  The two-body hadronic decays of B mesons into pseudoscalar and axial vector
mesons are studied within the framework of QCD factorization. The light-cone
distribution amplitudes (LCDAs) for $^3P_1$ and $^1P_1$ axial-vector mesons
have been evaluated using the QCD sum rule method. Owing to the G-parity, the
chiral-even two-parton light-cone distribution amplitudes of the $^3P_1$
($^1P_1$) mesons are symmetric (antisymmetric) under the exchange of quark and
anti-quark momentum fractions in the SU(3) limit. For chiral-odd LCDAs, it is
other way around. The main results are the following: (i) The predicted rates
for $a_1^\pm(1260)\pi^\mp$, $b_1^\pm(1235)\pi^\mp$, $b_1^0(1235)\pi^-$,
$a_1^+K^-$ and $b_1^+K^-$ modes are in good agreement with the data. However,
the naively expected ratios $Br(B^-\to a_1^0\pi^-)/Br(\ov B^0\to
a_1^+\pi^-)\leq 1$, $Br(B^-\to a_1^-\pi^0)/Br(\ov B^0\to a_1^-\pi^+)\sim
{1\over 2}$ and $Br(B^-\to b_1^0K^-)/Br(\ov B^0\to b_1^+K^-)\sim {1\over 2}$
are not borne out by experiment. This should be clarified by the improved
measurements of these decays. (ii) Since the $\bar B\to b_1K$ decays receive
sizable annihilation contributions, their rates are sensitive to the
interference between penguin and annihilation terms. The measurement of
$Br(\bar B^0\to b_1^+K^-)$ implies a destructive interference which in turn
indicates that the form factors for $B\to b_1$ and $B\to a_1$ transitions are
of opposite signs. (iii) Sizable power corrections such as weak annihilation
are needed to account for the observed rates of the penguin-dominated modes
$K_1^-(1270)\pi^+$ and $K_1^-(1400)\pi^+$.
