Nothing anomalous about two-loop heavy baryon chiral perturbation theory: Consistency with the low energy theorem for spin-dependent Compton scattering

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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 heavy baryon chiral perturbation theory.