Vector tetraquark state candidates: $Y(4260/4220)$, $Y(4360/4320)$, $Y(4390)$ and $Y(4660/4630)$

Abstract

In this article, we construct the $C\otimes {\gamma }_{\mu }C$ and $C{\gamma }_5\otimes {\gamma }_5{\gamma }_{\mu }C$ type currents to interpolate the vector tetraquark states, then carry out the operator product expansion up to the vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum rules. In calculations, we use the formula $\mu =\sqrt{M_Y^2-(2{\mathbb{M}}_c{)}^2}$ to determine the optimal energy scales of the QCD spectral densities, moreover, we take the experimental values of the masses of the $Y(4260/4220)$, $Y(4360/4320)$, $Y(4390)$ and $Y(4660/4630)$ as input parameters and fit the pole residues to reproduce the correlation functions at the QCD side. The numerical results support assigning the $Y(4660/4630)$ to be the $C\otimes {\gamma }_{\mu }C$ type vector tetraquark state $c\bar{c}s\bar{s}$, assigning the $Y(4360/4320)$ to be $C{\gamma }_5\otimes {\gamma }_5{\gamma }_{\mu }C$ type vector tetraquark state $c\bar{c}q\bar{q}$, and disfavor assigning the $Y(4260/4220)$ and $Y(4390)$ to be the pure vector tetraquark states.

Comments: 18 pages, 14 figures. arXiv admin note: text overlap with arXiv:1311.1046, arXiv:1607.00701