Soft gluons and gauge-invariant subtractions in NLO parton-shower Monte Carlo event generators

We address the problem of decomposing graphs in perturbative QCD into terms associated with particular regions. Motivated by asking how to incorporate next-to-leading order (NLO) QCD corrections in parton-shower algorithms, w e require that: (a) The integrand for the hard part is to be integrable eve n if the corrections are applied to a process that is not infrared and coll inear safe. (b) The splitting between the terms should be defined gauge-inv ariantly. (c) The dependence on cut-offs should obey homogeneous evolution equations. In the context of one-gluon-emission graphs for deep inelastic s cattering, we explain a subtractive technique that is based on gauge-invari ant Wilson-line operators. Appropriate organization of subtractions involvi ng the soft region allows a connection to previous work where evolution equ ations with respect to the directions of the Wilson lines have been derived .