Qcd Potential Model for Light-heavy Quarkonia and the Heavy Quark Effective Theory

We have investigated the spectra of light-heavy quarkonia with the use of a quantum-chromodynamic potential model which is similar to that used earlier for the heavy quarkonia. An essential feature of our treatment is the inclusion of the one-loop radiative corrections to the quark-antiquark potential, which contribute significantly to the spin-splittings among the quarkonium energy levels. Unlike cc̄ and bb̄, the potential for a light-heavy system has a complicated dependence on the light and heavy quark masses m and M , and it contains a spin-orbit mixing term. We have obtained excellent results for the observed energy levels of D, Ds, B , and Bs, and we are able to provide predicted results for many unobserved energy levels. We have also used our investigation to test the accuracy of the heavy quark effective theory. We find that the heavy quark expansion yields generally good results for the B and Bs energy levels provided that M −1 and M lnM corrections are taken into account in the quark-antiquark interactions. It does not, however, provide equally good results for the energy levels of D and Ds, which shows that the effective theory can be applied more accurately to the b quark than the c quark.