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

TL;DR

This paper re-evaluates mixing angles and mass relations of certain mesons using experimental data and models, predicting branching fractions for specific decay processes to guide future experimental tests.

Contribution

It provides updated values for $ heta_K$, $M_{K_{1B}}$, and $ heta_{h_1}$ using mass relations and models, and predicts decay branching fractions for future experimental validation.

Findings

Updated mixing angle $|{ heta _K}| = 42.6^ ext{o}$

Mass of $K_{1B}$ meson $1333.9$ MeV/c^2

Predicted branching fraction for $J/\psi$ decays to $h_1(1170)$ is higher

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.