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 $X\left(4630\right)$ as the $D_s^{\ast }{\overline{D}}_{s1}-D_{s1}{\overline{D}}_s^{\ast }$ tetraquark molecular state or ${\left[cs\right]}_P{\left[\overline{c}\overline{s}\right]}_A+{\left[cs\right]}_A{\left[\overline{c}\overline{s}\right]}_P$ tetraquark state with the $J^{PC}=1^{-+}$ , and assign the $X\left(3915\right)$ and $X\left(4500\right)$ as the 1S and 2S ${\left[cs\right]}_A{\left[\overline{c}\overline{s}\right]}_A$ tetraquark states, respectively, with the $J^{PC}=0^{++}$ . Then, we extend our previous works to investigate the LHCb’s new tetraquark candidate $X\left(4685\right)$ as the first radial excited state of the $X\left(4140\right)$ with the QCD sum rules and obtain the mass $M_X=4.70\pm 0.12\text{GeV}$ , which is in very good agreement with the experimental value $4684\pm 7_{-16}^{+13}\text{MeV}$ . 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 unsubstitutable role, and we can saturate the QCD sum rules with or without the two-meson scattering states.