$P$-wave coupled channel effects in electron-positron annihilation

Abstract

$P$-wave coupled channel effects arising from the $D\bar{D}$, $D{\bar{D}}^{\ast }+c.c.$, and $D^{\ast }{\bar{D}}^{\ast }$ thresholds in $e^{+}{e}^{-}$ annihilations are systematically studied. We provide an exploratory study by solving the Lippmann-Schwinger equation with short-ranged contact potentials obtained in the heavy quark limit. These contact potentials can be extracted from the $P$-wave interactions in the $e^{+}{e}^{-}$ annihilations, and then be employed to investigate possible isosinglet $P$-wave hadronic molecules. In particular, such an investigation may provide information about exotic candidates with quantum numbers $J^{PC}=1^{-+}$. In the mass region of the $D\bar{D}$, $D{\bar{D}}^{\ast }+c.c.$, and $D^{\ast }{\bar{D}}^{\ast }$ thresholds, there are two quark model bare states, i.e. the $\psi (3770)$ and $\psi (4040)$, which are assigned as $(1^3{D}_1)$ and $(3^1{S}_1)$ states, respectively. By an overall fit of the cross sections of $e^{+}{e}^{-}\to D\bar{D}$, $D{\bar{D}}^{\ast }+c.c.$, $D^{\ast }{\bar{D}}^{\ast }$, we determine the physical coupling constants to each channel and extract the pole positions of the $\psi (3770)$ and $\psi (4040)$. The deviation of the ratios from that in the heavy quark spin symmetry (HQSS) limit reflects the HQSS breaking effect due to the mass splitting between the $D$ and the $D^{\ast }$. Besides the two poles, we also find a pole a few MeV above the $D{\bar{D}}^{\ast }+c.c.$ threshold which can be related to the so-called $G(3900)$ observed earlier by BABAR and Belle. This scenario can be further scrutinized by measuring the angular distribution in the $D^{\ast }{\bar{D}}^{\ast }$ channel with high luminosity experiments.

arXiv comment15 pages, 2 figures

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Cited by in corpus (14)

• Hadronic molecules
• Strong decays of higher charmonium states into open-charm meson pairs
• The strong decay patterns of $Z_c$ and $Z_b$ states in the relativized quark model
• Charm-meson Triangle Singularity in $e^{+}{e}^{-}$ Annihilation into $D^{\ast 0}{\bar{D}}^0+\gamma$
• Precise Measurement of Born Cross Sections for $e^{+}{e}^{-}\to D\bar{D}$ at $\sqrt{s}=3.80-4.95$ GeV
• Disentangling the role of the $Y(4260)$ in $e^{+}{e}^{-}\to D^{\ast }{\bar{D}}^{\ast }$ and $D_s^{\ast }{\bar{D}}_s^{\ast }$ via line shape studies
• Global coupled-channel analysis of $e^{+}{e}^{-}\to c\bar{c}$ processes in $\sqrt{s}=3.75-4.7$ GeV
• Colloquium: Hadron Production in Open-charm Meson Pair at $e^{+}{e}^{-}$ Collider
• Production of $X(3872)$ and a Photon in $e^{+}{e}^{-}$ Annihilation
• The spin parity of $Z_c^{-}$(4100), $Z_1^{+}$(4050) and $Z_2^{+}$(4250)
• Analysis of BaBar, Belle, BES-II, CLEO and KEDR data on $\psi (3770)$ line shape and determination of the resonance parameters
• Electronic width of the $\psi (3770)$ resonance interfering with the background
• Resonance parameters of the vector charmoniumlike state $G(3900)$
• 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