Assignments of the  X   4140   ,  X   4500   ,  X   4630   , and  X   4685    Based on the QCD Sum Rules

Zhi-Gang Wang,Ruilin Zhu

doi:10.1155/2021/4426163

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 ∗ D ¯ s 1 − D s 1 D ¯ s ∗ tetraquark molecular state or c s P c ¯ s ¯ A + c s A c ¯ s ¯ P tetraquark state with the J P C = 1 − + , and assign the X 3915 and X 4500 as the 1S and 2S c s A c ¯ s ¯ A tetraquark states, respectively, with the J P C = 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 ± 0.12 GeV , which is in very good agreement with the experimental value 4684 ± 7 − 16 + 13 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.

Highlights

In 2009, the CDF collaboration observed an evidence for the Xð4140Þ in the J/ψφ mass spectrum for the first time with a significance of larger than 3:8σ [1]
We discuss the possible assignments of the Xð4140Þ, Xð4500Þ, Xð 4630Þ, and Xð4685Þ based on the QCD sum rules
We discuss the possible assignments of the Xð4630Þ and Xð4500Þ according to our previous calculations with the QCD sum rules

Summary

Introduction

In 2009, the CDF collaboration observed an evidence for the Xð4140Þ in the J/ψφ mass spectrum for the first time with a significance of larger than 3:8σ [1]. Decays using 6 times larger signal yields than previously analyzed and observed a hidden-charm and hiddenstrange tetraquark candidate Xð4685Þ and (Xð4630Þ) in the mass spectrum of the J/ψφ with a significance of 15 σ (5:5σ), the favored assignment of the spin parity is JP = 1+(1−), and the Breit-Wigner mass and width are 4684 ± 7+−1136 MeV (4626 ± 16+−11810 MeV) and 126 ± 15+−3471 MeV (174 ± 27+−17334 MeV), respectively [8]. The LHCb collaboration observed two new tetraquark (molecular) state candidates Zcsð4000Þ and Zcsð4220Þ in the mass spectrum of the J/ψK+ with the preferred spin parity JP = 1+ and updated the experimental values of the masses and widths of the Xð4500Þ and Xð4700Þ [8].

Possible Assignments of the Xð4630Þ and Xð 4500Þ Based on the QCD Sum Rules

Ds m4Ds m2c f

Numerical Results and Discussions

Conclusion