Determination of the lightest strange resonance $K_0^{\ast }(700)$ or $\kappa$, from a dispersive data analysis

In this work we present a precise and model-independent dispersive determination from data of the existence and parameters of the lightest strange resonance $\kappa \mathrm{/}{K}_0^{\ast }(700)$. We use both subtracted and unsubtracted partial-wave hyperbolic and fixed-$t$ dispersion relations as constraints on combined fits to $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ data. We then use the hyperbolic equations for the analytic continuation of the isospin $I=1\mathrm{/}2$ scalar partial wave to the complex plane, in order to determine the $\kappa \mathrm{/}{K}_0^{\ast }(700)$ and $K^{\ast }(892)$ associated pole parameters and residues.