The Quark Model and $b$ Baryons

Abstract

The recent observation at the Tevatron of ${\Sigma }_b^{\pm }$ ($uub$ and $ddb$) baryons within 2 MeV of the predicted ${\Sigma }_b-{\Lambda }_b$ splitting and of ${\Xi }_b^{-}$ $(dsb)$ 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 $M({\Xi }_b^{-})=5790$ to 5800 MeV is reviewed and similar methods used to predict the masses of the excited states ${\Xi }_b^{\prime }$ and ${\Xi }_b^{\ast }$. 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 ${\Xi }_b$--${\Xi }_b^{\prime }$ mixing are small. For S-wave $qqb$ states we predict $M({\Omega }_b)=6052.1\pm 5.6$ MeV, $M({\Omega }_b^{\ast })=6082.8\pm 5.6$ MeV, and $M({\Xi }_b^0)=5786.7\pm 3.0$ MeV. For states with one unit of orbital angular momentum between the $b$ quark and the two light quarks we predict $M({\Lambda }_{b[1/2]})=5929\pm 2$ MeV, $M({\Lambda }_{b[3/2]})=5940\pm 2$ MeV, $M({\Xi }_{b[1/2]})=6106\pm 4$ MeV, and $M({\Xi }_{b[3/2]})=6115\pm 4$ MeV. Results are compared with those of other recent approaches.

Comments: 20 pages, 1 figure, to be published in Annals of Physics. Eq. (58) corrected