Mass of the η_b and α_s from the Nonrelativistic Renormalization Group -: art. no. 242001

We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting, using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the eta(b) meson to be M(eta(b))=9421+/-11(th)(-8)(+9)(deltaalpha(s)) MeV. The experimental measurement of M(eta(b)) with a few MeV error would be sufficient to determine alpha(s)(M-Z) with an accuracy of +/-0.003. For the hyperfine splitting in charmonium, the use of the nonrelativistic renormalization group brings the perturbative prediction significantly closer to the experimental figure.