Asymptotically free partons at high energy

We describe the application of renormalization group improved perturbative QCD to inelastic lepton-hadron scattering at high centre-of-mass energy but comparatively low photon virtuality. We construct a high energy factorization theorem which complements the mass factorization theorem used for processes with high virtualities. From it we derive a renormalization group equation which resums all large logarithms at high energy, thereby extending to this regime asymptotic freedom and thus the full range of perturbative computational techniques. We discuss the solution of this equation in various limits, and in particular show that the high energy behaviour of physical cross sections is consistent with phenomenological expectations and unitarity bounds. (C) 1997 Published by Elsevier Science B.V.