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

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 Omnès 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 $\kappa /K_0^{\ast }(700)$ for the physical pion mass value and in the case of $\sigma /f_0(500)$, $\kappa /K_0^{\ast }(700)$ also for unphysical pion mass values.

14 pages, 6 figures, the version accepted for publication in Physical Review D