Mass splittings in ${\Sigma }_b$ and ${\Sigma }_b^{\ast }$

Abstract

The charged ${\Sigma }_b$ and ${\Sigma }_b^{\ast }$ states have recently been reported by the CDF Collaboration. The relation of their reported charge-averaged masses to expectations based on the quark model is reviewed briefly. A relation is proved among the $\Delta I=1$ electromagnetic mass differences ${\Sigma }_1\equiv M({\Sigma }^{+})-M({\Sigma }^{-})$, ${\Sigma }_1^{\ast }\equiv M({\Sigma }^{\ast +})-M({\Sigma }^{\ast -})$, ${\Sigma }_{b1}\equiv M({\Sigma }_b^{+})-M({\Sigma }_b^{-})$, and ${\Sigma }_{b1}^{\ast }\equiv M({\Sigma }_b^{\ast +})-M({\Sigma }_b^{\ast -})$. The relation is ${\Sigma }_{b1}^{\ast }-{\Sigma }_{b1}=(m_s/m_b)({\Sigma }_1^{\ast }-{\Sigma }_1),$ leading to the expectation ${\Sigma }_{b1}^{\ast }-{\Sigma }_{b1}=0.40\pm 0.07$ MeV.

Comments: 6 pages, 1 figure, to be published in Phys. Rev. D (Brief Reports). Numerical corrections; some text added