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

TL;DR

This paper studies the decay process eta -> pi+ pi- pi0 gamma within Chiral Perturbation Theory, utilizing generalized bremsstrahlung to connect radiative and non-radiative decay data, and calculates direct emission amplitudes at low order.

Contribution

It provides a detailed analysis of the eta radiative decay using Chiral Perturbation Theory, highlighting the role of one-loop diagrams and suppression of certain contributions.

Findings

Direct emission amplitude calculated at ${ m O}(p^4)$

Isospin conserving contributions are suppressed

Utilizes generalized bremsstrahlung to relate radiative and non-radiative decays

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 ${\cal O}(p^4)$ 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 ${\cal O}(p^6)$, are suppressed.