Asymptotic behavior of the fermion and gluon exchange amplitudes in massive quantum electrodynamics in the Regge limit

Abstract

We study the e⁺e⁻→γγ amplitude in massive quantum electrodynamics in the large-s and fixed-t limit. We compute the amplitude in the leading-logarithm and the next-to-the-leading-logarithm approximations, to all orders in perturbation theory, and also find the general form of the full amplitude up to any non-leading-logarithm approximation. We do not use any transverse-momentum cutoff for our calculation. We find that, up to the next-to-the-leading-logarithm approximation, the contribution to the positive-signature amplitude is given by a single Regge pole. We find the contribution to the Regge trajectory up to two-loop order. The contribution to the negative-signature channel is consistent with the exchange of a gluon and a Reggeized fermion, interacting with each other through a fourpoint Reggeon vertex. The technique we have used to calculate the fermion exchange amplitude may also be used to calculate the vector-particle exchange amplitude in massive quantum electrodynamics. We have calculated the gluon exchange amplitude in massive QED in the positive- and the negative-signature channels in the leading-logarithm approximation.