Dispersive determination of resonances from $\pi\pi$ scattering data

Abstract

We provide a precise, model- and parametrization-independent dispersive determination of the $f_0(500)$, $\rho(770)$, $f_0(980)$, $f_2(1270)$, $f_0(1370)$, $\rho(1450)$, $f_0(1500)$, and $\rho_3(1690)$ resonance pole parameters. They are obtained from the analytic continuation, by means of continued fractions, of forward dispersion relations, whose input is a recent global dispersive analysis of $\pi \pi$ scattering data. From this dispersive study, we find no indications of other resonant poles below 1.7 GeV. Beyond this energy, we also provide resonance pole parameters from the direct analytic continuation of Global Fits to the three existing incompatible datasets. Depending on the dataset we find poles for the $\rho(1700)$, $f_0(1710)$, $\rho(1900)$, $f_2(1950)$, and $f_0(2020)$ resonances. We also present the Argand diagrams of these Global Fits and illustrate that each resonance does not necessarily have to trace a full circle in the diagram.