  We show that the average multiplet masses in the baryon octet and decuplet
can be fitted with an average error of only $0.5\pm 0.3$ 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 as 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.
