Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order

TL;DR

This paper introduces a new local representation of differential cross-sections that cancels infrared singularities at any order, facilitating numerical computations in quantum field theory.

Contribution

It presents a novel local unitarity method using Loop-Tree Duality to eliminate infrared divergences in scattering cross-sections at all perturbative orders.

Findings

Successfully computed NLO differential cross-section for $e^+ e^- ightarrow d ar{d}$ without IR counterterms.

Demonstrated applicability to higher orders with N4LO interference term calculations.

Proved local IR divergence cancellation at any perturbative order.

Abstract

We propose a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Divergences for loop momenta with large magnitudes are regulated using local ultraviolet counterterms that reproduce the usual Lagrangian renormalisation procedure of quantum field theories. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process $e^+ e^- \rightarrow d \bar{d}$. We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a $1\rightarrow 2+X$ scalar scattering process.