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 $e^{+}e^{-}\to J/ψ\,π^{+}π^{-}$ 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-mass 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.