Baryon masses at second order in chiral perturbation theory

We analyze the octet baryon mass differences up to second order in chiral perturbation theory, including the effects of decupletintermediate states. We show that the Coleman-Glashow relation has computable corrections of order (m_m-m_u)m_s. Thesecorrections are numerically small, and in agreement with the data. We also show that corrections to the Σ equal-spacing rule aredominated by electromagnetic contributions, and that the Gell-Mann-Okubo formula has non-analytic corrections of order m_s²In m_s which cannot be computed from known matrix elements. We also show that the baryon masses cannot be used to extractmodel-independent information about the current quark masses.