ℛ⁡(3780) Resonance Interpreted as the 1^⁢3𝐷₁ -Wave Dominant State of Charmonium from Precise Measurements of the Cross Section of 𝑒⁺⁢𝑒⁻ → Hadrons

We report the precise measurements of the cross section of 𝑒+⁢𝑒−→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⁡(3760), ℛ⁡(3780), and ℛ⁡(3810). For the first time, we measure the ℛ⁡(3810) electronic width to be (19.4±7.4±12.1)  eV. For the ℛ⁡(3760) resonance, we measure the mass to be (3751.9±3.8±2.8)  MeV/𝑐2, the total width to be (32.8±5.8±8.7)  MeV, and the electronic width to be (184 ±75 ±86)  eV. For the ℛ⁡(3780) resonance, we measure its mass to be (3778.7±0.5±0.3)  MeV/𝑐2, total width to be (20.3±0.8±1.7)  MeV, and electronic width to be (265 ±67 ±83)  eV. Forty-seven years ago, the 𝜓⁡(3770) resonance was discovered, and was subsequently interpreted as the 1⁢3𝐷1 -wave dominant state of charmonium. However, our analysis of the total-hadron cross sections indicates that the 𝜓⁡(3770) is not a single state, but a complex system composed of the ℛ⁡(3760), ℛ⁡(3780), and ℛ⁡(3810) resonances. Among these, we interpret the ℛ⁡(3780) is a resonance dominated by the 1⁢3𝐷1 charmonium state.