  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 lattice QCD 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.
