Lightest Scalar Resonances and the Dynamics of the \gamma\gamma\to\pi\pi Reactions

TL;DR

This paper analyzes high-statistics Belle data on gamma-gamma to pion-pion reactions below 1.5 GeV, revealing the small direct couplings of light scalar resonances and emphasizing their four-quark transition mechanisms.

Contribution

It provides a detailed analysis of the dynamical mechanisms of gamma-gamma to pion-pion reactions and estimates decay widths of light scalar resonances, highlighting their four-quark nature.

Findings

Small direct gamma-gamma coupling constants for (600) and f_0(980)

Decay widths of (600)gamma o ext ext{(600)}gamma ext ext{(600)} and f_0(980)gamma o ext ext{(980)}gamma ext ext{(980)} estimated around 0.45 keV and 0.19 keV respectively

The role of chiral shielding of the (600) resonance is emphasized.

Abstract

The high-statistics Belle data on the \gamma\gamma\to\pi^+\pi^- and \gamma\gamma\to\pi^0\pi^0 reactions have been jointly analyzed. The main dynamical mechanisms of these reactions for energies below 1.5 GeV have been revealed. It has been shown that the direct coupling constants of the \sigma(600) and f_0(980) resonances with a \gamma\gamma pair are small and that the \sigma(600)\to\gamma\gamma and f_0(980)\to\gamma\gamma decays are four-quark transitions due primarily to \pi^+\pi^- and K^+K^- loop mechanisms, respectively. The role of the chiral shielding of the \sigma(600) resonance is emphasized. The widths of the f_0(980)\to\gamma\gamma and \sigma(600)\to\gamma\gamma decays averaged over the resonance mass distributions, as well as the width of the f_2(1270)\to\gamma\gamma decay, are estimated as (\Gamma_{f_0\to\gamma\gamma})_{\pi\pi}\approx 0.19 keV, (\Gamma_{\sigma \to\gamma\gamma})_{\pi\pi}\approx 0.45 keV, and \Gamma_{f_2\to\gamma\gamma}(m^2_{f_2})\approx 3.8$ keV.