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

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.