The Gell-Mann-Okubo relation for the baryon octet reads

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

Particle Physics, Ch SU(3) flavour and the hadron multiplets

Problem

The Gell-Mann-Okubo relation for the baryon octet reads 2(mN+mΞ)=3mΛ+mΣ2(m_N+m_\Xi) = 3m_\Lambda + m_\Sigma, with all masses in MeV/c2\mathrm{MeV}/c^2. Using the measured values mN=938.9 MeV/c2m_N = 938.9\,\mathrm{MeV}/c^2 (nucleon average), mΞ=1318.3 MeV/c2m_\Xi = 1318.3\,\mathrm{MeV}/c^2 (Ξ\Xi average) and mΛ=1115.7 MeV/c2m_\Lambda = 1115.7\,\mathrm{MeV}/c^2: ((a)) Rearrange the relation to predict mΣm_\Sigma. ((b)) The measured Σ\Sigma average mass is 1193.2 MeV/c21193.2\,\mathrm{MeV}/c^2. Find the percentage difference between the prediction and the measured value.

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