Mass splittings in $Σ_b$ and $Σ_b^*$

Abstract

The charged $Σ_b$ and $Σ^*_b$ 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 $ΔI = 1$ electromagnetic mass differences $Σ_1 \equiv M(Σ^+) - M(Σ^-)$, $Σ^*_1 \equiv M(Σ^{*+})- M(Σ^{*-})$, $Σ_{b1} \equiv M(Σ_b^+) - M(Σ_b^-)$, and $Σ^*_{b1} \equiv M(Σ_b^{*+}) - M(Σ_b^{*-})$. The relation is $Σ^*_{b1} - Σ_{b1} = (m_s/m_b)(Σ^*_1 - Σ_1),$ leading to the expectation $Σ^*_{b1} - Σ_{b1} = 0.40 \pm 0.07$ MeV.