Amplitude analysis of the anomalous decay $\eta'\to\pi^+\pi^-\gamma$

TL;DR

This paper performs an amplitude analysis of the decay $ ext{eta'} o ext{pi}^+ ext{pi}^- ext{gamma}$, using BESIII data, to understand the decay mechanisms and extract resonance properties.

Contribution

It introduces a novel amplitude model incorporating final-state interactions, anomaly effects, and isospin violation, providing new insights into the decay process and resonance parameters.

Findings

Anomaly contribution is essential to explain the data.

The decay width is dominated by the anomaly rather than isospin violation.

Pole positions and residues of $ ho$ and $oldsymbol{ extomega}$ are extracted.

Abstract

In this paper we perform an amplitude analysis of $\eta'\to\pi^+\pi^-\gamma$ and confront it with the latest BESIII data. Based on the final-state interaction theorem, we represent the amplitude in terms of an Omn\'es function multiplied by a form factor that corresponds to the contributions from left-hand cuts and right-hand cuts in the inelastic channels. We also take into account the isospin violation effect induced by $\rho-\omega$ mixing. Our results show that the anomaly contribution is mandatory in order to explain the data. Its contribution to the decay width of $\Gamma(\eta'\to\pi\pi\gamma)$ is larger than that induced by isospin violation. Finally we extract the pole positions of the $\rho$ and $\omega$ as well as their corresponding residues.