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 Σ+\Sigma^+ (uusuus) magnetic moment is μΣ+=13(4μu−μs)\mu_{\Sigma^+} = \tfrac13(4\mu_u - \mu_s). By the same wave-function construction with u↔du \leftrightarrow d, the Σ−\Sigma^- (ddsdds) moment is μΣ−=13(4μd−μs)\mu_{\Sigma^-} = \tfrac13(4\mu_d - \mu_s). Take mp=938.3 MeVm_p = 938.3\,\mathrm{MeV}, mu=md=336 MeVm_u = m_d = 336\,\mathrm{MeV}, ms=510 MeVm_s = 510\,\mathrm{MeV}, and μq=QqmpmqμN\mu_q = Q_q\dfrac{m_p}{m_q}\mu_N with Qd=Qs=−13Q_d = Q_s = -\tfrac13. ((a)) Find μd\mu_d and μs\mu_s in units of μN\mu_N. ((b)) Find μΣ−\mu_{\Sigma^-} and compare it with the measured value −1.160 μN-1.160\,\mu_N (PDG 2024).

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