Numerical integration of subtraction terms

TL;DR

This paper demonstrates a method to group various subtraction terms in NLO calculations into finite integrals suitable for numerical evaluation, facilitating extensions to NNLO in quantum field theory computations.

Contribution

It introduces a unified approach to combine subtraction terms into finite integrals, improving numerical evaluation in higher-order calculations.

Findings

Finite integrals for subtraction terms are numerically evaluable.

Method simplifies extension from NLO to NNLO calculations.

Enhances accuracy and efficiency of higher-order quantum corrections.

Abstract

Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections. These subtraction terms have to be added back. In this paper we show that at NLO the real subtraction terms, the virtual subtraction terms, the integral representations of the field renormalisation constants and -- in the case of initial-state partons -- the integral representation for the collinear counterterm can be grouped together to give finite integrals, which can be evaluated numerically. This is useful for an extension towards NNLO.