Evaluation of the spectra of baryons containing two heavy quarks in a bag model

Abstract

In this work, we evaluate the mass spectra of baryons which consist of two heavy quarks and one light quark in the MIT bag model. The two heavy quarks constitute a heavy scalar or axial-vector diquark. Concretely, we calculate the spectra of $|q(Q{Q}^{\ensuremath{'}}){⟩}_{1/2}$ and $|q(Q{Q}^{\ensuremath{'}}){⟩}_{3/2}$ where $Q$ and ${Q}^{\ensuremath{'}}$ stand for $b$ and/or $c$ quarks. Especially, for $|q(bc){⟩}_{1/2}$ there can be a mixing between $|q(bc{)}_{0}{⟩}_{1/2}$ and $|q(bc{)}_{1}{⟩}_{1/2}$ where the subscripts 0 and 1 refer to the spin state of the diquark (bc), the mixing is not calculable in the framework of quantum mechanics as the potential model is employed, but can be evaluated by the quantum field theory. Our numerical results indicate that the mixing is sizable.