Competing Sudakov Veto Algorithms

TL;DR

This paper analyzes various Sudakov veto algorithms used in Monte Carlo simulations, demonstrating their equivalence and introducing faster alternatives for improved computational efficiency.

Contribution

It provides a unified analysis of different competition algorithms in Sudakov veto methods and proposes more efficient algorithms for practical use.

Findings

Different competition algorithms produce the same distribution.

Some algorithms are significantly faster than current implementations.

The analysis confirms the equivalence of multiple algorithms.

Abstract

We present a way to analyze the distribution produced by a Monte Carlo algorithm. We perform these analyses on several versions of the Sudakov veto algorithm, adding a cutoff, a second variable and competition between emission channels. The analysis allows us to prove that multiple, seemingly different competition algorithms, including those that are currently implemented in most parton showers, lead to the same result. Finally, we test their performance and show that there are significantly faster alternatives to the commonly used algorithms.