  Based on a $2\times 2$ mass matrix, the mixing angle of the axial vector
states $f_1(1420)$ and $f_1(1285)$ is determined to be $51.5^{\circ}$, and the
theoretical results about the decay and production of the two states are
presented. The theoretical results are in good agreement with the present
experimental results, which suggests that $f_1(1420)$ can be assigned as the
partner of $f_1(1285)$ in the $^3P_1$ $q\bar{q}$ nonet. We also suggest that
the existence of $f_1(1510)$ needs further experimental confirmation.
