Abstract
By investigating the very closely lied $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ thresholds at about 4.43 GeV we propose that the $\psi(4415)$ and $\psi(4160)$ can be mixing states between the dynamic generated states of the strong $S$-wave $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ interactions and the quark model states $\psi(4S)$ and $\psi(2D)$. We investigate the $J/\psi K\bar{K}$ final states and invariant mass spectrum of $J/\psi K$ to demonstrate that nontrivial lineshapes can arise from such a mechanism. This process, which goes through triangle loop transitions, is located in the vicinity of the so-called "triangle singularity (TS)" kinematics. As a result, it provides a special mechanism for the production of exotic states $Z_{cs}$, which is the strange partner of $Z_c(3900)$, but with flavor contents of $c\bar{c}q\bar{s}$ (or $c\bar{c}s\bar{q}$) with $q$ denoting $u/d$ quarks. The lineshapes of the $e^+e^-\to J/\psi K\bar{K}$ cross sections and $J/\psi K \ (J/\psi \bar{K})$ spectrum are sensitive to the dynamically generated state, and we demonstrate that a pole structure can be easily distinguished from open threshold CUSP effects if an exotic state is created. A precise measurement of the cross section lineshapes can test such a mixing mechanism and provide navel information for the exotic partners of the $Z_c(3900)$ in the charmonium spectrum.
Highlights
During the past decade the observations of a large number of hadronic exotic candidates have initiated tremendous activities and efforts on understanding their dynamic nature in both experiment and theory
Similar to the production of Zcð3900Þ in eþe− → Yð4260Þ → J=ψππ via the intermediate D1ð2420ÞDþ c:c: where the so-called “triangle singularity (TS)” kinematics can be recognized, we find that the process eþe− → ψð4415Þ → J=ψKKvia the intermediate Ds1Ds þ c:c: and Ds0D Ãs þ c:c: is located at the edge of the TS kinematics
We investigate phenomena arising from the possible strong couplings of the degenerate thresholds Ds1Ds and Ds0D Ãs, which may lead to mixings between the dynamically generated hadronic molecule states and the nearby conventional charmonia ψð4SÞ and ψð2DÞ
Summary
During the past decade the observations of a large number of hadronic exotic candidates have initiated tremendous activities and efforts on understanding their dynamic nature in both experiment and theory. Recent studies indicate strong evidence for the hadronic molecule component of D1ð2420ÞDþ c:c: in its wave function while a compact core should be present as the consequence of heavy quark spin symmetry (HQSS) breaking effects [4,5,6,7,8] Following these interesting discoveries, many theoretical interpretations are proposed in the literature to understand the internal structures of those exotic candidates. Similar to the production process of Zcð3900Þ in eþe− → Yð4260Þ → J=ψππ where the S-wave threshold D1ð2420ÞDþ c:c: plays a crucial role for understanding the properties of Yð4260Þ and Zcð3900Þ [4], the process eþe− → J=ψKKaround the mass region of the thresholds of Ds1Ds and Ds0D Ãs in association with ψð4415Þ may provide important clues for the production of exotic state Zcs, which is the strange partner of Zcð3900Þ, but has flavor contents of ccqs (or ccsq ) with q denoting u=d quarks. A brief summary will be given in the last section
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