Partial summation of the perturbation expansion in high-energy quantum electrodynamics

Abstract

The renormalization group method is applied to the perturbation expansion of electromagnetic scattering cross-sections at high momentum transfer. It is shown that the limit of vanishing electron mass exists for high momentum transfer and high normalization momentum. In this limit the functional equations of the renormalization group provide a means to sum over «maximally logarithmic terms» to all orders starting only from the knowledge of the lowest order radiative corrections. The summation over soft particle emission which is included here, contains not only soft photons but also soft electron pairs. The summation over the soft photon emission is performed with an accuracy somewhat better than that provided by the renormalization group method. The terms that remain after the summation over «maximally logarithmic terms» and soft particle emission are of the relative order (α/π)2 ln (q2/m2) and (α/π) ΔE/q, wherem is the electron mass,q is the momentum transfer and ΔE is the experimental energy resolution. It is also found that in high-energy scattering the one-photon exchange strongly dominates over the exchange of several photons except for nearly forward or backward scattering in the c.m. system.