  Consideration of the analytic properties of pion-induced baryon self-energies
leads to new functional forms for the extrapolation of light baryon masses.
These functional forms reproduce the leading non-analytic behavior of chiral
perturbation theory, the correct non-analytic behavior at the $N \pi$ threshold
and the appropriate heavy-quark limit. They involve only three unknown
parameters, which may be obtained by fitting to lattice data. Recent dynamical
fermion results from CP-PACS and UKQCD are extrapolated using these new
functional forms. We also use these functions to probe the limit of
applicability of chiral perturbation theory to the extrapolation of lattice QCD
results.
