sigma and f_0(980) substructures from gamma-gamma to pi-pi, J/psi, phi radiative and D_s semi-leptonic decays

TL;DR

This paper uses an improved analytic K-matrix model to analyze gamma-gamma to pi-pi scatterings, extracting the widths of sigma and f_0(980) mesons, and explores their substructures and production in various decays, providing insights into their quark and gluonium components.

Contribution

It introduces an improved analytic K-matrix approach to extract scalar meson widths and investigates their substructures and production mechanisms in different decay processes.

Findings

Sigma gamma-gamma width is 0.16 keV, not favoring four-quark or molecule models.

F_0(980) gamma-gamma width is 0.28 keV, compatible with ar ss or gluonium components.

Total gamma-gamma widths are consistent with dispersion relations and PDG values.

Abstract

Using an improved "analytic K-matrix model", we reconsider the extraction of the sigma/f_0(600) and f_0(980) gamma-gamma widths from gamma-gamma to pi-pi scatterings data of Crystal Ball and Belle. Our main results are summarized in Tables 3 and 4. The averaged sigma "direct width" to gamma-gamma is 0.16(3) keV which confirms a previous result of [1] and which does neither favour a large four-quark (diquark-antidiquark) nor a molecule nor a pure \bar qq component. The "direct width" of the f_0(980) of 0.28(2) keV is much larger than the four-quark expectation but can be compatible with a \bar ss or gluonium component. We also found that the rescattering part of the amplitude is relatively large indicating an important contribution of the meson loops in the determination of the gamma-gamma total widths. This is mainly due to the large couplings of the sigma and f_0(980) to pi-pi and/or \bar KK, which can also be due to a light scalar gluonium with large OZI violating couplings but not necessary to a four-quark or molecule state. Our average results for the total (direct+rescattering) gamma-gamma widths: Gamma_sigma^{tot}= 3.08(82) keV, Gamma_{f_0}^{tot}= 0.16(1) keV} are comparable with the ones from dispersion relations and PDG values. Using the parameters from QCD spectral sum rules, we complete our analysis by showing that the production rates of unmixed scalar gluonia sigma_B(1) and G (1.5-1.6) agree with the data from J/\psi, phi radiative and D_s semi-leptonic decays.