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

TL;DR

This paper develops an analytic method to evaluate complex integrals in NNLO jet cross section calculations, utilizing integration-by-parts and harmonic polylogarithms, advancing precision in quantum field theory computations.

Contribution

It introduces a new analytic approach for evaluating integrals in NNLO jet cross sections using differential equations and harmonic polylogarithms, enhancing computational techniques.

Findings

Explicit analytic expressions for integrals in NNLO calculations

Use of harmonic polylogarithms extended basis

Potential applicability to other quantum field theory integrals

Abstract

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.