Efficient Color-Dressed Calculation of Virtual Corrections

TL;DR

This paper introduces an efficient algorithm for calculating virtual corrections in QCD processes at Next-to-Leading Order by extending color dressing to one-loop amplitudes, enabling scalable computations for complex scattering events.

Contribution

It presents a novel explicit algorithm for color dressing in one-loop amplitudes, improving the computational approach for NLO Monte Carlo generators.

Findings

Algorithm exhibits exponential complexity with external partons.

Successfully applied to n-gluon scattering virtual corrections.

Provides a scalable method for complex QCD calculations.

Abstract

With the advent of generalized unitarity and parametric integration techniques, the construction of a generic Next-to-Leading Order Monte Carlo becomes feasible. Such a generator will entail the treatment of QCD color in the amplitudes. We extend the concept of color dressing to one-loop amplitudes, resulting in the formulation of an explicit algorithmic solution for the calculation of arbitrary scattering processes at Next-to-Leading order. The resulting algorithm is of exponential complexity, that is the numerical evaluation time of the virtual corrections grows by a constant multiplicative factor as the number of external partons is increased. To study the properties of the method, we calculate the virtual corrections to $n$-gluon scattering.