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

Using the data samples of $1.31\times {10}^9$ $J\mathrm{/}\psi$ events and $4.48\times 10^8$ $\psi (3686)$ events collected with the BESIII detector, partial wave analyses on the decays $J\mathrm{/}\psi$ and $\psi (3686)\to {\pi }^{+}{\pi }^{-}{\eta }^{\mathrm{\prime }}$ are performed with a relativistic covariant tensor amplitude approach. The dominant contribution is found to be $J\mathrm{/}\psi$ and $\psi (3686)$ decays to $\rho {\eta }^{\mathrm{\prime }}$. In the $J\mathrm{/}\psi$ decay, the branching fraction ${\cal B}(J/\psi\to \rho\eta^\prime)$isdeterminedtobe$(7.90\pm0.19($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}$)\pm0.49($\mathrm{s}\mathrm{y}\mathrm{s}$))\times 10^{-5}$. Two solutions are found in the $\psi (3686)$ decay, and the corresponding branching fraction $\mathcal{B}(\psi (3686)\to \rho {\eta }^{\mathrm{\prime }})$ is $(1.02\pm 0.11(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.24(\mathrm{s}\mathrm{y}\mathrm{s}))\times {10}^{-5}$ for the case of constructive interference, and $(5.69\pm 1.28(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 2.36(\mathrm{s}\mathrm{y}\mathrm{s}))\times {10}^{-6}$ for destructive interference. As a consequence, the ratios of branching fractions between $\psi (3686)$ and $J\mathrm{/}\psi$ decays to $\rho {\eta }^{\mathrm{\prime }}$ are calculated to be $(12.9\pm 1.4(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 3.1(\mathrm{s}\mathrm{y}\mathrm{s}))$% and $(7.2\pm 1.6(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 3.0(\mathrm{s}\mathrm{y}\mathrm{s}))$%, respectively. We also determine the inclusive branching fractions of $J\mathrm{/}\psi$ and $\psi (3686)$ decays to ${\pi }^{+}{\pi }^{-}{\eta }^{\mathrm{\prime }}$ to be $(1.36\pm 0.02(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.08(\mathrm{s}\mathrm{y}\mathrm{s}))\times {10}^{-4}$ and $(1.51\pm 0.14(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.23(\mathrm{s}\mathrm{y}\mathrm{s}))\times {10}^{-5}$, respectively.