eta -> pi^+ pi^- pi^0 gamma in Chiral Perturbation Theory

Abstract

We analyse the radiative decay $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$ in the low--energy expansion of the Standard Model. We employ the notion of ``generalized bremsstrahlung'' to take full advantage of the theoretical and experimental information on the corresponding non-radiative $\eta \to 3\pi$ decay. The direct emission amplitude of $\mathcal{O}(p^4)$ is due to one-loop diagrams with intermediate pions (isospin violating) and kaons (isospin conserving). The isospin conserving contributions to direct emission, including vector meson exchange appearing at $\mathcal{O}(p^6)$, are suppressed.

Comments: 13 pages, 1 fig; minor modifications (results unchanged)