Determination of the Lightest Strange Resonance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>K</mml:mi><mml:mn>0</mml:mn><mml:mo>*</mml:mo></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mn>700</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>κ</mml:mi></mml:math>, from a Dispersive Data Analysis
J. R. Peláez, A. Rodas
Abstract
In this work we present a precise and model-independent dispersive determination from data of the existence and parameters of the lightest strange resonance $\ensuremath{\kappa}/{K}_{0}^{*}(700)$. We use both subtracted and unsubtracted partial-wave hyperbolic and fixed-$t$ dispersion relations as constraints on combined fits to $\ensuremath{\pi}K\ensuremath{\rightarrow}\ensuremath{\pi}K$ and $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}K\overline{K}$ data. We then use the hyperbolic equations for the analytic continuation of the isospin $I=1/2$ scalar partial wave to the complex plane, in order to determine the $\ensuremath{\kappa}/{K}_{0}^{*}(700)$ and ${K}^{*}(892)$ associated pole parameters and residues.