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 $|{\theta }_K|=(42.6\pm 2.2{)}^{\circ }$, $M_{K_{1B}}=1333.9\pm 4.6\mathrm{MeV}/c^2$ and ${\theta }_{h_1}=29.5\pm 2.0^{\circ }$. Using these calculations as input, we predict that the branching fraction of $J/\psi \to {\eta }^{\prime }(\eta )h_1(1170)$ is about one order higher than that of $J/\psi \to {\eta }^{\prime }(\eta )h_1(1415)$, which can be measured in future experiments to test the validity of these two models.

Comments: 6 pages, with no figure