Nf-contribution to the virtual correction for electroweak vector boson production at NNLO

TL;DR

This paper introduces a novel numerical method to evaluate complex two-loop scattering amplitudes in hadronic collisions, enabling the calculation of previously unknown NNLO electroweak vector boson production corrections.

Contribution

It presents a new approach combining numerical integration and local subtractions to handle singularities in multi-loop amplitudes at NNLO for the first time.

Findings

Successfully computed Nf-part of virtual corrections for three massive vector bosons

Demonstrated feasibility of combined numerical integration for complex amplitudes

Provided new perturbative corrections relevant to LHC physics

Abstract

Multi-loop scattering amplitudes are difficult to evaluate due to singularities of the integrals involved, especially with increasing number of loops, external legs, and mass scales. For the first time for hadronic collisions at two loops, we enable the combined numerical integration over loop momentum and phase space by tackling infrared, ultraviolet and threshold singularities simultaneously using local subtractions. We demonstrate the feasibility of our approach by calculating previously unknown perturbative corrections for processes of interest to the Large Hadron Collider, namely the Nf-part of the finite remainder of the phase-space integrated virtual corrections at next-to-next-to-leading order (NNLO) in QCD for the production of up to three massive electroweak vector bosons in proton-proton collisions.