The f0(1370) controversy from dispersive meson-meson scattering data analyses

TL;DR

This paper confirms the existence of the f0(1370) resonance using a novel dispersive analysis method, providing precise pole positions and couplings, and highlighting data-driven tensions between different scattering channels.

Contribution

Introduces a new dispersive approach for analyzing inelastic resonances, establishing the f0(1370) resonance with model-independent pole determinations.

Findings

Confirmed the f0(1370) resonance in meson-meson scattering data.

Determined the pole position at approximately 1245-i300 MeV.

Identified a second pole in Kar K data with consistent parameters.

Abstract

We establish the existence of the long-debated $f_0(1370)$ resonance in the dispersive analyses of meson-meson scattering data. For this, we present a novel approach using forward dispersion relations, valid for generic inelastic resonances. We find its pole at $(1245\pm 40)- i\,(300^{+30}_{-70})$ MeV in $\pi\pi$ scattering. We also provide the couplings as well as further checks extrapolating partial-wave dispersion relations or with other continuation methods. A pole at $(1380^{+70}_{-60})-i\,(220^{+80}_{-70})$ MeV also appears in the $\pi\pi\to K\bar K$ data analysis with partial-wave dispersion relations. Despite settling its existence, our model-independent dispersive and analytic methods still show a lingering tension between pole parameters from the $\pi\pi$ and $K\bar K$ channels that should be attributed to data.