$\gamma \gamma\to \pi^0 \pi^0$ as a test for the existence of a light $\sigma$ meson

We work out predictions of the Linear Sigma Model for the $\gamma \gamma \to\pi^0 \pi^0$ cross section. We consider the sigma width, which is introduced in a consistent way with chiral Ward identities. The results of Chiral Perturbation Theory are recovered in the $m_\sigma \to \infty$ limit. A fit to existing experimental results is consistent with a light and broad $\sigma$ meson.