Analysis of the semileptonic B_cto D₁⁰ transition in QCD sum rules and HQET

We investigate the structure of the $D_{1}^0(2420[2430]) (J^P=1^+)$ mesons via analyzing the semileptonic $B_{c}\to D_{1}^0 l\nu$ transition in the frame work of the three--point QCD sum rules and the heavy quark effective theory. We consider the $D_{1}^0$ meson in three ways; the pure $|c\bar{u}\rangle$ state, a mixture of two $|^3P_1\rangle$ and $|^1P_1\rangle$ states with a mixing angle $\theta$ and a combination of two mentioned states with mixing angle $\theta=35.3^\circ$ in the heavy quark limit. Taking into account the gluon condensate contributions, the relevant form factors are obtained for the three above conditions. These form factors are numerically calculated for $|c\bar{u}\rangle$ and the heavy quark limit cases. The obtained results for the form factors are used to evaluate the decay rates and the branching ratios. Also for mixed states, all of the mentioned physical quantities are plotted with respect to the unknown mixing angle $\theta$.