The Hyperfine Splittings in Bottomonium and the $B_q(q=n,s,c)$ Mesons

Abstract

A universal description of the hyperfine splittings (HFS) in bottomonium and the $B_q(q=n,s,c)$ mesons is obtained with a universal strong coupling constant ${\alpha }_s(\mu )=0.305(2)$ in a spin-spin potential. Other characteristics are calculated within the Field Correlator Method, taking the freezing value of the strong coupling independent of $n_f$. The HFS $M(B^{\ast })-M(B)=45.3(3)$ MeV, $M(B_s^{\ast })-M(B_s)=46.5(3)$ MeV are obtained in full agreement with experiment both for $n_f=3$ and $n_f=4$. In bottomonium, $M({\rm Y}(9460))-M({\eta }_b)=70.0(4)$ MeV for $n_f=5$ agrees with the BaBar data, while a smaller HFS, equal to 64(1) MeV, is obtained for $n_f=4$. We predict HFS $M({\rm Y}(2S))-M({\eta }_b(2S))=36(1)$ MeV, $M({\rm Y}(3S))-M(\eta (3S))=27(1)$ MeV, and $M(B_c^{\ast })-M(B_c)=57.5(10)$ MeV, which gives $M(B_c^{\ast })=6334(1)$ MeV, $M(B_c(2{}^1{S}_0))=6865(5)$ MeV, and $M(B_c^{\ast }(2S{}^3{S}_1))=6901(5)$ MeV.

Comments: 5 pages revtex4