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

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.

arXiv comment28 pages, uses FEYNMAN.tex file for drawing Feynman diagrams, version to be published in The European Physical Journal Plus

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