TTP04-06 $M(B^*_c)-M(B_c)$ Splitting from Nonrelativistic Renormalization Group

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 $M(B^*_c)-M(B_c)=65 \pm 24\,{(\rm th)}\,{}^{+19}_{-16}\,(\delta\alpha_s)$~MeV.