Low-Energy Theorems on Radiative Corrections

A general method is presented for evaluating, in a model-independent way, the soft-virtual-photon radiative corrections to an arbitrary hadronic process. It is shown that all the results concerning infrared divergences obtained within the theory of quantum electrodynamics of the electron-photon system are, in fact, exact in strong interactions. The problem of radiative corrections to low-energy theorems is the primary concern of this investigation. The threshold contributions of intermediate soft-photon states are nonanalytic in the photon frequency $\omega$. While the procedure is general enough to permit, in principle, the calculation of the leading terms (as $\omega \to 0$) of these radiative corrections to all orders in $e$, in this paper only the leading $e^2$ radiative corrections are computed explicitly: They are of the order $\ln \omega$ for the bremsstrahlung (as first noted by Soloviev) and of the order $\omega \ln \omega$ for pion photoproduction. Accordingly, in the presence of radiative corrections, there are no longer any low-energy theorems for the $O\left({\omega }^0\right)$ bremsstrahlung and $O\left(\omega \right)$ pion photoproduction amplitudes. The $e^4$ Compton amplitude $O\left({\omega }^2\ln \omega \right)$ is computed and shown to be independent of the target spin.