Analysis of the $B\to a_1(1260)$ form-factors with light-cone QCD sum rules

In this article, we calculate the $B\to a_1(1260)$ form-factors $V_1(q^2)$, $V_2(q^2)$, $V_3(q^2)$ and $A(q^2)$ with the $B$-meson light-cone QCD sum rules. Those form-factors are basic parameters in studying the exclusive non-leptonic two-body decays $B\to AP$ and semi-leptonic decays $B\to A l \nu_l$,$B\to A \bar{l}l$. Our numerical results are consistent with the values from the (light-cone) QCD sum rules. The main uncertainty comes from the parameter ${\omega }_0$ (or ${\lambda }_B$), which determines the shapes of the two-particle and three-particle light-cone distribution amplitudes of the $B$ meson, it is of great importance to refine this parameter.