The Quark Model and $b$ Baryons

The recent observation at the Tevatron of $Σ_b^{\pm}$ ($uub$ and $ddb$) baryons within 2 MeV of the predicted $Σ_b - Λ_b$ splitting and of $Ξ_b^-$ $(dsb)$ baryons at the Tevatron within a few MeV of predictions has provided strong confirmation for a theoretical approach based on modeling the color hyperfine interaction. The prediction of $M(Ξ^-_b) = 5790$ to 5800 MeV is reviewed and similar methods used to predict the masses of the excited states $Ξ_b^\prime$ and $Ξ_b^*$. The main source of uncertainty is the method used to estimate the mass difference $m_b - m_c$ from known hadrons. We verify that corrections due to the details of the interquark potential and to $Ξ_b$--$Ξ_b^\prime$ mixing are small. For S-wave $qqb$ states we predict $M(Ω_b) = 6052.1 \pm 5.6$ MeV, $M(Ω^*_b) = 6082.8 \pm 5.6$ MeV, and $M(Ξ_b^0) = 5786.7 \pm 3.0$ MeV. For states with one unit of orbital angular momentum between the $b$ quark and the two light quarks we predict $M(Λ_{b[1/2]}) = 5929 \pm 2$ MeV, $M(Λ_{b[3/2]}) = 5940 \pm 2$ MeV, $M(Ξ_{b[1/2]}) = 6106 \pm 4$ MeV, and $M(Ξ_{b[3/2]}) = 6115 \pm 4$ MeV. Results are compared with those of other recent approaches.

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