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We compute the hyperfine splitting in a heavy quarkonium composed of different flavors in next-to-leading logarithmic approximation using the nonrelativistic renormalization group. We predict the mass difference of the vector and pseudoscalar charm-bottom mesons to be $M(B^*_c)-M(B_c)=46 \pm 15 {(\rm th)} {}^{+13}_{-11} (\delta\alpha_s)$ MeV.

$M(B^*_c)-M(B_c)$ Splitting from Nonrelativistic Renormalization Group. (arXiv:hep-ph/0403080v5 UPDATED)