Electromagnetic corrections in eta --> 3 pi decays

TL;DR

This paper reevaluates electromagnetic corrections to eta decays into three pions at next-to-leading order, highlighting the significance of previously neglected effects and their impact on decay processes.

Contribution

It introduces a comprehensive analysis of electromagnetic effects at next-to-leading order, including previously disregarded terms of order e^2(m_u-m_d).

Findings

Electromagnetic corrections are generally small despite Coulomb poles and cusps.

Neglected effects of order e^2(m_u-m_d) are comparable to other electromagnetic contributions.

Overall corrections do not significantly alter decay amplitudes.

Abstract

We re-evaluate the electromagnetic corrections to eta --> 3 pi decays at next-to-leading order in the chiral expansion, arguing that effects of order e^2(m_u-m_d) disregarded so far are not negligible compared to other contributions of order e^2 times a light quark mass. Despite the appearance of the Coulomb pole in eta --> pi+ pi- pi0 and cusps in eta --> 3 pi0, the overall corrections remain small.