Independently Parameterised Momenta Variables and Monte Carlo IR Subtraction

TL;DR

This paper presents a new parameterization method for Monte Carlo phase space generation that simplifies handling infrared divergences in QCD processes, utilizing independent momentum generation and Grassmannian geometry.

Contribution

It introduces a novel independent parameterization of particle momenta for Monte Carlo simulations, improving treatment of IR divergences in high-order QCD calculations.

Findings

Efficient IR divergence treatment in $1\to n$ QCD processes.

Application of parameters with projection to Born subtraction at NNLO.

Geometric foundation in Grassmannian manifold.

Abstract

We introduce a system of parameters for the Monte Carlo generation of Lorentz invariant phase space that is particularly well-suited to the treatment of the infrared divergences that occur in the most singular, Born-like configurations of $1\to n$ QCD processes. A key feature is that particle momenta are generated independently of one another, leading to a simple parameterisation of all such IR limits. We exemplify the use of these variables in conjunction with the projection to Born subtraction technique at next-to-next-to-leading order. The geometric origins of this parameterisation lie in a coordinate chart on a Grassmannian manifold.