Why the Constituent Quark Model Works for Baryon Magnetic Moments

Starting from quantum chromodynamics, we find that aside from some terms that contribute only via the mixing of different Fock components, the baryon magnetic moment can be expressed as μB = Σ_qQ_q/(2 < k₀>_q) (2S_q-2S-_q +L_q–L-_q) , where < k₀>_q is the q flavor quark’s average relativistic energy inside the baryon, and S_q, L_q, S-_q , L-_q are quark and antiquark’s relativistic spin and orbital contributions to baryon spin. We demonstrate that within an error of 1/6, this expression can be parameterized as Σ_qQ_q/ ( 2m_q^eff )(2s_q-2s-_q), (where s is the nonrelativistic Pauli spin contribution and m_q^eff is of the order of the constituent quark mass) which is just what the nonrelativistic constituent quark model adopts to give a good account of octet baryon magnetic moments.