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

Abstract

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.