We show that the average multiplet masses in the baryon octet and decuplet can be fitted with an average error of only 0.5± 0.3 MeV in a meson loop expansion with chiral SU(6) couplings, with the hadrons treated as composite particles using a baryon-meson form factor. The form factor suppresses unphysical short distance effects and leads to a controllable expansion. We find, in contrast to the results of standard chiral perturbation theory, that pion loops are as important as kaon or eta loops

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... s would be expected when only intermediate- and long-distance contributions are retained. We also find that the contributions of decuplet intermediate states are important in the calculation of the masses, and those states must be included explicitly in a consistent theory. These results agree with those of our recent loop-expansion analysis of the baryon magnetic moments. We show, finally, that the parts of the loop contributions that change the tree-level structure of the baryon masses are small, but largely account for the violations of the baryon mass sum rules which hold at tree level.