Quantum-chromodynamic 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 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 splitting among the quarkonium energy levels. Unlike cc{} and bb{}, 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 D⁰, Dₛ, B⁰, and Bₛ, and we are able to provide predicted results for many unobserved energy levels. Our potential parameters for different quarkonia satisfy the constraints of quantum chromodynamics. 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 B⁰ and Bₛ energy levels provided that M^-1 and M^-1 ln M corrections are taken into account in the quark-antiquark interactions. It does not, however, provide equally good results for the energy levels of D⁰ and Dₛ, which indicates that the effective theory cannot be applied accurately to the c quark.