$\gamma \gamma \to {\pi }^0{\pi }^0$ 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.

Latex, 27 pages, 1 figure available on request

References in corpus (2)

• Low-Energy Photon-Photon Collisions to Two-Loop Order
• Two- and Three-Point Functions in the Extended NJL Model

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