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

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.