New mass formula for octet and decuplet baryons

The general parametrization method [Phys. Rev. D 40, 2997 (1989)] (an exact consequence of a QCD-like relativistic field theory) is used to parametrize the masses of 8 and 10 baryons to second order in flavor breaking. Because at first order in flavor breaking, three-quark contributions to octet masses are very small, we neglect such contributions at second order and derive a ‘‘corrected’’ Gell-Mann–Okubo formula; when written in a way free from electromagnetic corrections, it is 1/2(n+${\mathrm{\Xi }}^0$)+T=1/4(3Λ+${\mathrm{\Sigma }}^{+}$) with T=${\mathrm{\Xi }}^{\mathrm{*}\mathrm{-}}$-1/2(Ω+${\mathrm{\Sigma }}^{\mathrm{*}\mathrm{-}}$) and Σ^ ${}_{}{}^{+}{}_{}{}^{}$=2${\mathrm{\Sigma }}^{+}$-${\mathrm{\Sigma }}^0$+2(n-p). The two sides of the formula are respectively 1132.4±0.8 and 1133.9±0.1 MeV.