Scaling of theBandDmeson spectrum in lattice QCD

Abstract

We give results for the $B$ and the $D$ meson spectrum using NRQCD on the lattice in the quenched approximation. The masses of radially and orbitally excited states are calculated as well as $S$-wave hyperfine and $P$-wave fine structure. Radially excited $P$ states are observed for the first time. Radial and orbital excitation energies match well to experiment, as does the strange-nonstrange $S$-wave splitting. We compare the light and heavy quark mass dependence of various splittings to experiment. Our $B$ results cover a range in lattice spacings of more than a factor of two. Our $D$ results are from a single lattice spacing and we compare them to numbers in the literature from finer lattices using other methods. We see no significant dependence of physical results on the lattice spacing.