Resonance parameters of the vector charmoniumlike state $G(3900)$

Abstract

Motivated by the updated analysis of the $G(3900)$ by the BESIII collaboration, we perform a global analysis of the cross sections of the $e^{+}{e}^{-}\to D\bar{D}$, $e^{+}{e}^{-}\to D{\bar{D}}^{\ast }+c.c.$, $e^{+}{e}^{-}\to D^{\ast }{\bar{D}}^{\ast }$ processes, especially focusing on the properties of the $G(3900)$. As the energy region of interest is limited by the next opening threshold, i.e. the $D_1\bar{D}$ threshold, we focus on the energy region $[3.7,4.25]\mathrm{GeV}$, where three charmonia $\psi (1D)$, $\psi (3S)$ and $\psi (2D)$ explicitly contribute to the cross sections. By constructing the $P$-wave contact interaction between the $(D,D^{\ast })$ doublet and its antiparticle in the heavy quark limit, we extract the physical scattering amplitude by solving the Lippmann-Schwinger equation. No matter whether three or two charmonium states are included in our framework, we always find a dynamically generated state corresponding to the $G(3900)$, which suggests it to be a $P$-wave dynamically generated state. We also predict several dynamically generated states in the corresponding $1^{-+}$ channel. These states can be further searched for in the electron-positron annihilation process involving the emission of a single photon.

25 pages, 11 figures

References in corpus (15)

• Observation of Two Resonant Structures in e+e- to pi+ pi- psi(2S) via Initial State Radiation at Belle
• Measurement of e^+e^- to pi^+pi^-J/psi Cross Section via Initial State Radiation at Belle
• Measurement of the near-threshold $e^{+}{e}^{-}\to D\bar{D}$ cross section using initial-state radiation
• The puzzle of excessive non-$D\bar{D}$ component of the inclusive $\psi (3770)$ decay and the long-distant contribution
• Towards a dynamical understanding of the non-$D\bar{D}$ decay of $\psi (3770)$
• Observation of Three Charmoniumlike States with $J^{PC}=1^{--}$ in $e^{+}{e}^{-}\to D^{\ast 0}{D}^{\ast -}{\pi }^{+}$
• $P$-wave coupled channel effects in electron-positron annihilation
• Angular analysis of the $e^{+}{e}^{-}\to D^{(\ast )\pm }{D}^{\ast \mp }$ process near the open charm threshold using initial-state radiation
• Precise Measurement of Born Cross Sections for $e^{+}{e}^{-}\to D\bar{D}$ at $\sqrt{s}=3.80-4.95$ GeV
• Measurement of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{D}^{+}{D}^{-}$ cross sections at center-of-mass energies from 4.190 to 4.946 GeV
• Cross section measurements of the $e^{+}{e}^{-}\to D^{\ast +}{D}^{\ast -}$ and $e^{+}{e}^{-}\to D^{\ast +}{D}^{-}$ processes at center-of-mass energies from 4.085 to 4.600 GeV
• Lineshape of $e^{+}{e}^{-}\to D^{\ast }\bar{D}+c.c.$ and electromagnetic form factor of $D^{\ast }\to D$ transition in the time-like region
• Production of $D^{(\ast )}{\bar{D}}^{(\ast )}$ near the thresholds in $e^{+}{e}^{-}$ annihilation
• Pole trajectories from $S$- and $P$-wave $D{\bar{D}}^{\ast }$ interactions
• Production of $1^{-+}$ exotic charmonium-like states in electron-positron collisions

Cited by in corpus (1)

• 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