Low-Energy Theorems on Radiative Corrections

Abstract

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 $\ensuremath{\omega}$. While the procedure is general enough to permit, in principle, the calculation of the leading terms (as $\ensuremath{\omega}\ensuremath{\rightarrow}0$) 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 $\mathrm{ln}\ensuremath{\omega}$ for the bremsstrahlung (as first noted by Soloviev) and of the order $\ensuremath{\omega}\mathrm{ln}\ensuremath{\omega}$ for pion photoproduction. Accordingly, in the presence of radiative corrections, there are no longer any low-energy theorems for the $O({\ensuremath{\omega}}^{0})$ bremsstrahlung and $O(\ensuremath{\omega})$ pion photoproduction amplitudes. The ${e}^{4}$ Compton amplitude $O({\ensuremath{\omega}}^{2}\mathrm{ln}\ensuremath{\omega})$ is computed and shown to be independent of the target spin.