Speaker
Description
The most general QED four-photon amplitude that has been computed, so far, is the one with two photons on-shell and two off-shell. The generalization of this work to a fully off-shell calculation is presently still lacking. Here we present the result of such a calculation, although still with at least one of the legs taken in the low-energy limit, unifying the scalar and spinor QED cases. Despite the finiteness of these amplitudes we keep them in D dimensions to make them useful as building blocks for higher-loop amplitudes in dimensional regularization. The worldline representation is used together with an integration-by-parts procedure that leads, already at the integrand level, to compact expressions that are term-by-term gauge invariant and free of spurious ultraviolet divergences. We clarify the relation between this tensor basis and one used by Costantini, De Tollis and Pistoni.
For the case where one of the photons is in the low energy limit, we express the result in terms of generalized hypergeometric functions and their derivatives. For the case with two low-energy photons we obtain more general formulas than in previous works and we write this result in terms of the hypergeometric function 2F1. As a check on this latter result, we match the special case where k1 = −k2 with the known results for the scalar and spinor QED photon propagators in a constant external field. We also use it for a rederivation of the 2-loop scalar and spinor QED beta functions. Furthermore, we compute the Delbrück cross section at low energies for scalar and spinor QED.
