Dispersion relations for ${\eta }^{\prime }\to \eta \pi \pi$

Abstract

We present a dispersive analysis of the decay amplitude for ${\eta }^{\prime }\to \eta \pi \pi$ that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the $\pi \pi$ and $\pi \eta$ scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.

22 pages, 10 figures; v2: added footnote, version published in EPJC

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