$γγ\to π^0 π^0$ and $η\to π^0 γγ$ 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 $γγ\to π^0 π^0$ and the $η\to π^0 γγ$ amplitudes in Chiral Perturbation Theory. For $γγ\to π^0 π^0$ our results are compatible with both the experimental data and the two-loop calculation using meson resonance saturation. For the $η$ decay we find $Γ(η\toπ^0 γγ)=0.58\pm 0.3$ 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.