$\mathcal{R}(3780)$ Resonance Interpreted as the $1^3{D}_1$-Wave Dominant State of Charmonium from Precise Measurements of the Cross Section of $e^{+}{e}^{-}\to$ Hadrons

Abstract

We report the precise measurements of the cross section of $e^{+}{e}^{-}\to$ 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 $\mathcal{R}(3760)$, $\mathcal{R}(3780)$, and $\mathcal{R}(3810)$. For the first time, we measure the $\mathcal{R}(3810)$ electronic width to be $(19.4\pm 7.4\pm 12.1)$ eV. For the $\mathcal{R}(3760)$ resonance, we measure the mass to be $(3751.9\pm 3.8\pm 2.8)$ MeV/$c^2$, the total width to be $(32.8\pm 5.8\pm 8.7)$ MeV, and the electronic width to be $(184\pm 75\pm 86)$ eV. For the $\mathcal{R}(3780)$ resonance, we measure its mass to be $(3778.7\pm 0.5\pm 0.3)$ MeV/$c^2$, total width to be $(20.3\pm 0.8\pm 1.7)$ MeV, and electronic width to be $(265\pm 67\pm 83)$ eV. Forty-seven years ago, the $\psi (3770)$ 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 $\psi (3770)$ is not a single state, but a complex system composed of the $\mathcal{R}(3760)$, $\mathcal{R}(3780)$, and $\mathcal{R}(3810)$ resonances. Among these, we interpret the $\mathcal{R}(3780)$ is a resonance dominated by the $1^3{D}_1$ charmonium state.

References in corpus (9)

• Hadro-Charmonium
• Matching perturbative and Parton Shower corrections to Bhabha process at flavour factories
• Measurements of the cross sections for $e^{+}{e}^{-}\to \mathrm{hadrons}$ at 3.650, 3.6648, 3.773 GeV and the branching fraction for $\psi (3770)\to \mathrm{non}-D\bar{D}$
• Measurements of the braching fractions for psi(3770)--> D0D0-bar,D+D-,DD-bar$ and the resonance parameters of psi(3770) and psi(2S)
• Photon pair production at flavour factories with per mille accuracy
• Measurements of the continuum $R_{\mathrm{uds}}$ and $R$ values in $e^{+}{e}^{-}$ annihilation in the energy region between 3.650 and 3.872 GeV
• Precison Measurements of the Mass, the Widths of $\psi (3770)$ Resonance and the Cross Section $\sigma [e^{+}{e}^{-}\to \psi (3770)]$ at $E_{\mathrm{cm}}=3.7724$ GeV
• Diresonance in production and scattering of heavy mesons
• First Observation of a Three-Resonance Structure in $e^{+}{e}^{-}\to$Nonopen Charm Hadrons

Cited by in corpus (3)

• Global coupled-channel analysis of $e^{+}{e}^{-}\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV
• Unified coupled-channel description for the five near-threshold structures $\psi (3770)$, $G(3900)$, $R(3760)$, $R(3780)$ and $R(3810)$ from $e^{+}{e}^{-}$ annihilation
• Systematic analysis of the D-wave charmonium states with the QCD sum rules