How to regularize the infrared and mass singularities in QCD

The parton cross sections in perturbative QCD are mass (M) and infrared (IR) divergent. The singularities are prevented by on/off-shell parton masses or by dimensional regularization. All mass assignments must consistently be chosen in agreement with Kinoshita's double-cut rule. The 'off-shell' assignment, often used in the past, is incorrect. We demonstrate that Drell-Yan mass factorization in order αsub(s) is independent of all regularizations; the coefficient function is unique. (orig.)