Evidence for the Cusp Effect in $\eta'$ Decays into $\eta\pi^0\pi^0$

TL;DR

This study provides experimental evidence for the cusp effect in $ ext{eta'}$ decays into $ ext{eta} ext{pi}^0 ext{pi}^0$, analyzing a large dataset with nonrelativistic effective field theory to measure $ ext{pi} ext{pi}$ scattering parameters.

Contribution

First experimental observation of the cusp effect in $ ext{eta'}$ decays, with a measurement of the $ ext{pi} ext{pi}$ scattering length difference using a large dataset and effective field theory.

Findings

Evidence for cusp effect at 3.5 sigma significance.

Measured $ ext{pi} ext{pi}$ scattering length combination $a_0 - a_2 = 0.226 \

Results agree with theoretical predictions.

Abstract

Using a sample of $4.3\times 10^5$ $\eta'\to\eta\pi^0\pi^0$ events selected from the ten billion $J/\psi$ event dataset collected with the BESIII detector, we study the decay $\eta'\to\eta\pi^0\pi^0$ within the framework of nonrelativistic effective field theory. Evidence for a structure at $\pi^+\pi^-$ mass threshold is observed in the invariant mass spectrum of $\pi^0\pi^0$ with a statistical significance of around $3.5\sigma$, which is consistent with the cusp effect as predicted by the nonrelativistic effective field theory. After introducing the amplitude for describing the cusp effect, the $\pi\pi$ scattering length combination $a_0-a_2$ is determined to be $\rm 0.226\pm0.060_{stat}\pm0.013_{syst}$, which is in good agreement with theoretical calculation of $0.2644\pm0.0051$.