Amplitude analysis of the anomalous decay η ′ → π + π − γ

In this paper we perform an amplitude analysis of η′→π+π−γ and confront it with the latest BESIII data. Based on the final-state interaction theorem, we represent the amplitude in terms of an Omnés 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 ρ−ω mixing. Our results show that the anomaly contribution is mandatory in order to explain the data. Its contribution to the decay width of Γ(η′→ππγ) is larger than that induced by isospin violation. Finally we extract the pole positions of the ρ and ω as well as their corresponding residues.