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

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 $\kappa /K_0^{\ast }(700)$. 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 Omnès functions.

Comments: 10 pages, 1 figure, proceeding for "The 10th International Workshop on Chiral Dynamics"