K pi vector form factor constrained by tau ---> K pi nu_tau and K_l3 decays

TL;DR

This paper employs dispersive representations to analyze K pi form factors using tau decay data, constraining them with K_l3 decay results, and extracts parameters like the K*(892) mass, width, and scattering parameters.

Contribution

It introduces a dispersive analysis of K pi form factors constrained by tau and K_l3 decay data, providing precise determinations of form factor parameters and scattering thresholds.

Findings

Determined vector form factor slope and curvature from data.

Extracted K*(892) resonance mass and width.

Calculated phase-space integrals for K_l3 decays.

Abstract

Dispersive representations of the Kpi vector and scalar form factors are used to fit the spectrum of tau ---> K pi nu_tau obtained by the Belle collaboration incorporating constraints from results for K_l3 decays. The slope and curvature of the vector form factor are obtained directly from the data through the use of a three-times-subtracted dispersion relation. We find $\lambda_+'=(25.49 \pm 0.31) \times 10^{-3}$ and $\lambda_+"= (12.22 \pm 0.14) \times 10^{-4}$. From the pole position on the second Riemann sheet the mass and width of the $K^*(892)^{\pm}$ are found to be $m_{K^*(892)^\pm}=892.0\pm 0.5$~MeV and $\Gamma_{K^*(892)^\pm}=46.5\pm 1.1$~MeV. The phase-space integrals needed for K_l3 decays are calculated as well. Furthermore, the Kpi isospin-1/2 P-wave threshold parameters are derived from the phase of the vector form factor. For the scattering length and the effective range we find respectively $a_{1}^{1/2}\,= ( 0.166\pm 0.004)\,m_\pi^{-3}$ and $b_{1}^{1/2}\,=( 0.258\pm 0.009)\,m_\pi^{-5}$.