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

Understand

We present analytic evaluations of some integrals needed to give explicitly the integrated real-virtual integrated counterterms, based on a recently proposed subtraction scheme for next-to-next-to-leading order (NNLO) jet cross sections.

• After an algebraic reduction of the integrals, integration-by-parts identities are used for the reduction to master integrals and for the computation of the master integrals themselves by means of differential equations.
• The results are written in terms of one- and two-dimensional harmonic polylogarithms, once an extension of the standard basis is made.
• We expect that the techniques described here will be useful in computing other integrals emerging in calculations in perturbative quantum field theories.