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 $C\gamma_\alpha\otimes\stackrel{\leftrightarrow}{\partial}\mu\otimes\gamma^\alpha C$ (or $C\gamma\alpha\otimes\stackrel{\leftrightarrow}D_\mu\otimes\gamma^\alpha C$) type current with fully-strange quarks couples potentially to a tetraquark state with the mass $2.16 \pm 0.14 \,\rm{GeV}$, which supports assigning the $Y/\phi(2175)$ 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 $C\gamma_\mu\otimes \stackrel{\leftrightarrow}{\partial}\alpha \otimes\gamma^\alpha C + C\gamma^\alpha \otimes\stackrel{\leftrightarrow}{\partial}\alpha \otimes\gamma_\mu$ (or $C\gamma_\mu\otimes \stackrel{\leftrightarrow}D_\alpha \otimes\gamma^\alpha C + C\gamma^\alpha \otimes\stackrel{\leftrightarrow}D_\alpha \otimes\gamma_\mu$) are consistent with the $X(2200)$ and $X(2400)$ respectively, which lie in the region $2.20$ to $2.40\,\rm{GeV}$. The central values of the masses of the fully-strange vector tetraquark states with an explicit P-wave are about $2.16-3.13\,\rm{GeV}$ (or $2.16-3.16\,\rm{GeV}$), and the predictions for other fully-light vector tetraquark states with and without hidden-strange are also presented.