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

Abstract

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 1D13-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 1D13 charmonium state.