$\eta \to {\pi }^0\gamma \gamma$ to $\mathcal{O}(p{)}^6$ in Chiral Perturbation Theory

Abstract

The decay $\eta \to {\pi }^0\gamma \gamma$ is discussed in the framework of SU(3) chiral perturbation theory. The process is dominated by the $\mathcal{O}(p^6)$ in the momentum expansion where tree-level amplitudes from the effective Lagrangian ${\mathcal{L}}^6$ enter together with one--loop contributions from ${\mathcal{L}}^4$ and two--loop contributions from ${\mathcal{L}}^2$. We estimate the 6 independent ${\mathcal{L}}^6$ coupling constants by resonance saturation consistent with the pion production process $\gamma \gamma \to {\pi }^0{\pi }^0$ and calculate the pion--loop part of the one- and two--loop amplitude. Predictions for the total rate and spectrum of $\eta \to {\pi }^0\gamma \gamma$ are given together with a discussion of the uncertainties involved.

Comments: 24 pages, 3 tables and 8 figures. A LaTeX error has been fixed