A numerical approach to infrared divergent multi-parton phase space integrals
G. Heinrich
TL;DR
The paper demonstrates a numerical method, sector decomposition, to isolate infrared divergences in multi-parton phase-space integrals without explicit subtraction. It applies to NNLO real-emission contributions in e+e- → jets by transforming phase-space and real-virtual contributions into parameter integrals whose pole coefficients are extracted and evaluated numerically. The authors illustrate the approach with 1→4 and 1→5 phase spaces and with one-loop plus real emission, computing master phase-space integrals and volumes and validating results against known analytic checks. The method promises fully differential NNLO predictions without subtraction schemes, though it generates many intermediate functions and requires careful handling of non-polynomial phase-space structures and negative invariants.
Abstract
It is described how the method of sector decomposition can serve to disentangle overlapping infrared singularities, in particular those occurring in the calculation of the real emission part of e+e- to 2 jets and e+e- to 3 jets at NNLO.