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

We investigate the lineshape of the $e^{+}{e}^{-}\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$ cross section in the vicinity of the $D^{\ast }\bar{D}+c\mathrm{.}c\mathrm{.}$ threshold, where the ``so-called" $G(3900)$ is observed in the $e^{+}{e}^{-}\to D\bar{D}$ channel. To take into account the possible $D^{\ast }\bar{D}+c\mathrm{.}c\mathrm{.}$ open channel effects or possible contributions from $G(3900)$, we include the intermediate meson loop transitions in $e^{+}{e}^{-}\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$. As a consequence, a triangle singularity (TS) is fulfilled which can produce nontrivial structures in the $j\mathrm{/}\psi \pi$ invariant mass spectrum. Moreover, the TS transition also allows access to exotic quantum number of $(I,J^{P(C)})=(1,1^{-(-)})$ in the $J\mathrm{/}\psi \pi$ invariant spectrum. We present predictions for the $J\mathrm{/}\psi \pi$ 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 $J\mathrm{/}\psi \pi$ invariant mass spectrum. It can provide a theoretical guidance for future experimental search for these exotic candidates.