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

TL;DR

This paper analyzes the $e^{+}e^{-} o J/eta ext{pi}^{+} ext{pi}^{-}$ lineshape near the $D^{*}ar{D}+c.c.$ threshold, exploring how triangle singularities and open channel effects can produce structures indicative of exotic hidden charm states.

Contribution

It introduces a model incorporating intermediate meson loops and triangle singularities to distinguish between kinematic effects and genuine exotic resonances in the $J/eta ext{pi}$ spectrum.

Findings

Triangle singularity can produce observable structures in the spectrum.

Resonance signals from $Dar{D}$ P-wave scattering or tetraquarks can be identified.

Predictions provide guidance for experimental searches for exotic states.

Abstract

We investigate the lineshape of the $e^{+}e^{-}\to J/\psi\,\pi^{+}\pi^{-}$ 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 $e^{+}e^{-}\to J/\psi\,\pi^{+}\pi^{-}$. As a consequence, a triangle singularity (TS) is fulfilled which can produce nontrivial structures in the $j/\psi\pi$ invariant mass spectrum. Moreover, the TS transition also allows access to exotic quantum number of $(I,J^{P(C)})=(1,1^{-(-)})$ in the $J/\psi\pi$ invariant spectrum. We present predictions for the $J/\psi\,\pi$ 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 $J/\psi\pi$ invariant mass spectrum. It can provide a theoretical guidance for future experimental search for these exotic candidates.