Mass splittings in $\Sigma_b$ and $\Sigma_b^*$

Abstract

The charged $\Sigma_b$ and $\Sigma^*_b$ 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 $\Sigma_1 \equiv M(\Sigma^+) - M(\Sigma^-)$, $\Sigma^*_1 \equiv M(\Sigma^{*+})- M(\Sigma^{*-})$, $\Sigma_{b1} \equiv M(\Sigma_b^+) - M(\Sigma_b^-)$, and $\Sigma^*_{b1} \equiv M(\Sigma_b^{*+}) - M(\Sigma_b^{*-})$. The relation is $\Sigma^*_{b1} - \Sigma_{b1} = (m_s/m_b)(\Sigma^*_1 - \Sigma_1),$ leading to the expectation $\Sigma^*_{b1} - \Sigma_{b1} = 0.40 \pm 0.07$ MeV.