$R\left(3780\right)$ Resonance Interpreted as the $1{}^{3}{D}_{1}$-Wave Dominant State of Charmonium from Precise Measurements of the Cross Section of ${e}^{+}{e}^{-}\to \text{Hadrons}$

We report the precise measurements of the cross section of ${e}^{+}{e}^{-}\to \text{hadrons}$ at center-of-mass energies from 3.645 to 3.871 GeV. We thereby perform the most precise study of the cross sections and find a complex system composed of three resonances of $R\left(3760\right)$, $R\left(3780\right)$, and $R\left(3810\right)$. For the first time, we measure the $R\left(3810\right)$ electronic width to be $\left(19.4±7.4±12.1\right)\text{}\text{}\mathrm{eV}$. For the $R\left(3760\right)$ resonance, we measure the mass to be $\left(3751.9±3.8±2.8\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$, the total width to be $\left(32.8±5.8±8.7\right)\text{}\text{}\mathrm{MeV}$, and the electronic width to be $\left(184±75±86\right)\text{}\text{}\mathrm{eV}$. For the $R\left(3780\right)$ resonance, we measure its mass to be $\left(3778.7±0.5±0.3\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$, total width to be $\left(20.3±0.8±1.7\right)\text{}\text{}\mathrm{MeV}$, and electronic width to be $\left(265±67±83\right)\text{}\text{}\mathrm{eV}$. Forty-seven years ago, the $\psi \left(3770\right)$ resonance was discovered, and was subsequently interpreted as the $1{}^{3}{D}_{1}$-wave dominant state of charmonium. However, our analysis of the total-hadron cross sections indicates that the $\psi \left(3770\right)$ is not a single state, but a complex system composed of the $R\left(3760\right)$, $R\left(3780\right)$, and $R\left(3810\right)$ resonances. Among these, we interpret the $R\left(3780\right)$ is a resonance dominated by the $1{}^{3}{D}_{1}$ charmonium state.