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 $\Gamma (\sigma \to \gamma \gamma )\cong 0.126\mathrm{keV}$. The smallness of the result and the relative weight between its components, $\frac{{\Gamma }_{\gamma \gamma \to S_1}}{\Gamma \gamma \gamma \to \pi \pi \to S_1}<1$, suggests that the scalar $0^{++}$ meson is mainly a $Q^2{\bar{Q}}^2$ state.

Comments: 14 pages, 6 figures. Part of the paper rewritten and enlarged, including a discussion on pi-pi phase shifts. Added references