$\gamma \gamma \to \pi^0 \pi^0$ and $\eta \to \pi^0 \gamma \gamma$ at low energy within the Extended Nambu Jona-Lasinio Model

Abstract

Within the Extended Nambu Jona-Lasinio model, we calculate the $O(p^6)$ counterterms entering the low-energy expansion of the $\gamma \gamma \to \pi^0 \pi^0$ and the $\eta \to \pi^0 \gamma \gamma$ amplitudes in Chiral Perturbation Theory. For $\gamma \gamma \to \pi^0 \pi^0$ our results are compatible with both the experimental data and the two-loop calculation using meson resonance saturation. For the $\eta$ decay we find $\Gamma(\eta\to\pi^0 \gamma\gamma)=0.58\pm 0.3$ eV which is in agreement with experiment within one standard deviation. We also give predictions for the neutral pion polarizabilities and compare them with the results obtained from resonance saturation.