Evaluation of the \(\theta_K\) and the Mixing angle \(\theta _{h_1}\)

The \(\theta_K\) has been re-evaluated via mass relations and latest experimental results, meanwhile, the \(M_{K_{1B}}\) also be obtained. Based on the singlet-octet mixing model and quark-flavor mixing model, the \(\theta_{h_1}\) has been recalculated with a modified formula, by inputting \(M_{K_{1B}}\) instead of \(\theta_K\). The values are calculated to be \(|{\theta _K}| = {(42.6 \pm 2.2)^ \circ }\), \(M_{K_{1B}} = 1333.9 \pm 4.6\ {\rm{MeV}}/c^{2}\) and \(\theta _{h_1} = 29.5\pm 2.0^\circ\). Using these calculations as input, we predict that the branching fraction of \(J/\psi \to \eta'(\eta)h_1(1170)\) is about one order higher than that of \(J/\psi \to \eta'(\eta)h_1(1415)\), which can be measured in future experiments to test the validity of these two models.