### Speaker

Ms
Judith Plenter
(Helmholtz-Institut für Strahlen- und Kernphysik, Bonn-Cologne Graduate School of Physics and Astronomy)

### Description

It has been shown that the decay amplitude $\eta'\rightarrow \pi^+\pi^-\gamma$ has an important impact on the dispersion-theoretical analysis of the singly-virtual $\eta'$ transition form factor [1]. Consequently, we expect that the *doubly*-virtual transition form factor can be understood in more detail, starting from an analysis of the decay $\eta'\rightarrow2(\pi^+\pi^-)$. It was found that the $\eta'$ decay into four charged pions is clearly dominated by $\rho$ resonances [2]. The thus predicted branching ratio has recently been confirmed by a measurement of the BESIII collaboration [3]. The $a_2$ tensor meson corrects the amplitude of $ \eta' \rightarrow \pi^+\pi^-\gamma$ noticeably [4] and should therefore also be incorporated into the decay at hand. We use a resonance model to describe the tree-level contribution of the $a_2$ to the decay $ \eta' \rightarrow 2(\pi^+\pi^-)$ and amend the resulting amplitude through a dispersive analysis of the universal $\pi\pi$ final-state interactions. This leads to non-factorizing contributions to the doubly-virtual $\eta'$ transition form factor needed for the light-by-light scattering contribution to the anomalous magnetic moment of the muon and will allow to judge the validity of the factorization ansatz currently used therein.
References:
- [1] C. Hanhart *et al.* (2013), arXiv:1307.5654 [hep-ph]
- [2] F. K. Guo, B. Kubis and A. Wirzba (2011), arXiv:1111.5949 [hep-ph]
- [3] M. Ablikim *et al.* [BESIII Collaboration] (2014), arXiv:1404.0096 [hep-ex]
- [4] B. Kubis and J. Plenter (2015), arXiv:1504.02588 [hep-ph]

### Summary

Corrections to the decay amplitude of $\eta'\rightarrow2(\pi^+\pi^-)$ due to the $a_2$ meson, calculated using a resonance model amended by a dispersive analysis, lead to non-factorizing contributions to the doubly-virtual $\eta'$ transition form factor.

### Primary author

Ms
Judith Plenter
(Helmholtz-Institut für Strahlen- und Kernphysik, Bonn-Cologne Graduate School of Physics and Astronomy)

### Co-author

Bastian Kubis
(Bonn University)