An Iterative Rejection Sampling Method

TL;DR

This paper introduces an iterative rejection sampling method that improves the efficiency of event generation in high energy physics by producing more unweighted events without additional calculations of the matrix element squared.

Contribution

It presents a novel iterative generalization of rejection sampling that enhances event generation efficiency in complex multi-dimensional functions like $|M|^2$.

Findings

More unweighted events generated compared to standard methods

No extra calculations of $|M|^2$ needed

Practical benefits demonstrated in simple examples

Abstract

In the note we consider an iterative generalisation of the rejection sampling method. In high energy physics, this sampling is frequently used for event generation, i.e. preparation of phase space points distributed according to a matrix element squared $|M|^2$ for a scattering process. In many realistic cases $|M|^2$ is a complicated multi-dimensional function, so, the standard von Neumann procedure has quite low efficiency, even if an error reducing technique, like VEGAS, is applied. As a result of that, many of the $|M|^2$ calculations go to ``waste''. The considered iterative modification of the procedure can extract more ``unweighted'' events, i.e. distributed according to $|M|^2$. In several simple examples we show practical benefits of the technique and obtain more events than the standard von Neumann method, without any extra calculations of $|M|^2$.