Rates of $D_0^{\ast }(2400)$, $D_J^{\ast }(3000)$ as the $D_0^{\ast }(2P)$ and $D_0^{\ast }(3P)$ in $B$ Decays

Abstract

In this paper, we use the instantaneous Bethe-Salpeter method to calculate the semi-leptonic and non-leptonic production of the orbitally excited scalar $D_0^{\ast }$ in $B$ meson decays. When the final state is $1P$ state $D_0^{\ast }(2400)$, our theoretical decay rate is consistent with experimental data. For $D_J^{\ast }(3000)$ final state, which was observed by LHCb collaboration recently and here treated as the orbitally excited scalar $D_0^{\ast }(2P)$, its rate is in the order of $10^{-4}\sim 10^{-6}$. We find the special node structure of $D_0^{\ast }(2P)$ wave function possibly results in the suppression of its branching ratio and the abnormal uncertainty. The $3P$ states production rate is in the order of $10^{-5}$.

Comments: 17 pages, 26 figures