Subtraction method for NLO corrections in Monte-Carlo event generators for leptoproduction

In the case of the gluon-fusion process in deep-inelastic leptoproduction, I explicitly show how to incorporate NLO corrections in a Monte-Carlo event generator by a subtraction method. I calculate the parton densities to be used by the event generator in terms of MS densities. The method is generalizable. A particular motivation for treating the gluon-fusion process is to treat diffractive deep-inelastic scattering properly, since in diffractive scattering the gluon density dominates the quark densities. I also propose a modified algorithm for treating parton kinematics in event generators; the new algorithm results in much simpler formulae for the NLO corrections. A disadvantage of the new method is that some of the generated events may have negative weights. However, an adjustable cut-off function is present in the formalism, and this permits a renormalization-group-like transformation that can be used to at least reduce the proportion of events with negative weights.