Virtual Corrections to the NLO Splitting Functions for Monte Carlo: the non-singlet case

Construction of a QCD cascade at the NLO level requires recalculation of the splitting functions in a different manner [1]. We describe the calculation of some of the virtual contributions to the non-singlet splitting function. In order to be compatible with the earlier calculated real contributions [2], the principal value prescription for regularizing the infrared singularities must be used in a new way. We illustrate this new scheme on simple examples. For the calculations we wrote a Mathematica package called Axiloop. We describe its current status.