  The energies of different angular momentum states of a heavy-light meson were
measured on a lattice by Michael and Peisa in Phys. Rev. D 58, 34506 (1998). We
have now repeated this study using a larger, quenched lattice to check that
there the finite size effects are under control. Also the effect of quenching
is studied by using dynamical fermion configurations. In the latter case the
lattice spacing a is smaller, which allows one to make an estimate of a -> 0
corrections. The new measurements confirm the earlier calculated energy
spectrum.
  From some theoretical considerations it is expected that, for high angular
momentum states, the multiplets should be inverted compared with the Coulomb
spectrum, i.e. L- should lie higher than L+ (see H. J. Schnitzer Phys. Lett. B
226, 171 (1989)). This happens when a pure scalar confining potential is
present. Here the notation L+(-) means that the light quark spin couples to
angular momentum L giving the total j=L+/- 1/2. Experimentally this inversion
is not seen for P-wave mesons, and lattice measurements now suggest that there
is no inversion in the D-wave either. Indeed we find that the spin-orbit
splitting is very small for both values L=1 and 2. This almost exact
cancellation need not be a coincidence, and could probably be understood by
using straightforward symmetry arguments (P.R. Page, T. Goldman and J.N.
Ginocchio, Phys. Rev. Lett. 86, 204 (2001)).
