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Using a data sample corresponding to an integrated luminosity of 11.3 $\rmfb^{-1}$ collected at center-of-mass energies from $4.23$ to $4.70$ GeV withthe BESIII detector, we measure the product of the $e^+e^-\to\pi^+\pi^-\psi_2(3823)$ cross section and the branching fraction$\mathcal{B}[\psi_2(3823)\to \gamma\chi_{c1}]$.  For the first time, resonance structure is observed in the cross section lineshape of $e^+e^-\to \pi^+\pi^-\psi_2(3823)$ with significances exceeding$5\sigma$.  A fit to data with two coherent Breit-Wigner resonances modeling the$\sqrt{s}$-dependent cross section yields $M(R_1)=4406.9\pm 17.2\pm 4.5$MeV/$c^2$, $\Gamma(R_1)=128.1\pm 37.2\pm 2.3$ MeV, and $M(R_2)=4647.9\pm 8.6\pm0.8$ MeV/$c^2$, $\Gamma(R_2)=33.1\pm 18.6\pm 4.1$ MeV.  Though weakly disfavored by the data, a single resonance with$M(R)=4417.5\pm26.2\pm3.5$ MeV/$c^2$, $\Gamma(R)=245\pm48\pm13$ MeV is alsopossible to interpret data.  This observation deepens our understanding of the nature of the vectorcharmoniumlike states.  The mass of the $\psi_2(3823)$ state is measured as $(3823.12\pm 0.43\pm0.13)$ MeV/$c^2$, which is the most precise measurement to date.

Observation of resonance structures in $e^+e^-\to \pi^+\pi^-\psi_2(3823)$ and mass measurement of $\psi_2(3823)$