Anomalous Magnetic Moments of Baryons in a Static Cutoff Perturbation Theory

Abstract

A universal coupling between pions and baryons should lead to anomalous moments comparable in magnitude for all the baryons except for the $\ensuremath{\Lambda}$ and ${\ensuremath{\Sigma}}^{0}$ whose anomalous moments for reasons of isotopic spin symmetry should receive no direct contribution from the pion field. To estimate the influence of the $K$-mesonic field on these moments, a static, cutoff, second-order perturbation calculation is made on the assumption that all baryons have spin \textonehalf{} and the same parity, that the $K$ meson is a pseudoscalar, and that the $K$-mesonic interaction with the baryons is charge independent. Along the same lines a fourth-order calculation of the pionic contributions to these moments is also made. Baryon currents are neglected in these calculations and cutoff momenta based on the rest mass of the baryon emitting the meson were uniformly used for all processes. The $\ensuremath{\Lambda}$ and ${\ensuremath{\Sigma}}^{0}$ moments are negative with a value of only about 0.5 nuclear magnetons even if the $K$-meson coupling constants are large and judiciously chosen, a value which is therefore indicated as an upper limit, if no special enhancement effect is considered. If the $K$-meson couplings are all considerably smaller than the universal pion baryon coupling, then the $\ensuremath{\Lambda}$ and ${\ensuremath{\Sigma}}^{0}$ moments are quite small but the other hyperons have moments of comparable magnitude as is generally to be expected. If all $K$-coupling constants are large, our considerations show that $p$, $n$, ${\ensuremath{\Sigma}}^{+}$, and ${\ensuremath{\Xi}}^{\ensuremath{-}}$ may still have comparable anomalous moments but the ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ is indicated to have a somewhat larger and the ${\ensuremath{\Xi}}^{0}$ a somewhat smaller moment than these. A pion coupling to the hyperons different from that to the nucleons would manifest itself in characteristic ways in terms of anomalous magnetic moments, for large or small values of the $K$-coupling constants.