Assignments of the $X(4140)$, $X(4500)$, $X(4630)$ and $X(4685)$ based on the QCD sum rules

Abstract

In this article, we take into account our previous calculations based on the QCD sum rules, and tentatively assign the $X(4630)$ as the $D_s^{\ast }{\bar{D}}_{s1}-D_{s1}{\bar{D}}_s^{\ast }$ tetraquark molecular state or $[cs{]}_P[\bar{c}\bar{s}{]}_A+[cs{]}_A[\bar{c}\bar{s}{]}_P$ tetraquark state with the $J^{PC}=1^{-+}$, and assign the $X(3915)$ and $X(4500)$ as the 1S and 2S $[cs{]}_A[\bar{c}\bar{s}{]}_A$ tetraquark states respectively with the $J^{PC}=0^{++}$. Then we extend our previous works to investigate the LHCb's new tetraquark candidate $X(4685)$ as the first radial excited state of the $X(4140)$ with the QCD sum rules, and obtain the mass $M_X=4.70\pm 0.12\mathrm{GeV}$, which is in very good agreement with the experimental value $4684\pm 7{}_{-16}^{+13}\mathrm{MeV}$. Furthermore, we investigate the two-meson scattering state contributions in details, and observe that the two-meson scattering states alone cannot saturate the QCD sum rules, the contributions of the tetraquark states play an un-substitutable role, we can saturate the QCD sum rules with or without the two-meson scattering states.

Comments: 17 pages, 2 figure