Contributions of the C-odd axial-vector resonances to eta --> pi 0 gamma gamma and gamma gamma --> pi 0 pi 0.

Abstract

We consider the contributions of the $C$-odd axial-vector resonances (${b}_{1}$, ${h}_{1}$) to $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}\ensuremath{\gamma}$, as well as those of the usual $C$-odd vector resonances ($\ensuremath{\rho}$, $\ensuremath{\omega}$) and chiral loops. Inclusion of ${b}_{1}(1235)$, ${h}_{1}(1170)$, ${h}_{1}(1380)$ increases the decay width of $\ensuremath{\eta}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}\ensuremath{\gamma}$, improving the theoretical prediction. The measurement of the $\ensuremath{\gamma}\ensuremath{\gamma}$ spectrum can test our model. We also discuss the effects of these $C$-odd axial-vector resonances on electromagnetic interactions of neutral pions: $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and electric and magnetic polarizabilities of ${\ensuremath{\pi}}^{0}$.