Rates of \(D^{}_{0}(2400)\), \( D_J^(3000) \) as the \(D^{}_{0}(2P)\) and \(D^{}_{0}(3P)\) in \(B\) Decays

In this paper, we use the instantaneous Bethe-Salpeter method to calculate the semi-leptonic and non-leptonic production of the orbitally excited scalar \( D_0^* \) in \( B \) meson decays. When the final state is \( 1P \) state \( D_0^*(2400) \), our theoretical decay rate is consistent with experimental data. For \( D_J^*(3000) \) final state, which was observed by LHCb collaboration recently and here treated as the orbitally excited scalar \(D^{*}_{0}(2P)\), its rate is in the order of \( 10^{-4} \sim 10^{-6}\). We find the special node structure of \(D^{*}_{0}(2P)\) 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 \( 10^{-5}\).