Numerical evaluation of NLO multiparton processes

TL;DR

This paper presents a numerical algorithm for evaluating NLO multiparton processes, focusing on virtual loop integrals using subtraction methods and contour deformation, demonstrated on e+ e- to n jets.

Contribution

It introduces an extension of the subtraction method combined with contour deformation for numerical evaluation of virtual NLO loop integrals in multiparton processes.

Findings

Successfully evaluated virtual corrections for up to seven jets.

Demonstrated numerical stability and efficiency of the method.

Applicable to leading color contributions in e+ e- collisions.

Abstract

We discuss an algorithm for the numerical evaluation of NLO multiparton processes. We focus hereby on the virtual part of the NLO calculation, i.e. on evaluating the one-loop integration numerically. We employ and extend the ideas of the subtraction method to the virtual part and we use subtraction terms for the soft, collinear and ultraviolet regions, which allows us to evaluate the loop integral numerically in four dimensions. A second ingredient is a method to deform the integration contour of the loop integration into the complex plane. The algorithm is derived on the level of the primitive amplitudes, where we utilise recursive relations to generate the corresponding one-loop off-shell currents. We discuss the numerical behavior of the approach and the application to the leading colour contribution in e+ e- --> n jets, with n up to seven.