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 ηb meson to be
M(ηb)=9421±10(th)+9−8(δαs) MeV.
The experimental measurement of M(ηb) with a few MeV error would be
sufficient to determine αs(MZ) with an accuracy of ±0.003.
The use of the nonrelativistic renormalization group is mandatory to reproduce
the experimental value of the hyperfine splitting in charmonium.