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With a sample of 225.3 million $J/\psi$ events taken with the BESIIIdetector, the decay $J/\psi\rightarrow \gamma 3(\pi^+\pi^-)$ is analyzed. Astructure at 1.84 GeV/c$^2$ is observed in the $3(\pi^+\pi^-)$ invariant massspectrum with a statistical significance of 7.6$\sigma$ . The mass and widthare measured to be $M=1842.2\pm 4.2^{+7.1}_{-2.6}$ MeV/c$^2$ and $\Gamma=83\pm14 \pm 11$ MeV. The product branching fraction is determined to be$B(J/\psi\rightarrow\gamma X(1840))\times B(X(1840)\rightarrow3(\pi^+\pi^-))=(2.44\pm0.36^{+0.60}_{-0.74})\times 10^{-5}$. No $\eta^\prime$signals are observed in the $3(\pi^+\pi^-)$ invariant mass spectrum, and theupper limit of the branching fraction for the decay $\eta^\prime\rightarrow3(\pi^+\pi^-)$ is set to be $3.1\times10^{-5}$ at a 90% confidence level.

Observation of a structure at 1.84 GeV/c$^2$ in the $3(\pi^+\pi^-)$ mass spectrum in $J/\psi\rightarrow \gamma 3(\pi^+\pi^-)$ decays