The fully-light vector tetraquark states with explicit P-wave via the QCD sum rules

Abstract

In this paper, we apply the QCD sum rules to study the vector fully-light tetraquark states with an explicit P-wave between the diquark and antidiquark pair. We observed that the $C{\gamma }_{\alpha }\otimes {\overleftrightarrow{\partial }}_{\mu }\otimes {\gamma }^{\alpha }C$ (or $C{\gamma }_{\alpha }\otimes {\overleftrightarrow{D}}_{\mu }\otimes {\gamma }^{\alpha }C$) type current with fully-strange quarks couples potentially to a tetraquark state with the mass $2.16\pm 0.14\mathrm{GeV}$, which supports assigning the $Y/\varphi (2175)$ as the diquark-antidiquark type tetraquark state with the $J^{PC}=1^{--}$. The $qs\bar{q}\bar{s}$ and $ss\bar{s}\bar{s}$ vector tetraquark states with the structure $C{\gamma }_{\mu }\otimes {\overleftrightarrow{\partial }}_{\alpha }\otimes {\gamma }^{\alpha }C+C{\gamma }^{\alpha }\otimes {\overleftrightarrow{\partial }}_{\alpha }\otimes {\gamma }_{\mu }$ (or $C{\gamma }_{\mu }\otimes {\overleftrightarrow{D}}_{\alpha }\otimes {\gamma }^{\alpha }C+C{\gamma }^{\alpha }\otimes {\overleftrightarrow{D}}_{\alpha }\otimes {\gamma }_{\mu }$) are consistent with the $X(2200)$ and $X(2400)$ respectively, which lie in the region $2.20$ to $2.40\mathrm{GeV}$. The central values of the masses of the fully-strange vector tetraquark states with an explicit P-wave are about $2.16-3.13\mathrm{GeV}$ (or $2.16-3.16\mathrm{GeV}$), and the predictions for other fully-light vector tetraquark states with and without hidden-strange are also presented.

Comments: 20 pages, 17 figures