A Calculational Formalism for One-Loop Integrals

TL;DR

The paper develops a calculational framework to efficiently compute one-loop, multi-leg QCD amplitudes by cleanly separating infrared and ultraviolet divergences from the finite parts. It combines a Davydychev-style decomposition with augmented recursion relations to reduce N-point tensor integrals to a master basis of known divergent and finite integrals, enabling numerical evaluation of the finite remainder. A dedicated analytic method determines infrared divergent coefficients by mapping to triangle master integrals, while a systematic subtraction scheme prevents double counting of soft/collinear poles. The approach promises scalable NLO Monte Carlo capabilities for processes with many external legs, with extensions to massive propagators and practical implementations via recursive or constructive numerical strategies. Overall, it offers a practical path to NLO predictions for high-multiplicity multi-jet and vector-boson plus jet processes at hadron colliders, constrained chiefly by computational power.

Abstract

We construct a specific formalism for calculating the one-loop virtual corrections for standard model processes with an arbitrary number of external legs. The procedure explicitly separates the infrared and ultraviolet divergences analytically from the finite one-loop contributions, which can then be evaluated numerically using recursion relations. Using the formalism outlined in this paper, we are in position to construct the next-to-leading order corrections to a variety of multi-leg QCD processes such as multi-jet production and vector-boson(s) plus multi-jet production at hadron colliders. The final limiting factor on the number of particles will be the available computer power.