Spectroscopy of the three-heavy-quark system

We describe a way to include asymptotic freedom in the potential energy for a baryon composed of three heavy quarks, which is based on the Born-Oppenheimer approximation to the MIT bag model. The running coupling constant appears in both the two-body Coulomb terms and the three-body confining term of the potential energy. The Schrödinger equation with this potential is solved using a hyperspherical expansion, and spectra are obtained for the baryons $b^3$, $c^3$, and ${\Omega }^{-}\left(s^3\right)$. Comparisons of these systems with the corresponding $q\overline{q}$ systems are made using the same running coupling constant and bag parameters for the baryons and the mesons.