Strong Decays of the Orbitally Excited Scalar $D^{*}_{0}$ Mesons

TL;DR

This paper calculates the strong decay widths of excited scalar D mesons using the relativistic Bethe-Salpeter method, suggesting that the recently observed $D_J^*(3000)$ is likely a $2^3P_0$ state based on width comparisons.

Contribution

It provides a theoretical analysis of decay widths for excited D mesons, proposing the $D_J^*(3000)$ as a $2^3P_0$ state based on decay width calculations.

Findings

Calculated decay widths for $D_0^*(2400)$ and $D_J^*(3000)$.

$D_J^*(3000)$ width matches experimental data assuming $2^3P_0$ assignment.

Supports $D_J^*(3000)$ as a $0^+(2P)$ state.

Abstract

We calculate the two-body strong decays of the orbitally excited scalar mesons $D_0^*(2400)$ and $D_J^*(3000)$ by using the relativistic Bethe-Salpeter (BS) method. $D_J^*(3000)$ was observed recently by the LHCb Collaboration, the quantum number of which has not been determined yet. In this paper, we assume that it is the $0^+(2P)$ state and obtain the transition amplitude by using the PCAC relation, low-energy theorem and effective Lagrangian method. For the $1P$ state, the total widths of $D_0^*(2400)^{0}$ and $ D_0^*(2400)^+$ are 226 MeV and 246 MeV, respectively. With the assumption of $0^+(2P)$ state, the widths of $D_J^*(3000)^0$ and $D_J^*(3000)^+$ are both about 131 MeV, which is close to the present experimental data. Therefore, $D_J^*(3000)$ is a strong candidate for the $2^3P_0$ state.