Chiral Perturbation Theory Predictions for $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$

Abstract

The $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ decay is discussed in the general context of Chiral Perturbation Theory (ChPT), assuming that the low--energy constants (counter--terms) are saturated by vector-meson resonances. The $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ amplitude can be separated in two distinct pieces: the inner bremsstrahlung, $A^{(IB)}$, and the structure dependent (or direct emission), $A^{(SD)}$, amplitudes. The former -- which essentially contains the same physics as $A(\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0)$ -- is found to dominate over the second one -- which looks more interesting from the ChPT point of view.

14 pages, 4 figures. PS file (96/8 N/P) available at http://www.nordita.dk/locinfo/preprints.html