Light single-gluon hybrid states with various (exotic) quantum numbers

We apply the QCD sum rule method to study the light single-gluon hybrid states with various (exotic) quantum numbers. We construct twenty-four single-gluon hybrid currents, and use eighteen of them to calculate the masses of forty-four single-gluon hybrid states with the quark-gluon contents q q g ($q=u/d$) and s s g. We concentrate on the hybrid states with the exotic quantum number JPC = 1⁻⁺, whose masses and widths are calculated to be M_| q q g;1⁻1⁻⁺ =1.67+0.15-0.17 GeV, Γ_| q q g;1⁻1⁻⁺ = 530⁺⁵⁴⁰₋₃₃₀ MeV, M_| q q g;0⁺1⁻⁺ = 1.67+0.15-0.17 GeV, Γ_| q q g;0⁺1⁻⁺ = 120⁺¹⁶⁰₋₁₁₀ MeV, M_| s s g;0⁺1⁻⁺ = 1.84+0.14-0.15 GeV, and Γ_| s s g;0⁺1⁻⁺ = 100⁺¹¹⁰-~80 MeV. Our results support the interpretations of the π₁(1600) and η₁(1855) as the hybrid states | q q g;1⁻1⁻⁺ and | s s g;0⁺1⁻⁺, respectively. Considering the uncertainties, our results suggest that the π₁(1600) and η₁(1855) may also be interpreted as the hybrid states | q q g;1⁻1⁻⁺ and | q q g;0⁺1⁻⁺, respectively. To differentiate these two assignments and to verify whether they are hybrid states or not, we propose to examine the a₁(1260) π decay channel in future experiments.