The Hyperfine Splittings in Heavy-Light Mesons and Quarkonia

Abstract

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 ${\Delta }_{HF}(b\bar{b})=M({\rm Y}(9460))-M({\eta }_b(1S))=63.4$ MeV for $n_f=4$ and 71.1 MeV for $n_f=5$ are obtained; just latter agrees with recent BaBar data. For unobserved excited states we predict $M({\rm Y}(2S))-M({\eta }_b(2S))=36(2)$ MeV, $M({\rm Y}(3S))-M(\eta (3S))=28(2)$ 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.

13 pages

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• Variational Analysis of Mass Spectra and Decay Constants for Ground State Pseudoscalar and Vector Mesons in Light-Front Quark Model
• Higher excitations of the $D$ and $D_s$ mesons
• The radial Regge trajectories and leptonic widths of the isovector mesons
• Purely leptonic decays of the ground charged vector mesons
• Hyperfine splitting and the experimental candidates for η_b(2S)
• Unified covariant treatment of hyperfine splitting for heavy and light mesons
• Two body relativistic wave equations
• QED spectra in the path integral formalism
• Relativistic two fermion treatment of hyperfine transitions
• Relativistic two-body calculation of $b\bar{b}$-mesons radiative decays