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$B \to A$ transitions in the light-cone QCD sum rules with the chiral current

In this article, we calculate the form-factors of the transitions $B \to a_1(1260)$, $b_1(1235) $ in the leading-order approximation using the light-cone QCD sum rules. In calculations, we choose the chiral current to interpolate the $B$-meson, which has outstanding advantage that the twist-3 light-cone distribution amplitudes of the axial-vector mesons have no contributions, and the resulting sum rules for the form-factors suffer from much less uncertainties. Then we study the semi-leptonic decays $B \to a_1(1260) l\barν_l$, $b_1(1235) l\barν_l$ $(l=e,μ,τ)$, and make predictions for the differential decay widths and decay widths, which can be confronted with the experimental data in the coming future.