$f_1 (1285) \to e^+e^-$ decay and direct $f_1$ production in $e^+e^-$ collisions

The width of the $f_1 (1285) \to e^+e^-$ decay is calculated in the vector meson dominance model. The result depends on the relative phase between two coupling constants describing $f_1 \to \rho^0\gamma$ decay. The width $\Gamma (f_1 \to e^+e^-)$ is estimated to be $\simeq 0.07-0.19$ eV. Direct $f_1$ production in $e^+e^-$ collisions is discussed, and the $e^+e^- \to f_1\to a_0 \pi \to \eta \pi \pi$ cross section is calculated. Charge asymmetry in the $e^+e^- \to \eta \pi^+ \pi^-$ reaction due to interference between $e^+e^- \to f_1$ and $e^+e^- \to \eta \rho^0$ amplitudes is studied.