O(1/M^3) effects for heavy-light mesons in lattice NRQCD

The masses of spin-singlet and spin-triplet S-wave mesons containing a single heavy quark are computed in the quenched approximation. The light quark action and gauge field action are both classically-improved and tadpole-improved, and the couplings to the heavy quark are organized by the 1/M expansion of tadpole-improved NRQCD. At each of two lattice spacings, near 0.22fm and 0.26fm, meson masses are obtained for heavy quarks spanning the region between charmed and bottom mesons. Results up to O(1/M), O(1/M^2) and O(1/M^3) are displayed separately, so that the convergence of the heavy quark expansion can be discussed. Also, the effect of each term in the O(1/M^3) contribution is computed individually. For bottom mesons the 1/M-expansion appears to be satisfactory, but the situation for charmed mesons is less clear.