The $Z_b(10610)$ and $Z_b(10650)$ as axial-vector tetraquark states in the QCD sum rules

Abstract

In this article, we study the axial-vector mesons $Z_b(10610)$ and $Z_b(10650)$ with the $C{\gamma }_{\mu }-C{\gamma }_5$ type and $C{\gamma }_{\mu }-C{\gamma }_{\nu }$ type interpolating currents respectively by carrying out the operator product expansion to the vacuum condensates up to dimension-10. In calculations, we explore the energy scale dependence of the QCD spectral densities of the hidden bottom tetraquark states in details for the first time, and suggest a formula $\mu =\sqrt{M_{X/Y/Z}^2-(2{\mathbb{M}}_b{)}^2}$ with the effective mass ${\mathbb{M}}_b=5.13\mathrm{GeV}$ to determine the energy scales. The numerical results favor assigning the $Z_b(10610)$ and $Z_b(10650)$ as the $C{\gamma }_{\mu }-C{\gamma }_5$ type and $C{\gamma }_{\mu }-C{\gamma }_{\nu }$ type hidden bottom tetraquark states, respectively. We obtain the mass of the $J^{PC}=1^{++}$ hidden bottom tetraquark state as a byproduct, which can be compared to the experimental data in the futures. Furthermore, we study the strong decays $Z_b^{\pm }(10610)\to {\rm Y}{\pi }^{\pm },{\eta }_b{\rho }^{\pm }$ with the three-point QCD sum rules, the decay widths also support assigning the $Z_b(10610)$ as the $C{\gamma }_{\mu }-C{\gamma }_5$ type hidden bottom tetraquark state.

Comments: 21 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1312.1537, arXiv:1311.1046