Parameters of scalar resonances from the combined analysis of data on processes $\pi\pi\to\pi\pi,K\bar{K},\eta\eta$ and $J/\psi$ decays

TL;DR

This paper performs a combined analysis of scattering and decay data to determine the properties of scalar mesons, especially the $f_0(500)$, using a method based on analyticity and unitarity, revealing a preference for a wider resonance.

Contribution

It introduces a unified analysis approach combining multiple datasets and decay channels to accurately extract parameters of scalar resonances, particularly the $f_0(500)$.

Findings

Two possible $f_0(500)$ parameter sets with different widths were identified.

BESIII data favors a wider $f_0(500)$ resonance.

Analysis provides insights into scalar meson spectroscopy.

Abstract

A combined analysis of data on isoscalar S-wave processes $\pi\pi\to\pi\pi,K\overline{K},\eta\eta$ and on decays $J/\psi\to\phi\pi\pi,\phi K\overline{K}$ from the DM2, Mark III and BESIII collaborations is performed to study $f_0$ mesons. The method of analysis is based on analyticity and unitarity and uses an uniformization procedure. In the analysis limited only to the multi-channel $\pi\pi$-scattering data, two possible sets of parameters of the $f_0(500)$ were found: in both cases the mass was about 700 MeV but the total width was either about 600 or 930 MeV. The extension of the analysis using only the DM2 and Mark III data on the $J/\psi$ decays does not allow to choose between these sets. However, the data from BESIII on the di-pion mass distribution in the decay $J/\psi\to\phi\pi^+\pi^-$ clearly prefers the wider $f_0(500)$ state. Spectroscopic implications from results of the analysis are also discussed.