Reanalysis of the $Z_c(4020)$, $Z_c(4025)$, $Z(4050)$ and $Z(4250)$ as tetraquark states with QCD sum rules

Abstract

In this article, we calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and study the $C{\gamma }_{\mu }-C{\gamma }_{\nu }$ type scalar, axial-vector and tensor tetraquark states in details with the QCD sum rules. In calculations, we use the formula $\mu =\sqrt{M_{X/Y/Z}^2-(2{\mathbb{M}}_c{)}^2}$ to determine the energy scales of the QCD spectral densities. The predictions $M_{J=2}=\left(4.02_{-0.09}^{+0.09}\right)\mathrm{GeV}$, $M_{J=1}=\left(4.02_{-0.08}^{+0.07}\right)\mathrm{GeV}$ favor assigning the $Z_c(4020)$ and $Z_c(4025)$ as the $J^{PC}=1^{+-}$ or $2^{++}$ diquark-antidiquark type tetraquark states, while the prediction $M_{J=0}=\left(3.85_{-0.09}^{+0.15}\right)\mathrm{GeV}$ disfavors assigning the $Z(4050)$ and $Z(4250)$ as the $J^{PC}=0^{++}$ diquark-antidiquark type tetraquark states. Furthermore, we discuss the strong decays of the $0^{++}$, $1^{+-}$, $2^{++}$ diquark-antidiquark type tetraquark states in details.

Comments: 24 pages, 17 figures. arXiv admin note: substantial text overlap with arXiv:1311.1046, arXiv:1312.2652, arXiv:1403.0810, arXiv:1312.7489