Infrared and mass regularization in AF field theories. Pt. 2

We determine the non-leading QCD corrections to deep inelastic (DI) scattering and to the Drell-Yan (DY) process by analysing the order g2 parton cross sections. Using the insight and the techniques developed in the more simple environment of PHI36, we regularize and subsequently remove the mass (M), infrared (IR), and ultraviolet (UV) divergences of the (double) cut graphs with the methods exposed in paper I. The QCD calculations are technically more involved. New M divergences are found, IR singularities occur, and overlapping M and IR singularities exist leading to double poles if n-dimensional regularization is used. Gluon gauge invariance must be satisfied. Although the off-shell method leads to gauge-dependent parton cross sections, the correction terms extracted via M factorization remain gauge invariant. The off-shell mass assignment was ill-defined in the past and did not satisfy the double cut rule: we explain the implications. The correction terms are explicitly shown to be independent of any regularization method. Defining the scale-dependent momentum distribution to consist of logQ2 terms only, their influence in DI scattering is moderate, but considerable in DY massive μμ pair production for Q2 <= 100 GeV2. (orig.)