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

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 $0.2644\pm0.0051$.