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.
Highlights
There has long been an interest in the study of anomalous decays, which are driven by the chiral anomaly of QCD.1 The η0/η → πþπ−γ decays are typical processes for exploring the box anomaly and investigating the ρ − ω mixing mechanism
Based on the final-state interaction theorem, we represent the amplitude in terms of an Omnes function multiplied by a form factor that corresponds to the contributions from left-hand cuts and right-hand cuts in the inelastic channels
The decay width of η0 → πþπ−γ provided by the Particle Data Group (PDG) [61] is implemented in our fit to constrain the unknown normalization factor N
Summary
There has long been an interest in the study of anomalous decays, which are driven by the chiral anomaly of QCD. The η0/η → πþπ−γ decays are typical processes for exploring the box anomaly and investigating the ρ − ω mixing mechanism. The η0/η → πþπ−γ decays are typical processes for exploring the box anomaly and investigating the ρ − ω mixing mechanism. They are useful to extract the pion vector form factor [2,3,4,5] and the form factors of η0/η → γγà transitions [3,4,5], helping us to further test, e.g., the Pascalutsa-Vanderhaeghen lightby-light sum rule [6,7,8]. The isospin-violating ρ − ω interference is constructed by invoking the resonance chiral theory (RχT) [32,33,34,35,36,37,38] The explicit expressions of the isospin-violating form factors in RχT are relegated to the Appendix
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
