Spectra of heavy-light mesons in a relativistic model

TL;DR

This paper calculates the spectra and wave functions of heavy-light mesons using a relativistic quark model based on a heavy-quark expansion, successfully matching most experimental data and providing interpretations for newly observed states.

Contribution

It introduces a relativistic quark model with a heavy-quark expansion to accurately compute heavy-light meson spectra, including new state assignments.

Findings

Results agree with experimental data for most states.

The model explains the nature of the $D_{sJ}^*(2860)$ as a 1D state.

The model accommodates newly observed heavy-light mesons.

Abstract

The spectra and wave functions of heavy-light mesons are calculated within a relativistic quark model, which is based on a heavy-quark expansion of the instantaneous Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation. The kernel we choose is the standard combination of linear scalar and Coulombic vector. The effective Hamiltonian for heavy-light quark-antiquark system is calculated up to order $1/m_Q^2$. Our results are in good agreement with available experimental data except for the anomalous $D_{s0}^*(2317)$ and $D_{s1}(2460)$ states. The newly observed heavy-light meson states can be accommodated successfully in the relativistic quark model with their assignments presented. The $D_{sJ}^*(2860)$ can be interpreted as the $|1^{3/2}D_1\rangle$ and $|1^{5/2}D_3\rangle$ states being members of the 1D family with $J^P=1^-$ and $3^-$.