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Nuclear and Particle Physics

Dispersive Analysis of Mesonic 3-Body Decays

by Tobias Isken (U. Bonn)



I will present a dispersive analysis of mesonic 3-body decay amplitudes based on the fundamental principles of analyticity and unitarity. In the described dispersion-theoretical framework the leading final-state interactions are fully taken into account. The formalism relies only on the respective 2-body scattering phase shifts.

The first part of the talk will focus on hadronic $\eta^\prime$ decays. The $eta^\prime\to\eta\pi\pi$ decay offers several features of interest [arXiv:1705.04339 [hep-ph]]: due to final-state interactions it can be used to constrain $\eta\pi$ scattering. It shows a cusp effect in the neutral channel ($\eta^\prime\to\eta\pi^{0}\pi^{0}$) within the physical decay region. The decay is also an essential input for a study of inelastic effects in the decay $\eta^\prime\to3\pi$.

The second part of the talk is focused on the $\omega\to3\pi$ decay. I will demonstrate how the dispersive framework can be used to investigate the quark mass dependence for a 3-body resonance [arXiv:1808.08957 [hep-ph]]. This may be used as an extrapolation tool for lattice QCD calculations. Here the $\omega$ serves as paradigm case, the framework can be generalised to other 3-body decay processes.

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