$M(B_c^{\ast })-M(B_c)$ Splitting from Nonrelativistic Renormalization Group

Abstract

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 $M(B_c^{\ast })-M(B_c)=46\pm 15(\mathrm{th}){}_{-11}^{+13}(\delta {\alpha }_s)$ MeV.

Comments: Eq.(22) and Appendix corrected, numerical results slightly changed. arXiv admin note: text overlap with arXiv:hep-ph/0312086