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

Construction of a QCD cascade at the NLO level requires recalcula-tion 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 con-tributions [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. PACS numbers: 12.38.-t, 12.38.Bx, 12.38.Cy 1