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The masses of spin-singlet and spin-triplet S-wave mesons containing a singleheavy quark are computed in the quenched approximation. The light quark actionand gauge field action are both classically-improved and tadpole-improved, andthe couplings to the heavy quark are organized by the 1/M expansion oftadpole-improved NRQCD. At each of two lattice spacings, near 0.22fm and0.26fm, meson masses are obtained for heavy quarks spanning the region betweencharmed and bottom mesons. Results up to O(1/M), O(1/M^2) and O(1/M^3) aredisplayed separately, so that the convergence of the heavy quark expansion canbe discussed. Also, the effect of each term in the O(1/M^3) contribution iscomputed individually. For bottom mesons the 1/M-expansion appears to besatisfactory, but the situation for charmed mesons is less clear.Comment: 23 pages including 12 figures, substantial revisio

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:math>effects for heavy-light mesons in lattice NRQCD

O(1/M3)effects for heavy-light mesons in lattice NRQCD