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

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