Regarding the axial-vector mesons

Abstract

The implications of the $f_1(1285)-f_1(1420)$ mixing for the $K_1(^3P_1)-K_1(^1P_1)$ mixing angle is investigated. Based on the $f_1(1285)-f_1(1420)$ mixing angle $\sim 50^\circ$ suggested from the analysis for a substantial body of data concerning the $f_1(1420)$ and $f_1(1285)$, the masses of the $K_1(^3P_1)$ and $K_1(^1P_1)$ are determined to be $\sim 1307.35\pm 0.63$ MeV and $1370.03\pm 9.69$ MeV, respectively, which therefore suggests that the $K_1(^3P_1)-K_1(^1P_1)$ mixing angle is about $\pm (59.55\pm 2.81)^\circ$. Also, it is found that the mass of the $h^\prime_1(^1P_1)$ (mostly of $s\bar{s}$) state is about $1495.18\pm 8.82$ MeV. Comparison of the predicted results and the available experimental information of the $h_1(1380)$ shows that without further confirmation on the $h_1(1380)$, the assignment of the $h_1(1380)$ as the $s\bar{s}$ member of the $^1P_1$ meson nonet may be premature.