Higher-Order Low-Energy Theorems for Nucleon Compton Scattering

The well-known zero- and first-order (in photon energy) low-energy theorems for nucleon Compton scattering have recently been derived by Abarbanel and Goldberger using only the physical helicity amplitudes for the process and exploiting their kinematical singularities and zeros. We use this approach to study higher-order terms in photon energy and find the result, not entirely new, that four of the six independent helicity amplitudes are determined in second order by the mass, charge, and magnetic moment of the nucleon. Therefore, these parameters together with two structure-dependent constants, which can be interpreted approximately as electric and magnetic polarizabilities, completely determine the Compton scattering to second order in energy. Similar simplifications occurring in the structure of higher-order terms in energy are also discussed. The kinematical singularity structure of helicity amplitudes is a manifestation of Lorentz invariance. We claim to have fully exploited the requirements of Lorentz invariance and therefore to have derived the complete set of low-energy theorems for this process.