Dispersive analysis of the $\pi\pi$ and $\pi K$ scattering data

TL;DR

This paper performs a comprehensive, data-driven dispersive analysis of $$ and $$ meson scattering, identifying scalar resonance poles and providing results consistent with Roy-like analyses through a numerical $N/D$ method.

Contribution

It introduces a novel dispersive analysis combining conformal parametrization and the $N/D$ method for $$ and $$ scattering, including coupled-channel effects and resonance pole extraction.

Findings

Identified poles for $(500)$, $f_0(980)$, and $^*(700)$ resonances.

Achieved results consistent with Roy-like analyses.

Provided a coupled-channel analysis including $Kar{K}$ channels.

Abstract

We present a data-driven analysis of the S-wave $\pi\pi \to \pi\pi\,(I=0,2)$ and $\pi K \to \pi K\,(I=1/2, 3/2)$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are parametrized using the expansion in a suitably constructed conformal variable, which accounts for its analytical structure. The partial-wave dispersion relation is solved numerically using the $N/D$ method. The fits to the experimental data supplemented with the constraints from chiral perturbation theory at threshold and Adler zero give the results consistent with Roy-like (Roy-Steiner) analyses. For the $\pi\pi$ scattering we present the coupled-channel analysis by including additionally the $K\bar{K}$ channel. By the analytic continuation to the complex plane, we found poles associated with the lightest scalar resonances $\sigma/f_0(500)$, $f_0(980)$, and $\kappa/K_0^*(700)$. For all the channels we also performed the fits directly to the Roy-like (Roy-Steiner) solutions in the physical region, in order to minimize the $N/D$ uncertainties in the complex plane and to extract the most constrained Omn\`es functions.