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 (BS) equations for the heavy diquarks and the doubly heavy baryons, respectively, to leading order in a $1/m_Q$ expansion. The BS 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 non-leptonic decay widths for the doubly heavy baryons emitting a pseudo-scalar meson are calculated within the model.

Corrections to the text, two references added, version accepted for publication in Physical Review D

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• Solving Bethe-Salpeter equation for two fermions in Minkowski space
• Studying the scalar bound states of the $K\bar{K}$ system in the Bethe-Salpeter formalism
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