The Hyperfine Splittings in Heavy-Light Mesons and Quarkonia

Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the $B_q$ (q=n,s) mesons are shown to be in full agreement with experiment if a universal coupling ${\alpha }_{HF}=0.310$ is taken in perturbative spin-spin potential. It gives $M(B^{\ast })-M(B)=45.7(3)$ MeV, $M(B_s^{\ast })-M(B_s)=46.7(3)$ MeV ($n_f=4$), while in bottomonium $\Delta_{HF}(b\bar b)=M(\Upsilon(9460))-M(\eta_b(1S))=63.4$MeVfor$n_f=4$and71.1MeVfor$n_f=5$ are obtained; just latter agrees with recent BaBar data. For unobserved excited states we predict $M(\mathrm{{\rm Y}}(2S))-M({\eta }_b(2S))=36(2)$ MeV, $M(\mathrm{{\rm Y}}(3S))-M(\eta (3S))=28(2)$ MeV, and also $M(B_c^{\ast })=6334(4)$ MeV, $M(B_c(2S))=6868(4)$ MeV, $M(B_c^{\ast }(2S))=6905(4)$ MeV. The mass splittings between $D(2^3{S}_1)-D(2^1{S}_0)$, $D_s(2^3{S}_1)-D_s(2^1{S}_0)$ are predicted to be $\sim 70$ MeV, which are significantly smaller than in several other studies.