Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering

TL;DR

This paper performs a comprehensive, data-driven dispersive analysis of $$ and $$ scattering processes, integrating experimental, lattice, and Roy analysis data to identify scalar resonance poles and validate theoretical models.

Contribution

It introduces a novel combined analysis of $$ and $$ scattering using partial-wave dispersion relations and conformal expansions, including coupled-channel effects and resonance pole extraction.

Findings

Consistent Omne8s matrix with recent Roy analyses.

Identification of poles for $(500)$, $f_0(980)$, and $K_0^*(700)$ resonances.

Validation of the dispersive approach against experimental and lattice data.

Abstract

We present a data-driven analysis of the resonant S-wave $\pi\pi \to \pi\pi$ and $\pi K \to \pi K$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion in a suitably constructed conformal variable. The fits are performed to experimental and lattice data as well as Roy analyses. For the $\pi\pi$ scattering we present both a single- and coupled-channel analysis by including additionally the $K\bar{K}$ channel. For the latter the central result is the Omn\`es matrix, which is consistent with the most recent Roy and Roy-Steiner results on $\pi\pi \to \pi\pi$ and $\pi\pi \to K\bar{K}$, respectively. 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 the physical pion mass value and in the case of $\sigma/f_0(500)$, $\kappa/K_0^*(700)$ also for unphysical pion mass values.