Study of $J/ψ$ and $ψ(3686)$ decays to $π^+π^-η^\prime$

Using the data samples of $1.31\times 10^9$ $J/ψ$ events and $4.48\times 10^8$ $ψ(3686)$ events collected with the BESIII detector, partial wave analyses on the decays $J/ψ$ and $ψ(3686) \to π^+π^-η^\prime$ are performed with a relativistic covariant tensor amplitude approach. The dominant contribution is found to be $J/ψ$ and $ψ(3686)$ decays to $ρη^\prime$. In the $J/ψ$ decay, the branching fraction ${\cal B}(J/ψ\to ρη^\prime)$ is determined to be $(7.90\pm0.19(\mathrm{stat})\pm0.49(\mathrm{sys}))\times 10^{-5}$. Two solutions are found in the $ψ(3686)$ decay, and the corresponding branching fraction ${\cal B}(ψ(3686)\to ρη^\prime)$ is $(1.02\pm0.11(\mathrm{stat})\pm0.24(\mathrm{sys}))\times 10^{-5}$ for the case of constructive interference, and $(5.69\pm1.28(\mathrm{stat})\pm2.36(\mathrm{sys}))\times 10^{-6}$ for destructive interference. As a consequence, the ratios of branching fractions between $ψ(3686)$ and $J/ψ$ decays to $ρη^\prime$ are calculated to be $(12.9\pm1.4(\mathrm{stat})\pm3.1(\mathrm{sys}))$\% and $(7.2\pm1.6(\mathrm{stat})\pm3.0(\mathrm{sys}))$\%, respectively. We also determine the inclusive branching fractions of $J/ψ$ and $ψ(3686)$ decays to $π^+π^-η^\prime$ to be $(1.36\pm0.02(\mathrm{stat})\pm0.08(\mathrm{sys}))\times 10^{-4}$ and $(1.51\pm0.14(\mathrm{stat})\pm 0.23(\mathrm{sys}))\times 10^{-5}$, respectively.