The Gell-Mann-Okubo octet mass relation is 12(m_N+m_ ) = 14(3m_ +m_ )

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Symmetry and Flavour, Ch SU(3) flavour: weights, tensor products and the mass formulas

Problem

The Gell-Mann-Okubo octet mass relation is

\tfrac12(m_N+m_\Xi) = \tfrac14(3m_\Lambda+m_\Sigma),

with isospin-averaged masses. Using the isospin-averaged masses

m_N = 938.92\,\mathrm{MeV}

m_\Lambda = 1115.68\,\mathrm{MeV}

and

m_\Sigma = 1193.15\,\mathrm{MeV}

, predict the isospin-averaged mass of the

\Xi

and compare it with the measured value

m_\Xi = 1318.3\,\mathrm{MeV}

(from

m_{\Xi^0}=1314.86\,\mathrm{MeV}

and

m_{\Xi^-}=1321.71\,\mathrm{MeV}

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