Theory of fermion exchange in massive quantum electrodynamics at high energy. II. Sixth-order perturbation theory

In this paper we present the details of our sixth-order perturbation theory calculation of the high-energy behavior of Compton scattering near the backward direction and pair annihilation. For each of these matrix elements, a formula is obtained not only for the leading term, which is real, but also for the leading imaginary part. Momentum-space techniques are used throughout. In particular we impose a cutoff in the transverse momentum and then compute the behavior as $s (the{{0ex}{0ex}}square{{0ex}{0ex}}of{{0ex}{0ex}}the{{0ex}{0ex}}center{-}of{-}mass{{0ex}{0ex}}energy){→}{∞}$. With this procedure there are 3 Feynman diagrams which contibute to the leading real part. These 3 diagrams each give a factor of $ln²s$ and an intergral over transverse-momentum space. Each of these 3 transverse integrals separately diverge as ${k}ₘₐₓ{→}{∞}$ but when added together the ${k}ₘₐₓ{→}{∞}$ limit may be taken and the result agrees with the result previously obtained by Feynman parameters. To complete the evaluation of the leading imaginary part a fourth diagram is needed.