Spectra of heavy-light mesons in a relativistic model

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 $D_{s0}^{\ast }(2317)$ 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 $D_{sJ}^{\ast }(2860)$ can be interpreted as the $|1^{3/2}{D}_1⟩$ and $|1^{5/2}{D}_3⟩$ states being members of the 1D family with $J^P=1^{-}$ and $3^{-}$.

Comments: 13 pages, 2 tables, 4 figures