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

In this article, we study the axial-vector mesons Zb(10610) and Zb(10650) with the Cγμ–Cγ5Cγμ–Cγ5 type and Cγμ–CγνCγμ–Cγν 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 detail for the first time, and suggest a formula μ=MX/Y/Z2−(2Mb)2 with the effective mass Mb=5.13 GeVMb=5.13 GeV to determine the energy scales. The numerical results favor assigning the Zb(10610) and Zb(10650) as the Cγμ–Cγ5Cγμ–Cγ5 type and Cγμ–CγνCγμ–Cγν type hidden bottom tetraquark states, respectively. We obtain the mass of the JPC=1++JPC=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 Zb±(10610)→ϒπ±,ηbρ± with the three-point QCD sum rules, the decay widths also support assigning the Zb(10610) as the Cγμ–Cγ5Cγμ–Cγ5 type hidden bottom tetraquark state.