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

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

1995-08-31

arxiv.org/abs/hep-ph/9508407v2

Nucl.Phys. B459 (1996) 283-310

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/0550-3213(95)00598-6

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 ${\cal{O}}(p^6)$ 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 $\gamma \gamma \to \pi^0 \pi^0$ 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.

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