Evaluation of the $\hat{I}{¸}_K$ and the Mixing angle $\hat{I}{¸}_{h_1}$

Abstract

The $\hat{I}{¸}_K$ 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 $\hat{I}{¸}_{h_1}$ has been recalculated with a modified formula, by inputting $M_{K_{1B}}$ instead of $\hat{I}{¸}_K$. The values are calculated to be $|\hat{I}{¸}_K|=(42.6\pm 2.2{)}^{\circ }$, $M_{K_{1B}}=1333.9\pm 4.6\mathrm{MeV}/c^2$ and $\hat{I}{¸}_{h_1}=29.5\pm 2.0^{\circ }$. Using these calculations as input, we predict that the branching fraction of $J/\ddot{I}ˆ\to \hat{I}{\cdot }^{\prime }(\hat{I}\cdot )h_1(1170)$ is about one order higher than that of $J/\ddot{I}ˆ\to \hat{I}{\cdot }^{\prime }(\hat{I}\cdot )h_1(1415)$, which can be measured in future experiments to test the validity of these two models.

6 pages, with no figure