$\gamma \gamma \to {\pi }^0{\pi }^0$ and $\eta \to {\pi }^0\gamma \gamma$ at $O(p^6)$ in the NJL model

Abstract

We discuss the processes $\gamma \gamma \to {\pi }^0{\pi }^0$ and $\eta \to {\pi }^0\gamma \gamma$ at $O(p^6)$ in the momentum expansion. The calculation involves tree--level, one--loop and two--loop diagrams of a chiral effective lagrangian which is obtained by a bosonization of the NJL model. The importance of integrating out meson resonances (reduction) is pointed out. Our final results for the total cross section of $\gamma \gamma \to {\pi }^0{\pi }^0$ are in good agreement with the experimental data of the Crystal Ball Collaboration. For the width of the $\eta \to {\pi }^0\gamma \gamma$ decay we obtain the value $0.11$ eV which has to be compared with the experimental value of $(0.84\pm 0.18)$ eV. Alternatively, taking empirical parameters from a vector--meson--dominance model the prediction for the decay width is $0.35$ eV. We present a prediction for the differential decay probability as a function of $m_{\gamma \gamma }^2/m_{\eta }^2$.

arXiv comment16 pages, LaTeX, 2 figures included. Complete Postscript file is available at http://cv.jinr.dubna.su/~lanyov/save/gg-prep.ps

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• A theoretical analysis of the doubly radiative decays ${\eta }^{(\prime )}\to {\pi }^0\gamma \gamma$ and ${\eta }^{\prime }\to \eta \gamma \gamma$
• The Physics of DAFNE and KLOE
• Search for the radiative decay $\eta \to {\pi }^0\gamma \gamma$ in the SND experiment at VEPP-2M
• Chiral perturbation theory - Success and challenge
• Quadrupole polarizabilities of the pion in the Nambu--Jona-Lasinio model
• Process eta -> pi^0 gamma gamma in the Nambu-Jona-Lasinio model
• Leptophobic dark photon interpretation of the ${\eta }^{\left(\prime \right)}\to {\pi }^0\left(\eta \right)\gamma \gamma$ puzzle
• Chiral Symmetry and Low Energy Pion-Nucleon Scattering
• Photoproduction of neutral pion pairs in the Coulomb field of the nucleus
• Pion Polarizability in the NJL model and Possibilities of its Experimental Studies in Coulomb Nuclear Scattering