Study of $J/\psi$ and $\psi (3686)$ decays to ${\pi }^{+}{\pi }^{-}{\eta }^{\prime }$

Using the data samples of $1.31\times {10}^{9}J/\psi$ events and $4.48\times {10}^8\psi (3686)$ events collected with the BESIII detector, partial wave analyses on the decays $J/\psi$ and $\psi (3686)\to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ are performed with a relativistic covariant tensor amplitude approach. The dominant contribution is found to be $J/\psi$ and $\psi (3686)$ decays to $\rho {\eta }^{\prime }$. In the $J/\psi$ decay, the branching fraction $\mathcal{B}(J/\psi \to \rho {\eta }^{\prime })$ is determined to be $(7.90\pm 0.19(\mathrm{stat})\pm 0.49(\mathrm{sys}))\times {10}^{-5}$. Two solutions are found in the $\psi (3686)$ decay, and the corresponding branching fraction $\mathcal{B}(\psi (3686)\to \rho {\eta }^{\prime })$ is $(1.02\pm 0.11(\mathrm{stat})\pm 0.24(\mathrm{sys}))\times {10}^{-5}$ for the case of destructive interference, and $(5.69\pm 1.28(\mathrm{stat})\pm 2.36(\mathrm{sys}))\times {10}^{-6}$ for constructive interference. As a consequence, the ratios of branching fractions between $\psi (3686)$ and $J/\psi$ decays to $\rho {\eta }^{\prime }$ are calculated to be $(12.9\pm 1.4(\mathrm{stat})\pm 3.1(\mathrm{sys}))\%$ and $(7.2\pm 1.6(\mathrm{stat})\pm 3.0(\mathrm{sys}))\%$, respectively. We also determine the inclusive branching fractions of $J/\psi$ and $\psi (3686)$ decays to ${\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ to be $(1.36\pm 0.02(\mathrm{stat})\pm 0.08(\mathrm{sys}))\times {10}^{-4}$ and $(1.51\pm 0.14(\mathrm{stat})\pm 0.23(\mathrm{sys}))\times {10}^{-5}$, respectively.

Figure 1

Dalitz plots for (a) $J/\psi \to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ and (b) $\psi (3686)\to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ with events in the ${\eta }^{\prime }$ signal region.

Figure 2

Distribution of $M_{\eta {\pi }^{+}{\pi }^{-}}$ for (a) $J/\psi$ and (b) $\psi (3686)$ decays. The red dashed line is the signal MC shape convolved with a Gaussian, the green dotted line is the class I background described by a 2nd Chebychev function, the blue dash-dotted line is the class II background, dominated by $J/\psi \to {\mu }^{+}{\mu }^{-}{\eta }^{\prime }$, described by the MC simulation, the black solid line is the overall fit result, and the dots with error bars are the data.

Figure 3

Comparisons of the distributions of $M_{{\pi }^{+}{\pi }^{-}}$ between data and PWA fit projections for the decay $J/\psi \to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$.

Figure 4

Comparisons between data and PWA fit projections for the decay $J/\psi \to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ (shown in the first row), and for the decay $\psi (3686)\to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ (shown in the bottom row). The left is for the distributions of $M_{{\eta }^{\prime }{\pi }^{+}}$, and the middle and the right are for the distributions of $\cos {\theta }_{{\pi }^{+}}$ and $\cos {\theta }_{\eta }$. The dots with error bars are data, and the red solid line shows the PWA fit projection.

Figure 5

Comparisons of the distributions of $M_{{\pi }^{+}{\pi }^{-}}$ between data and PWA fit projections for the decay $\psi (3686)\to {\pi }^{+}{\pi }^{-}{\eta }^{\prime }$ with (a) destructive and (b) constructive interferences.