Electromagnetic Masses of Baryons and Pseudoscalar Mesons

Abstract

A new method to calculate all the electromagnetic masses of baryons and pseudoscalar mesons is proposed. We assume that medium-strong and electromagnetic mass splittings, respectively, come from scalar operators ${S}_{8}$ and ${S}_{3}$ which belong to nonchiral subalgebra $U(3)\ifmmode\times\else\texttimes\fi{}U(3)$ of Gell-Mann's $\mathrm{SU}(6)$. Therefore we write the Hamiltonian as $H={H}_{0}+\ensuremath{\delta}m{S}_{8}+\ensuremath{\delta}{M}_{e}{S}_{3}$. Further, taking into account minimal electromagnetic interaction, we show that we get two types of contributions to electromagnetic mass differences. The first is the tadpole type and depends only on the single parameter $\frac{\ensuremath{\delta}{m}_{e}}{\ensuremath{\delta}m}$ for all electromagnetic mass differences of baryons and pseudoscalar mesons. The second is the conventional type from elastic electromagnetic form factors. In this way one can explain all electromagnetic mass differences of baryons as well as of pseudoscalar mesons in terms of a single parameter, except for the kaon, for which one gets the proper sign but not the proper magnitude.