Measurement of the matrix element for the decay ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$

The Dalitz plot of ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ decay is studied using $(225.2\pm 2.8)\times {10}^6$ $J/\psi$ events collected with the BESIII detector at the BEPCII $e^{+}{e}^{-}$ collider. With the largest sample of ${\eta }^{\prime }$ decays to date, the parameters of the Dalitz plot are determined in a generalized and a linear representation. Also, the branching fraction of $J/\psi \to \gamma {\eta }^{\prime }$ is determined to be $(4.84\pm 0.03\pm 0.24)\times {10}^{-3}$, where the first error is statistical and the second systematic.

Figure 1

(a) The $\cos \theta$ distribution of charged tracks for events satisfying selection criteria. (b) The distributions of the total energy in the EMC for events satisfying selection criteria. Dots are data, and the histogram shows $J/\psi \to \mathrm{\text{inclusive}}$ simulated events.

Figure 2

The $\eta {\pi }^{+}{\pi }^{-}$ invariant mass distribution of the final candidate events. The dots with error bars represent data, and the solid curve is the result of the fit described in the text. The dashed curve is the background polynomial.

Figure 3

(a) The experimental Dalitz diagram for the decay ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ in terms of the variables $X$ and $Y$ with the $\eta {\pi }^{+}{\pi }^{-}$ mass in the ${\eta }^{\prime }$ mass region. The corresponding projections on variables $X$ and $Y$ are shown in (b) and (c), respectively, where the dashed histograms are from a MC signal sample with ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$ events produced with phase space, and the solid histograms are the fitted results described in the text.

Figure 4

Dependence of the square of the ${\eta }^{\prime }$ decay matrix element on the Dalitz variables $X$ and $Y$. The solid lines are the results of the fits of the data described in the text.

Figure 5

Experimental distributions of the variable $Y$ in various intervals of $X$ with the fitting function (histogram) for the general decomposition parametrization.