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

TL;DR

This paper calculates the masses of doubly heavy baryons using the Bethe-Salpeter formalism, considering heavy diquarks and light quarks, and provides predictions with and without the heavy quark limit.

Contribution

It introduces a numerical solution of Bethe-Salpeter equations for heavy diquarks and baryons, improving mass predictions in the quark-diquark model with detailed corrections.

Findings

Mass of $\\Xi_{cc}^{(\ast)}$ around 3.60-3.65 GeV in heavy quark limit.

Mass of $\\Xi_{cc}$ around 3.53-3.56 GeV without heavy quark limit.

Predicted masses for various doubly heavy baryons and estimated correction sizes.

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 diquarkes 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 $\Xi_{cc}^{(\ast)}$ is obtained in both approaches, $3.60\sim3.65\,\rm GeV$ ($\Xi_{cc}^{(\ast)}$) under the heavy quark limit, $3.53\sim3.56\,\rm GeV$ for $\Xi_{cc}$ and $3.61\sim3.63\,\rm GeV$ for $\Xi_{cc}^\ast$ without taking the heavy quark limit. The masses of $\Xi_{bc}^\prime$, $\Xi_{bc}^{(\ast)}$, $\Xi_{bb}^{(\ast)}$, $\Omega_{cc}^{(\ast)}$, $\Omega_{bc}^\prime$, $\Omega_{bc}^{(\ast)}$ and $\Omega_{bb}^{(\ast)}$ are also predicted in the same way. We find that the corrections to the results in the heavy quark limit are about $-0.02\,\rm GeV\sim-0.11\,\rm GeV$ for the masses of the doubly heavy baryons.