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

## TL;DR

This study calculates the production rates of excited scalar D mesons in B decays using the Bethe-Salpeter method, aligning with experimental data for certain states and predicting suppressed rates for others.

## Contribution

It applies the instantaneous Bethe-Salpeter approach to predict production rates of excited D mesons in B decays, providing insights into their wave functions and decay behaviors.

## Key findings

- The decay rate for D_0^*(2400) matches experimental data.
- The production rate of D_J^*(3000) is suppressed due to wave function node structure.
- The 3P states have production rates around 10^{-5}.

## 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^* $ 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}$.