PARTON DENSITIES BEYOND PERTURBATION-THEORY

I compute non-perturbative corrections to the kernel governing the evolution of non-singlet parton densities. The model used is QED in the limit of many charged particles. I find an infrared renormalon at b(0)t = -1, where t is the Borel variable and b(0) is the first coefficient of the beta-function. This term has a non-trivial dependence on the variable x = -q(2)/(2p . q) and its coefficient scales as X(3)/(1 - x)(2) (p is the momentum of the hadron and q is the momentum transfer). An extrapolation of my results to QCD implies a breakdown of the parton model near the elastic region.