  In this work, we explore the ground state mass spectrum of the bottom-charm
baryon states in the framework of the QCD sum rules in a comprehensive way. In
calculations, we distinguish the contributions of the positive-parity and
negative-parity baryon states unambiguously, and investigate the energy scale
dependence of the QCD sum rules in details and observe that the acceptable
energy scales are $\mu=2.0\sim 2.8\,\rm{GeV}$, while the best energy scale is
$\mu=2.0\,\rm{GeV}$. The predictions can be confronted to the experimental data
in the future and shed light on the QCD low energy dynamics.
