Insights into $Q^2 \bar{Q}^2$ states from an effective perspective

TL;DR

This paper uses an effective field theory approach to analyze the two-photon decay of the lightest scalar meson, suggesting it is predominantly a tetraquark state based on experimental data and theoretical modeling.

Contribution

It extends chiral perturbation theory to study scalar meson couplings and provides evidence for the tetraquark nature of the lightest scalar meson.

Findings

The decay width of the sigma meson to two photons is approximately 0.126 keV.

The scalar meson is mainly a $Q^2ar{Q}^2$ (tetraquark) state.

The two-photon coupling analysis supports the tetraquark interpretation.

Abstract

We discuss the two photon coupling of the lightest scalar meson on the basis of an extension of $\chi$PT. Using low energy data on the pion form-factor and the $\gamma\gamma\to \pi^+\pi^-(\pi^0\pi^0)$ cross-sections as inputs, we find $\Gamma(\sigma\to\gamma\gamma) \cong 0.126~\rm{keV} $. The smallness of the result and the relative weight between its components, ${\Gamma_{\gamma\gamma\to S_1}\over \Gamma{ \gamma\gamma\to\pi\pi\to S_1}} < 1$, suggests that the scalar $0^{++}$ meson is mainly a $Q^2\bar{Q}^2$ state.