Spectra of heavy–light mesons in a relativistic model

Abstract

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 $$1/m_Q^2$$ 1 / m Q 2 . Our results are in good agreement with available experimental data except for the anomalous $$D_{s0}^*(2317)$$ D s 0 ∗ ( 2317 ) and $$D_{s1}(2460)$$ D s 1 ( 2460 ) states. The newly observed heavy–light meson states can be accommodated successfully in the relativistic quark model with their assignments presented. The $$D_{sJ}^*(2860)$$ D s J ∗ ( 2860 ) can be interpreted as the $$|1^{3/2}D_1\rangle $$ | 1 3 / 2 D 1 ⟩ and $$|1^{5/2}D_3\rangle $$ | 1 5 / 2 D 3 ⟩ states being members of the 1D family with $$J^P=1^-$$ J P = 1 - and $$3^-$$ 3 - .