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We present analytic evaluations of some integrals needed to give explicitlythe integrated real-virtual integrated counterterms, based on a recentlyproposed subtraction scheme for next-to-next-to-leading order (NNLO) jet crosssections. After an algebraic reduction of the integrals, integration-by-partsidentities are used for the reduction to master integrals and for thecomputation of the master integrals themselves by means of differentialequations. The results are written in terms of one- and two-dimensionalharmonic polylogarithms, once an extension of the standard basis is made. Weexpect that the techniques described here will be useful in computing otherintegrals emerging in calculations in perturbative quantum field theories.

Analytic integration of real-virtual counterterms in NNLO jet cross sections I