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

With a sample of 225.3 million $J/psi$ events taken with the BESIII detector, the decay $J/psirightarrow gamma 3(pi^+pi^-)$ is analyzed. A structure at 1.84 GeV/c$^2$ is observed in the $3(pi^+pi^-)$ invariant mass spectrum with a statistical significance of 7.6$sigma$ . The mass and width are measured to be $M=1842.2pm 4.2^{+7.1}_{-2.6}$ MeV/c$^2$ and $Gamma=83pm 14 pm 11$ MeV. The product branching fraction is determined to be $B(J/psirightarrowgamma X(1840))times B(X(1840)rightarrow 3(pi^+pi^-))=(2.44pm0.36^{+0.60}_{-0.74})times 10^{-5}$. No $eta^prime$ signals are observed in the $3(pi^+pi^-)$ invariant mass spectrum, and the upper limit of the branching fraction for the decay $eta^primerightarrow 3(pi^+pi^-)$ is set to be $3.1times10^{-5}$ at a 90% confidence level.