  We have presented a detailed study of twist-2 and twist-3 light-cone
distribution amplitudes of $1^3P_1$ and $1^1P_1$ axial-vector mesons, based on
QCD conformal partial wave expansion. Applying equations of motion, the
twist-three two-parton light-cone distribution amplitudes can be expressed in
terms of leading-twist and twist-three three-parton light-cone distribution
amplitudes. The relevant G-parity invariant and violating parameters,
containing the corrections due to the SU(3) breaking effects, are evaluated
from the QCD sum rule method. The results for axial-vector decay constants of
$1^3P_1$ states are presented. The values of tensor decay constants and
Gegenbauer moments of the leading twist distribution amplitudes for $1^1P_1$
states are updated. Using Gell-Mann-Okubo mass formula, the mixing angle for
the $f_8$ and $f_1$ of $1^3P_1$ states is $\theta_{^3P_1}\sim 38^\circ$, and
that for $h_8$ and $h_1$ of $1^1P_1$ states is $\theta_{^1P_1}\sim 10^\circ$.
The detailed properties for physical states $f_1(1285), f_1(1420), h_1(1170)$,
and $h_1(1380)$ are given. Assuming the mixing angle between $K_{1A}$ and
$K_{1B}$ to be $\theta_K=45^\circ$ or $-45^\circ$, we also give the detailed
study for $K_1(1270)$ and $K_1(1400)$. Using the conformal partial wave
expansion, we obtain the models for light-cone distribution amplitudes,
containing contributions up to conformal spin 9/2. It is interesting to note
that some distribution amplitudes have significant asymmetric behaviors, which
should be phenomenologically attractive.
