Low-Energy Theorems fore4Compton Scattering Amplitudes

Abstract

Unitarity and fixed-momentum-transfer dispersion relations are used to evaluate the contribution to the ${e}^{4}$ Compton amplitude from the intermediate state of target plus soft photon. It is found that the leading term goes like ${\ensuremath{\omega}}^{2}\mathrm{ln}\ensuremath{\omega}$ for scattering of photons of low frequency ($\ensuremath{\omega}$) by either spin-0 or spin-\textonehalf{} targets. The ${e}^{4}$ amplitudes up to this order (${\ensuremath{\omega}}^{2}\mathrm{ln}\ensuremath{\omega}$) are shown to be structure-independent as a consequence of the usual Compton-scattering low-energy theorems, which have been proven rigorously only in order ${e}^{2}$.