$η\to π^0 γγ$ to ${\cal{O}}(p)^6$ in Chiral Perturbation Theory

Abstract

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