Bethe-Salpeter equation for doubly heavy baryons in the covariant instantaneous approximation

Abstract

In the heavy quark limit, a doubly heavy baryon is regarded as composed of a heavy diquark and a light quark. We establish the Bethe-Salpeter equations for the heavy diquarks and the doubly heavy baryons, respectively, to leading order in a 1/mQ expansion. The Bethe-Salpeter equations are solved numerically under the covariant instantaneous approximation with the kernels containing scalar confinement and one-gluon-exchange terms. The masses for the heavy diquarks and the doubly heavy baryons are obtained, and the nonleptonic decay widths for the doubly heavy baryons emitting a pseudoscalar meson are calculated within the model.