Calculation of resonances from $K \pi$ scattering

TL;DR

This paper determines the properties of various strange resonances in pion-kaon scattering below 1.8 GeV using a model-independent analytic continuation method with Padé approximants, ensuring consistency with dispersion relations.

Contribution

It introduces a model-independent approach to extract resonance parameters from scattering data using Padé approximants and dispersion relations.

Findings

Accurate determination of resonance masses and widths

Identification of pole positions without model assumptions

Consistent resonance parameters with dispersion relations

Abstract

We present a determination of the mass, width and coupling of the strange resonances appearing in pion-kaon scattering below 1.8 GeV, namely the much debated $K^*_0(800)$ or $\kappa$, the scalar $K^*_0(1430)$, the $K^*(892)$ and $K^*(1410)$ vectors, the spin-two $K^*_2(1430)$ as well as the spin-three $K^*_3(1780)$. The parameters of each resonance are determined using a direct analytic continuation of the pion-kaon partial waves by means of Pad\'e approximants, thus avoiding any particular model description of their pole positions and residues, while taking into account the analytic requirements imposed by dispersion relations.