Evidence for the Cusp Effect in ${\eta }^{\mathrm{\prime }}$ Decays into $\eta {\pi }^0{\pi }^0$

Using a sample of $4.3\times {10}^5$ ${\eta }^{\mathrm{\prime }}\to \eta {\pi }^0{\pi }^0$ events selected from the ten billion $J\mathrm{/}\psi$ event dataset collected with the BESIII detector, we study the decay ${\eta }^{\mathrm{\prime }}\to \eta {\pi }^0{\pi }^0$ 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 $0.226\pm {0.060}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.013}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$, which is in good agreement with theoretical calculation of $0.2644\pm 0.0051$.