$γγ\to π^0 π^0$ as a test for the existence of a light $σ$ meson

Abstract

We work out predictions of the Linear Sigma Model for the $γγ\toπ^0 π^0$ 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 $m_σ\to \infty$ limit. A fit to existing experimental results is consistent with a light and broad $σ$ meson.