  The leading order contributions of processes involving anomalous pion-photon
vertices to forward spin-dependent Compton scattering from nucleons are
considered in heavy-baryon chiral perturbation theory. These all involve the
exchange of three pions between one or two photons and the nucleon, and hence
are two-loop processes. We find that the sum of these processes vanishes in the
manner predicted by the low energy theorem of Low, Gell-Mann and Goldberger as
the photon energy goes to zero. This provides the first consistency test of
two-loop HBCPT.
