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Study of the $e^{+}e^{-}\to J/ψ\,π^{+}π^{-}$ lineshape near the $D^{*}\bar{D}+c.c.$ threshold and possible signals for exotic hidden charm states

Jun Wang, Qiang Zhao

Abstract

We investigate the lineshape of the $e^{+}e^{-}\to J/ψ\,π^{+}π^{-}$ cross section in the vicinity of the $D^{*}\bar{D}+c.c.$ threshold, where the ``so-called" $G(3900)$ is observed in the $e^+e^-\to D\bar{D}$ channel. To take into account the possible $D^{*}\bar{D}+c.c.$ open channel effects or possible contributions from $G(3900)$, we include the intermediate meson loop transitions in $e^{+}e^{-}\to J/ψ\,π^{+}π^{-}$. As a consequence, a triangle singularity (TS) is fulfilled which can produce nontrivial structures in the $j/ψπ$ invariant mass spectrum. Moreover, the TS transition also allows access to exotic quantum number of $(I,J^{P(C)})=(1,1^{-(-)})$ in the $J/ψπ$ invariant spectrum. We present predictions for the $J/ψ\,π$ invariant-mass spectrum and our results clarify the different manifestations of the kinematic effects and genuine resonances. In particular, we show that resonance structures arising from the $P$-wave $D\bar{D}$ scatterings or hidden charm tetraquark state with $(I,J^{P(C)})=(1,1^{-(-)})$ can be identified by the $J/ψπ$ invariant mass spectrum. It can provide a theoretical guidance for future experimental search for these exotic candidates.

Study of the $e^{+}e^{-}\to J/ψ\,π^{+}π^{-}$ lineshape near the $D^{*}\bar{D}+c.c.$ threshold and possible signals for exotic hidden charm states

Abstract

We investigate the lineshape of the cross section in the vicinity of the threshold, where the ``so-called" is observed in the channel. To take into account the possible open channel effects or possible contributions from , we include the intermediate meson loop transitions in . As a consequence, a triangle singularity (TS) is fulfilled which can produce nontrivial structures in the invariant mass spectrum. Moreover, the TS transition also allows access to exotic quantum number of in the invariant spectrum. We present predictions for the invariant-mass spectrum and our results clarify the different manifestations of the kinematic effects and genuine resonances. In particular, we show that resonance structures arising from the -wave scatterings or hidden charm tetraquark state with can be identified by the invariant mass spectrum. It can provide a theoretical guidance for future experimental search for these exotic candidates.
Paper Structure (7 sections, 15 equations, 4 figures, 3 tables)

This paper contains 7 sections, 15 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Formalism
  3. Effective Lagrangians
  4. Relevant Coupling Constants
  5. Numerical Results and Discussions
  6. Fit results
  7. Summary

Figures (4)

  • Figure 1: Schematic diagrams for the $e^{+}e^{-}\to J/\psi\,\pi^{+}\pi^{-}$ process, where $\mathcal{D}=(D^{0},D^{+})$ and $\bar{\mathcal{D}}=(\bar{D}^{0},D^{-})$. (a) shows the tree-level diagram, (b) corresponds to the loop diagram without intermediate resonance in $\mathcal{D} \bar{\mathcal{D}} \to J / \psi \pi$, and (c) represents the loop diagram with an intermediate resonance in $\mathcal{D} \bar{\mathcal{D}} \to J / \psi \pi$.
  • Figure 2: Fitted lineshape of the total cross section for $e^{+}e^{-}\to J/\psi\,\pi^{+}\pi^{-}$. Panel (a) illustrates the results for scenario-I with $\mathcal{D}\bar{\mathcal{D}}\to J/\psi\,\pi$ by a contact interaction. Panel (b) illustrates the results for scenario-II with $\mathcal{D}\bar{\mathcal{D}}\to J/\psi\,\pi$ via an intermediate resonance.
  • Figure 3: Invariant mass spectrum of $J / \psi \pi^{+}$ (identical for $J / \psi \pi^{-}$) where $\mathcal{D} \bar{\mathcal{D}} \to J / \psi \pi$ by a contact interaction for different $\sqrt{s}$. Panel (a) corresponds to the results of Fit-1. Panel (b) corresponds to the results of Fit-2.
  • Figure 4: Invariant mass spectrum of $J / \psi \pi^{+}$ (identical for $J / \psi \pi^{-}$) where $\mathcal{D} \bar{\mathcal{D}} \to J / \psi \pi$ via an intermediate resonance for different $\sqrt{s}$. Panel (a) corresponds to the results of Fit-1. Panel (b) corresponds to the results of Fit-2.