BrokenSU(3)Symmetry, Sum Rules, and the Magnetic Moments of the Baryons

Motivated by the increasing accuracy with which the magnetic moments of strange baryons are being measured, we present a calculation of these moments in broken $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry without appeal to a highly detailed theory of symmetry breaking. As primary ingredients in the calculation, we assume only the $\mathrm{SU}\left(2\right)\mathrm{}$ transformation properties of the electromagnetic current, the octet transformation property of the symmetry-breaking medium-strong interaction, and the validity of the Drell-Hearn-Gerasimov sum rule for the anomalous moments. Saturating this sum rule with the dominant states, the decuplet and a singlet, but making no $\mathrm{SU}\left(3\right)\mathrm{}$ assumptions on the couplings of these states or their masses, we find that all eight baryon anomalous magnetic moments and the ${\Sigma }^0\Lambda$ transition moment can be expressed in terms of ${\kappa }_n$, ${\kappa }_{\Lambda }$, and ${{\kappa }_{\Sigma }}^{+}$ through relations that are valid in broken symmetry with an expected accuracy of about 10%. Further assuming the absence of the 27, in the current, we have, in addition, ${{\kappa }_{\Sigma }}^{+}={\kappa }_n-4\mathrm{}{\kappa }_{\Lambda }$. We also find that our saturation assumption implies the absence of a unitary singlet piece in the electromagnetic current in the symmetry limit, so that the existing particle spectrum supports the hypothesis of a pure octet transformation property for the electromagnetic current. We also examine the Drell-Hearn-Gerasimov sum rule for high-spin systems, and this forward-direction sum rule would appear to require towers of states require towers of states for its saturation. Forward-direction sum rules for the nonflip Compton amplitude, based on the absence of fixed or moving poles in the $J$ plane with $I=2\mathrm{}$, are also considered and found to be consistent with the results obtained from the magnetic-moment sum rules.