Electromagnetic effects in eta --> 3 pi

TL;DR

This paper re-evaluates electromagnetic corrections in eta decays to three pions at next-to-leading order, highlighting the significance of previously neglected effects and confirming that overall corrections are small despite complex features.

Contribution

It introduces a detailed analysis of electromagnetic effects at NLO, emphasizing the importance of e^2(m_d-m_u) terms often overlooked in eta decay calculations.

Findings

Electromagnetic corrections are small overall.

Effects of order e^2(m_d-m_u) are non-negligible.

Complex features like Coulomb poles and cusps are present but do not dominate corrections.

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_d-m_u) 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.