Quark model of baryon magnetic moments

The magnetic moments of the baryon octet and the ${\Sigma }^0\to {\Lambda }^0$ transition moment are calculated for the most general form of wave function describing an essentially nonrelativistic constitutent quark model. For definiteness the quarks are taken to have Dirac moments. Flavor symmetry is assumed, that is, the Landé $g$ factor is taken to be the same for all the baryons, an assumption that is justified by the small probabilities ${\left({}_{}{}^2{}_{}{}^{}P\right)}^2$, ${\left({}_{}{}^4{}_{}{}^{}P\right)}^2$, and ${\left({}_{}{}^4{}_{}{}^{}D\right)}^2$ suggested by our final results. All of the measured moments can be fitted by this model. Results of making the fit are the following: (1) the ratios of intrinsic quark moments are $\frac{{\mu }_u}{{\mu }_d}=-1.93\mathrm{}\pm 0.09$, $\frac{{\mu }_s}{{\mu }_d}=0.79\mathrm{}\pm 0.12$, (2) the total admixture of decimet and singlet states with the octet amounts to 10±14%, (3) if $\left|{\mu }_d\right|$ is assumed to be 1 nuclear magneton (${\mu }_N$), the probabilities of admixed angular momentum states satisfy the condition $\frac{2}{3}{\left({}_{}{}^2{}_{}{}^{}P\right)}^2-\frac{1}{3}{\left({}_{}{}^4{}_{}{}^{}P\right)}^2+{\left({}_{}{}^4{}_{}{}^{}D\right)}^2=0.05\mathrm{}\pm 0.09$, and (4) within the context of the model there is an upper bound on the absolute value of the ${\Sigma }^0\to {\Lambda }^0$ transition moment equal to $(1.97\mathrm{}\pm 0.14){\mu }_N$ and depending only on the measured values of the seven magnetic moments. A more precise measurement of the transition moment is needed to confirm that it does not exceed this bound. Numerical values are also specified for two matrix elements that may be useful for determining more detailed properties of the wave function in specific models but they will be very model dependent. At present, all of the qualitative features of these results would appear to be consistent with a dynamical model based on simple potentials between constituent quarks augmented by spin-orbit couplings and SU(3)-breaking interactions of the order of magnitude of the "hyperfine" interaction of De Rújula, Georgi, and Glashow.