A numerical method for NNLO calculations

TL;DR

The paper introduces a sector decomposition framework to systematically isolate infrared and ultraviolet poles in dimensionally regularized multi-loop and phase-space integrals, enabling their numerical evaluation. It breaks the method into four steps: generate primary sectors, iteratively decompose to factor singularities, extract poles in $\epsilon$, and compute pole coefficients numerically or analytically. The approach is extended to phase-space integrals and validated with benchmark results from massless double boxes, including off-shell configurations, and an NNLO e+e- → 2 jets example illustrating triple-collinear factorization. Overall, the work demonstrates that numerical pole extraction can support NNLO calculations and paves the way for fully numerical radiative-correction evaluations.

Abstract

A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.