S and P-wave heavy-light mesons in lattice NRQCD
  The mass spectrum of S and P-wave mesons containing a single heavy quark is computed in the quenched approximation, using NRQCD up to third order in the inverse heavy quark mass expansion. Previous results found third order contributions which are as large in magnitude as the total second order contribution for the charmed S-wave spin splitting. The present work considers variations such as anisotropic lattices, Landau link tadpole improvement, and a highly-improved light quark action, and finds that the second order correction to the charmed S-wave spin splitting is about 20% of the leading order contribution, while the third order correction is about 20%(10%) for D^*-D(D_s^*-D_s). Nonleading corrections are very small for the bottom meson spectrum, and are statistically insignificant for the P-wave charmed masses. The relative orderings among P-wave charmed and bottom mesons, and the sizes of the mass splittings, are discussed in light of experimental data and existing calculations. 
Randy Lewis and R. M. Woloshyn