Lowest vector tetraquark states: $Y(4260/4220)$ or $Z_c(4100)$

Abstract

In this article, we take the $Y(4260/4220)$ as the vector tetraquark state with $J^{PC}=1^{--}$, and construct the $C{\gamma }_5\otimes {\overleftrightarrow{\partial }}_{\mu }\otimes {\gamma }_{5}C$ type diquark-antidiquark current to study its mass and pole residue with the QCD sum rules in details by taking into account the vacuum condensates up to dimension 10 in a consistent way. The predicted mass $M_Y=4.24\pm 0.10\mathrm{GeV}$ is in excellent agreement with experimental data and supports assigning the $Y(4260/4220)$ to be the $C{\gamma }_5\otimes {\overleftrightarrow{\partial }}_{\mu }\otimes {\gamma }_{5}C$ type vector tetraquark state, and disfavors assigning the $Z_c(4100)$ to be the $C{\gamma }_5\otimes {\overleftrightarrow{\partial }}_{\mu }\otimes {\gamma }_{5}C$ type vector tetraquark state. It is the first time that the QCD sum rules have reproduced the mass of the $Y(4260/4220)$ as a vector tetraquark state.

Comments: 13 pages, 4 figures. arXiv admin note: text overlap with arXiv:1803.05749