Factorization for Hard Exclusive Electroproduction

The processes discussed in this talk were ep → eMp, ep → eγp, and ep → eμμp, all in the deep-inelastic region where Q is large. The factorization theorems that I will discuss provide a sound basis for the phenomenology of these processes, which was discussed extensively at this workshop. They express the amplitudes for the processes in terms of operator matrix elements and perturbatively calculable coefficient functions. As always, the fundamental problem is that we do not know how to solve QCD exactly, and we must appeal to approximations. In high energy processes, such as we consider here, large ranges of scales and of rapidities are important. The factorization theorems demonstrate that enormous simplifications occur in suitable asymptotic limits, and then enable calculations to be done in perturbation theory, where asymptotic freedom implies that hard scattering coefficients etc. can be usefully approximated by low-order Feynman graph calculations. My presentation of the arguments tends to be graphical, since I find this is the easiest way to exhibit their structure. However they correspond to quantitative mathematical proofs. The principles are quite general; the processes under discussion turn out to provide the simplest situations for explaining how to prove factorization theorems. Although the proofs are apparently based on Feynman graph arguments, some of the key elements are actually nonperturbative, as I will emphasize.