(s)$ and $F_0^{K\pi}(s)$. Both form factors are constructed such that they fulfil constraints posed by analyticity and unitarity. A good description of the experimental measurement is achieved by incorporating two vector resonances and working with a three-times subtracted dispersion relation in order to suppress higher-energy contributions. The resonance parameters of the charged $K^*(892)$ meson, defined as the pole of $F_+^{K\pi}(s)$ in the complex $s$-plane, can be extracted, with the result $M_{K^*}=892.0 \pm 0.9 $MeV and $\Gamma_{K^*}=46.2 \pm 0.4 $MeV. Finally, employing the three-subtracted dispersion relation allows to determine the slope and curvature parameters $\lambda_+^{'}=(24.7\pm 0.8)\cdot 10^{-3}$ and $\lambda_+^{''}=(12.0\pm 0.2)\cdot 10^{-4}$ of the vector form factor $F_+^{K\pi}(s)$ directly from the data.