The ( ) magnetic moment is

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

Symmetry and Flavour, Ch The constituent quark model: wave functions, magnetic moments and hyperfine masses

Problem

The Ξ0\Xi^0 (ussuss) magnetic moment is μΞ0=13(4μs−μu)\mu_{\Xi^0} = \tfrac13(4\mu_s - \mu_u). Exchanging u↔du \leftrightarrow d gives the Ξ−\Xi^- (dssdss) moment μΞ−=13(4μs−μd)\mu_{\Xi^-} = \tfrac13(4\mu_s - \mu_d). Take mp=938.3 MeVm_p = 938.3\,\mathrm{MeV}, md=336 MeVm_d = 336\,\mathrm{MeV}, ms=510 MeVm_s = 510\,\mathrm{MeV}, with μd=−13mpmdμN\mu_d = -\tfrac13\dfrac{m_p}{m_d}\mu_N and μs=−13mpmsμN\mu_s = -\tfrac13\dfrac{m_p}{m_s}\mu_N. ((a)) Evaluate μd\mu_d and μs\mu_s in units of μN\mu_N. ((b)) Find μΞ−\mu_{\Xi^-} and compare it with the measured value −0.651 μN-0.651\,\mu_N (PDG 2024).

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