First Observation of a Three-Resonance Structure in $e^+e^-\rightarrow$Nonopen Charm Hadrons

We report the measurement of the inclusive cross sections for $e^+e^-$$\rightarrow$nOCH (where nOCH denotes non-open charm hadrons) with improved precision at center-of-mass (c.m.) energies from 3.645 to 3.871 GeV. We observe three resonances: $\mathcal R(3760)$, $\mathcal R(3780)$, and $\mathcal R(3810)$ with significances of $8.1\sigma$, $13.7\sigma$, and $8.8\sigma$, respectively. The $\mathcal R(3810)$ state is observed for the first time, while the $\mathcal R(3760)$ and $\mathcal R(3780)$ states are observed for the first time in the nOCH cross sections. Two sets of resonance parameters describe the energy-dependent line shape of the cross sections well. In set I [set II], the $\mathcal R(3810)$ state has mass $(3805.7 \pm 1.1 \pm 2.7)$ [$(3805.7 \pm 1.1 \pm 2.7)$] MeV/$c^2$, total width $(11.6 \pm 2.9 \pm 1.9)$ [$(11.5 \pm 2.8 \pm 1.9)$] MeV, and an electronic width multiplied by the nOCH decay branching fraction of $(10.9\pm 3.8\pm 2.5)$ [$(11.0\pm 3.4\pm 2.5)$] eV. In addition, we measure the branching fractions ${\mathcal B}[{\mathcal R}(3760)$$\rightarrow$nOCH$]=(25.2 \pm 16.1 \pm 30.4)\% [(6.4 \pm 4.8 \pm 7.7)\%]$ and ${\mathcal B}[\mathcal R(3780)$$\rightarrow$nOCH$]=(12.3 \pm 6.6 \pm 8.3)\% [(10.4 \pm 4.8 \pm 7.0)\%]$ for the first time. The $\mathcal R(3760)$ state can be interpreted as an open-charm (OC) molecular state, but containing a simple four-quark state component. The $\mathcal R(3810)$ state can be interpreted as a hadrocharmonium state.