D-wave excited tetraquark states with and *

Abstract

We study the mass spectra of D-wave excited $cs\bar{c}\bar{s}$ tetraquark states with $J^{PC}=1^{++}$ and $1^{+-}$ in both symmetric $\mathbf{6}_{cs}\otimes\bar{\mathbf{6}}_{\bar{c}\bar{s}}$ and antisymmetric $\bar{\mathbf{3}}_{cs}\otimes\mathbf{3}_{\bar{c}\bar{s}}$ color configurations by using the QCD sum rule method. We construct the D-wave diquark-antidiquark type of $cs\bar{c}\bar{s}$ tetraquark interpolating currents in various excitation structures with $(L_\lambda,L_\rho\{l_{\rho_1},l_{\rho_2}\})=(2,0\{0,0\}),(1,1\{1,0\}),(1,1\{0,1\}),(0,2\{1,1\}),(0,2\{2,0\}),(0,2\{0,2\})$. Our results support to interpret the recently observed $X(4685)$ resonance as a D-wave $cs\bar{c}\bar{s}$ tetraquark state with $J^{PC}=1^{++}$ in the $(2,0\{0,0\})$ or $(0,2\{2,0\})$ excitation mode, although some other possible excitation structures cannot be excluded exhaustively within theoretical errors. Moreover, our results provide a mass relation $6_{\rho\rho}<3_{\lambda\lambda}<3_{\lambda\rho}<3_{\rho\rho}$ and $6_{\rho\rho}<3_{\lambda\lambda}<6_{\lambda\lambda}<3_{\rho\rho}$ for the positive and negative $\mathbb{C}$-parity D-wave $cs\bar{c}\bar{s}$ tetraquarks, respectively. We suggest searching for these possible D-wave $cs\bar{c}\bar{s}$ tetraquarks in both the hidden-charm channels $J/\psi\phi$, $\eta_c\phi$ and open-charm channels such as $D_s\bar{D}_s^*$, $D_{s}\bar{D}_{s1}^*$ and so on. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

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