Magnetic Moments of the Baryons

The anomalous magnetic moments of the baryon octet are calculated in broken $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry using low-energy pole dominance as a dynamical model and keeping only the lowest lying intermediate states, the psuedoscalar-meson—baryon states. By using dispersion theory, the anomalous moments are related to an energy integral over the $S_{\frac{1}{2}}$ and $P_{\frac{1}{2}}$ photomeson production amplitudes, which at low energy and for vanishing meson mass are exactly given by the pole terms. From this exact information we calculate the low-energy contribution to the anomalous moments, keeping all orders in baryon and meson mass splittings and using the $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric strong-coupling constants. We are able to account for the dominant contribution to the proton and neutron magnetic moment and find in addition, for an $\frac{F}{D}$ ratio∼0.6, that $K\left(\Lambda \right)\sim 0.4K\left(n\right)\mathrm{}$, in agreement with the observed value. The $\mathrm{SU}\left(3\right)\mathrm{}$ predictions for the other moments and the ${\Sigma }^0\to \Lambda +\gamma$ transition moment are found to be more badly violated.