MUMUG: a fast Monte Carlo generator for radiative muon pair production (a pedagogical tutorial)

TL;DR

This paper presents a pedagogical tutorial on creating a fast Monte Carlo generator for the process e+e- to mu+mu- gamma, illustrating the methods with detailed explanations suitable for students.

Contribution

It provides a step-by-step guide to developing a Monte Carlo generator from scratch, including matrix element calculation and algorithm implementation, tailored for educational purposes.

Findings

Efficient Monte Carlo algorithm using acceptance-rejection method.

Detailed pedagogical exposition of helicity amplitude and Monte Carlo techniques.

Practical example for high energy physics education.

Abstract

A fast leading-order Monte Carlo generator for the process $e^+e^-\to\mu^+\mu^-\gamma$ is described. In fact, using the $e^+e^-\to\mu^+\mu^-\gamma $ process as an example, we provide a pedagogical demonstration of how a Monte Carlo generator can be created from scratch. The $e^+ e^- \to \mu^+ \mu^- \gamma$ process was chosen, since in this case we are not faced with either too trivial or too difficult a task. Matrix elements are calculated using the helicity amplitude method. Monte Carlo algorithm uses the acceptance-rejection method with an appropriately chosen simplified distribution that can be generated using an efficient algorithm. We provide a detailed pedagogical exposition of both the helicity amplitude method and the Monte Carlo technique, which we hope will be useful for high energy physics students.