Improving the Kpi vector form factor through Kl3 constraints

TL;DR

This paper refines the $K o\pi$ vector form factor by integrating $K_{l3}$ decay constraints into a dispersion relation, improving parameter precision and providing updated resonance and phase-shift data.

Contribution

It introduces a combined dispersion relation approach incorporating $K_{l3}$ constraints to improve the $K o\pi$ form factor analysis.

Findings

Precise determination of form factor slope and curvature.

Updated $K^*(892)$ resonance parameters.

Calculated phase-space integrals and phase-shift parameters.

Abstract

The $K\pi$ vector form factor, $F_+^{K\pi}$, used to reproduce the Belle spectrum of $\tauKpi$ decays is described by means of a three-times subtracted dispersion relation also incorporating constraints from $K_{l3}$ decays. The slope and curvature of $F_+^{K\pi}$ are fitted to the data yielding $\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$ and $\lambda_+"= (12.22 \pm 0.14) \times 10^{-4}$. The pole parameters of the $K^*(892)^\pm$ are found to be $m_{K^*(892)^\pm}= 892.0\pm 0.5$ MeV and $\Gamma_{K^*(892)^\pm}= 46.5 \pm1.1$ MeV. The phase-space integrals relevant for $K_{l3}$ analyses and the $P$-wave isospin-1/2 $K\pi$ phase-shift threshold parameters are also calculated.