Measurement of the decay $\eta^{\prime}\to\pi^{0}\pi^{0}\eta$ at MAMI

TL;DR

This paper reports a precise experimental measurement of the decay $ ext{η'} o ext{π}^0 ext{π}^0 ext{η}$, observing a cusp structure consistent with theoretical predictions based on $ ext{ππ}$ scattering lengths, using data from MAMI.

Contribution

First observation of a cusp structure in $ ext{η'}$ decay consistent with nonrelativistic effective-field theory predictions, with improved statistical accuracy over previous studies.

Findings

Measured decay matrix element with smaller uncertainties.

Observed a cusp below the $ ext{π}^+ ext{π}^-$ mass threshold.

Results agree with theoretical predictions based on $ ext{ππ}$ scattering lengths.

Abstract

An experimental study of the $\eta'\to \pi^0\pi^0\eta \to 6\gamma$ decay has been conducted with the best up-to-date statistical accuracy, by measuring $\eta'$ mesons produced in the $\gamma p \to \eta' p$ reaction with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The results obtained for the standard parametrization of the $\eta'\to \pi^0\pi^0\eta$ matrix element are consistent with the most recent results for $\eta'\to\pi\pi\eta$ decays, but have smaller uncertainties. The available statistics and experimental resolution allowed, for the first time, an observation of a structure below the $\pi^+\pi^-$ mass threshold, the magnitude and sign of which, checked within the framework of the nonrelativistic effective-field theory, demonstrated good agreement with the cusp that was predicted based on the $\pi\pi$ scattering length combination, $a_0-a_2$, extracted from $K \to 3\pi$ decays.