Electromagnetic mass differences of hadrons with ${\mathrm{SU}\mathrm{}\left(6\right)\mathrm{}}_W\times \mathrm{O}\mathrm{}\left(3\right)\mathrm{}$ couplings and form factors

A systematic account of a few typical electromagnetic mass differences of hadrons ($N,\Sigma$; $K,\pi$) is presented within the framework provided by a broken-${\mathrm{SU}\mathrm{}\left(6\right)\mathrm{}}_W\times \mathrm{O}\mathrm{}\left(3\right)\mathrm{}$ model of hadron couplings. The model, which has specified combinations of couplings of "magnetic" and "charge" origin, is characterized by the supermultiplet form factors at the hadron vertices. The parameters of these functions on the mass shell have been determined recently via a study of the decay widths of the resonances. Using these form factors, suitably extended off the mass shell of the vector meson so as to render the calculations formally free from series and integral divergences, the coupling scheme is found to provide a reasonable description of the mass differences through the twin mechanisms of dominance of magnetic contribution over charge contribution and that of ($L+1\mathrm{}$) wave couplings over ($L-1\mathrm{}$). A formal connection of this approach with the more conventional dispersion-theoretic one can be established through the observation that the subtraction term (necessary for $\Delta I=1\mathrm{}$ cases of mass differences) finds a close parallel to the couplings of magnetic origin (which have extra momentum dependence vis-à-vis the charge couplings) thus making the magnetic couplings relatively more important for the $\Delta I=1\mathrm{}$ cases according to Harari's interpretation. The model is not so successful for $\Delta I=2\mathrm{}$ mass differences which are dominated by the (weaker) charge couplings.