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

TL;DR

This paper develops and solves Bethe-Salpeter equations for doubly heavy baryons and diquarks in the heavy quark limit, predicting their masses and decay widths using a covariant instantaneous approximation.

Contribution

It introduces a novel framework for calculating properties of doubly heavy baryons using Bethe-Salpeter equations in the heavy quark limit, including numerical solutions and decay predictions.

Findings

Calculated masses of heavy diquarks and doubly heavy baryons.

Predicted non-leptonic decay widths involving pseudo-scalar mesons.

Established a covariant instantaneous approximation approach for these systems.

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.