Electromagnetic Mass Differences in theSU(6)Baryon Bootstrap Model

Abstract

The $\mathrm{SU}(6)$ baryon bootstrap model is used to calculate the baryon 56 electromagnetic mass parameters in a first-order expansion in the electromagnetic mass parameters of the constituent 56 baryon and 35 meson multiplets. The direct electromagnetic corrections are approximated by a consideration of the one-photon-exchange contribution. The resulting equations that give the baryonic electromagnetic mass parameters in terms of the mesonic electromagnetic mass parameters and a driving-term contribution have no free parameters. The vector-meson contributions are found to be smaller than the pseudoscalar-meson contributions. Seven electromagnetic mass sum rules that correspond to the vanishing of the 2695 component in the baryonic mass spectrum appear as a consequence of the model. The $U$-spin approach of $\mathrm{SU}(3)$ is adopted to estimate the mesonic electromagnetic mass mixing parameters. The baryonic electromagnetic mass differences that are calculated from these numbers, and the experimental values for the mesonic electromagnetic-mass differences, are in reasonable agreement with experiment. We list explicit representations of the reduced matrix elements of the strong and electromagnetic mass operator in the 56 and 35 representations.