$M(B^*_c)-M(B_c)$ 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 $M(B^*_c)-M(B_c)=46 \pm 15 {(\rm th)} {}^{+13}_{-11} (\delta\alpha_s)$ MeV. 
A.A. Penin, A. Pineda, V.A. Smirnov, M. Steinhauser