In this work we have studied hadronic charmless two-body B decays involving p-wave mesons in final state. We have calculated branching ratios of $B\to AT$ decays (where $A$ and $T$ denotes a $^3P_1$ axial-vector and a tensor meson, respectively), using $B \to T$ form factors obtained in the covariant light-front (CLF) approach, and the full effective Hamiltonian. We have obtained that $\mathcal{ B}(B^{ 0} \to a_{ 1}^{ +}a_{ 2}^{ -}) =42.47 \times10^{ -6}$, $\mathcal{ B}(B^{ +} \to a_{ 1}^{ +}a_{ 2}^{ 0}) = 22.71 \times10^{ -6}$, $\mathcal{ B}(B \to f_{ 1}K_{ 2}^{ *}) = (2.8-4) \times 10^{ -6}$ (with $f_{ 1}=, f_{ 1}(1285),f_{ 1}(1420)$) for $\theta_{ ^{ 3}P_{ 1}} = 53.2^{ \circ}$, $\mathcal{ B}(B \to f_{ 1}(1420)K_{ 2}^{ *}) = (5.91-6.42) \times 10^{ -6}$ with $\theta_{ ^{ 3}P_{ 1}} = 27.9^{ \circ}$, $\mathcal{ B}(B \to K_{ 1}a_{ 2})= (1.7 - 5.7) [1-9.3] \times10^{ -6}$ for $\theta_{ K_{ 1}} = -37^{ \circ} [-58^{ \circ}]$ where $K_1 = K_1(1270), K_1(1400)$. It seems that these decays can be measured in experiments at $B$ factories. Additionally, we have found that $\mathcal{ B}(B \to K_{ 1}(1270)a_{ 2})/\mathcal{ B}(B \to K_{ 1}(1400)a_{ 2})$ and $\mathcal{ B}(B \to f_1(1420)K_{ 2}^{ *})/\mathcal{ B}(B \to f_1(1285)K_{ 2}^{ *})$ ratios could be useful to determine numerical values of mixing angles $\theta_{ K_{ 1}}$ and $\theta_{ ^{ 3}P_{ 1}}$, respectively.
Categories: hep-ph