Semi-leptonic Production of $D_{sJ}(3040)$ and $D_J(3000)$ in $B_s$ and $B$ Decays

In this paper, we study the productions of the newly detected states $D_{sJ}(3040)$ and $D_J(3000)$ observed by BABAR Collaboration and LHCb Collaboration. We assume these states to be the $D_s(2P)$ and $D(2P)$ states with the quantum number $J^P=1^+$ in our work. The results of improved Bethe-Salpeter method indicate that the semi-leptonic decays via $B_s$ and $B$ into $D_{sJ}(3040)$ and $D_J(3000)$ have considerable branching ratios, for example, Br($bar{B}_s^0 rightarrow D{_{sJ}^+}(3040)e^-bar{ u}{_e}$)=$5.79times10^{-4}$, Br($bar{B}^0rightarrow D_{J}^+(3000)e^-bar{ u}{_e}$)=$2.63times10^{-4}$, which shows that these semi-leptonic decays can be accessible in experiments.