6533b7dbfe1ef96bd12708a0

RESEARCH PRODUCT

Data-driven dispersive analysis of the ππ and πK scattering

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description

We present a data-driven analysis of the resonant $S$-wave $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K\ensuremath{\rightarrow}\ensuremath{\pi}K$ 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 $\ensuremath{\pi}\ensuremath{\pi}$ scattering we present both a single- and a coupled-channel analysis by including additionally the $K\overline{K}$ 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 $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}K\overline{K}$, respectively. By the analytic continuation to the complex plane, we found poles associated with the lightest scalar resonances $\ensuremath{\sigma}/{f}_{0}(500)$, ${f}_{0}(980)$, and $\ensuremath{\kappa}/{K}_{0}^{*}(700)$ for the physical pion mass value and in the case of $\ensuremath{\sigma}/{f}_{0}(500)$, $\ensuremath{\kappa}/{K}_{0}^{*}(700)$ also for unphysical pion mass values.