The Sudakov Veto Algorithm Reloaded

TL;DR

This paper provides a comprehensive analysis and generalization of the Sudakov veto algorithm used in parton shower simulations, including cases with non-positive definite kernels, enhancing its applicability.

Contribution

It introduces a generalized version of the Sudakov veto algorithm that accounts for infrared cutoffs and develops new algorithms for non-positive definite kernels.

Findings

Proved a general form of the Sudakov veto algorithm including infrared cutoff dependence.

Developed algorithms for non-positive definite splitting kernels.

Enhanced the accuracy of parton shower simulations in complex scenarios.

Abstract

We perform a careful analysis of the main Monte Carlo algorithm used in parton shower simulations, the Sudakov veto algorithm. We prove a general version of the algorithm, directly including the dependence on the infrared cutoff. Taking this as a starting point, we then consider non-positive definite splitting kernels, as encountered when dealing with sub-leading colour correlations or splitting kernels beyond leading order. New algorithms suited for these situations are developed.