R(3780) Resonance Interpreted as the 1^{3}D_{1}-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/c^{2}, 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/c^{2}, 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^{3}D_{1}-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^{3}D_{1} charmonium state.