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We calculate the branching ratios and polarization fractions of the $B \toa_1 b_1$ decays in the perturbative QCD(pQCD) approach at leading order, where$a_1$($b_1$) stands for the axial-vector $a_1(1260)[b_1(1235)]$ state. Bycombining the phenomenological analyses with the perturbative calculations, wefind the following results: (a) the large decay rates around $10^{-5}$ to$10^{-6}$ of the $B \to a_1 b_1$ decays dominated by the longitudinalpolarization(except for the $B^+ \to b_1^+ a_1^0$ mode) are predicted andbasically consistent with those in the QCD factorization(QCDF) within errors,which are expected to be tested by the Large Hadron Collider and Belle-IIexperiments. The large $B^0 \to a_1^0 b_1^0$ branching ratio could providehints to help explore the mechanism of the color-suppressed decays. (b) therather different QCD behaviors between the $a_1$ and $b_1$ mesons result in thedestructive(constructive) contributions in the nonfactorizable spectatordiagrams with $a_1(b_1)$ emission. Therefore, an interesting pattern of thebranching ratios appears for the color-suppressed $B^0 \to a_1^0 a_1^0, a_1^0b_1^0,$ and $b_1^0 b_1^0$ modes in the pQCD approach, $Br(B^0 \to b_1^0 b_1^0)> Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \to a_1^0 a_1^0)$, which is differentfrom $Br(B^0 \to b_1^0 b_1^0) \sim Br(B^0 \to a_1^0 b_1^0) \gtrsim Br(B^0 \toa_1^0 a_1^0)$ in the QCDF and would be verified at future experiments. (c) thelarge naive factorization breaking effects are observed in these $B \to a_1b_1$ decays. Specifically, the large nonfactorizable spectator(weakannihilation) amplitudes contribute to the $B^0 \to b_1^+ a_1^-(B^+ \to a_1^+b_1^0\; {\rm and}\; B^+ \to b_1^+ a_1^0)$ mode(s), which demand confirmationsvia the precise measurements.

Hadronic decays of $B \to a_1(1260) b_1(1235)$ in the perturbative QCD approach