Masses of doubly heavy baryons in the Bethe-Salpeter equation approach

Abstract

A doubly heavy baryon can be regarded as composed of a heavy diquark and a light quark. In this picture, we study the masses of the doubly heavy diquarks in the Bethe-Salpeter (BS) formalism first, which are then used as one of the inputs in studying the masses of the doubly heavy baryons in the quark-diquark model. We establish the BS equations for both the heavy diquarks and the heavy baryons with and without taking the heavy quark limit, respectively. These equations are solved numerically with the kernel containing the scalar confinement and one-gluon-exchange terms. The mass of the doubly charmed baryon Ξcc(⁎) is obtained in both approaches, 3.60∼3.65GeV (Ξcc(⁎)) under the heavy quark limit, 3.53∼3.56GeV for Ξcc and 3.61∼3.63GeV for Ξcc⁎ without taking the heavy quark limit. The masses of Ξbc′, Ξbc(⁎), Ξbb(⁎), Ωcc(⁎), Ωbc′, Ωbc(⁎) and Ωbb(⁎) are also predicted in the same way. We find that the corrections to the results in the heavy quark limit are about −0.02GeV∼−0.11GeV for the masses of the doubly heavy baryons.