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

TL;DR

This paper derives explicit analytic expressions for integrals of real-virtual counterterms in NNLO jet cross sections, using Mellin-Barnes techniques to facilitate subtraction scheme calculations in QCD.

Contribution

It provides the first complete analytic evaluation of all integrals needed for the subtraction scheme at NNLO in QCD, employing Mellin-Barnes representations.

Findings

Analytic expressions for integrals in the subtraction scheme.

Numerical and analytical computation of Laurent expansion coefficients.

Enhanced precision in NNLO jet cross section calculations.

Abstract

We present analytic expressions of all integrals required to complete the explicit evaluation of the real-virtual integrated counterterms needed to define a recently proposed subtraction scheme for jet cross sections at next-to-next-to-leading order in QCD. We use the Mellin-Barnes representation of these integrals in $4-2\epsilon$ dimensions to obtain the coefficients of their Laurent expansions around $\epsilon=0$. These coefficients are given by linear combinations of multidimensional Mellin-Barnes integrals. We compute the coefficients of such expansions in $\epsilon$ both numerically and analytically by complex integration over the Mellin-Barnes contours.