How-to: write a parton-level Monte Carlo particle physics event generator

Abstract

This article provides an introduction to the principles of particle physics event generators that are based on the Monte Carlo method. Following some preliminaries, instructions on how to build a basic parton-level Monte Carlo event generator for the hard interaction are given through exercises. Indications on how to proceed to full-event simulations are given (the related course was given as part of the “Advanced Scientific Computing Workshop” at ETH Zürich in July 2014).

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The exercises and the respective solutions related to this publication have been made available at the URL https://apapaefs.web.cern.ch/apapaefs/mchowto.html.].

Notes

  1. 1.

    Formerly known as HERWIG++.

  2. 2.

    http://www.ippp.dur.ac.uk/~richardn/talks/.

  3. 3.

    http://www.hep.manchester.ac.uk/u/seymour/thesis/.

  4. 4.

    That is, with equal probability to lie anywhere within the given interval.

  5. 5.

    A summary of the rate of convergence of the various techniques is given in Table 3 in Appendix D.

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Acknowledgements

The author would like to thank Christoph Grab and Nicolas Chanon the opportunity to lecture at the “Advanced Scientific Computing Workshop” at ETH Zürich, as well the students who attended the course, providing helpful feedback. Support is acknowledged in part by the Swiss National Science Foundation (SNF) under Contract 200020-149517, by the European Commission through the “LHCPhenoNet” Initial Training Network PITN-GA-2010-264564, MCnetITN FP7 Marie Curie Initial Training Network PITN-GA-2012-315877 and by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme (Grant No. PIEF-GA-2013-622071).

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Correspondence to Andreas Papaefstathiou.

Appendices

Constants

The constants in this section are given to provide agreement with the MadGraph event generator. They appear in Table 2.

Table 2 Constants used throughout this article, given to provide agreement with MadGraph

Parton density functions using LHAPDF

At the time of writing, the latest version of the LHAPDF package is 6.1.3. It is recommended to use this or a latter version for the exercises given here. The library can be interfaced to either C++, FORTRAN or Python. Since the solutions to the exercises are given in Python, the PDFs should be initialized as:

figurea

and the PDF should be called as:

figureb

where FLAVOUR should be replaced by the quark flavours contributing to the process: 1 for down-quarks, 2 for up, 3 for strange, 4 for charm and negative values for the corresponding anti-quarks. The gluon, not used here, is given by 21. Note that this actually gives \(x \times f(x)\) and thus one has to divide by the momentum fraction to get f(x). Moreover, this specific function takes as input the scale and not the scale squared.

The Les Houches event file format

The file header and the first event in a Les Houches-accord event file have the following form:

figurec

The first row after \(\mathtt {<}\)init\(\mathtt {>}\) shows the ids of the incoming hadrons, their energy and the PDF numbers (10042 in this case). The following line shows the cross section and the error. The first event follows, containing the particle ids, their status codes and mother information, colour information, their momenta, and whether they are stable particles or not. See Ref. [26] for more details.

Convergence

See Table 3.

Table 3 The rate of convergence with the number of points N used for each method in d-dimensions

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Papaefstathiou, A. How-to: write a parton-level Monte Carlo particle physics event generator. Eur. Phys. J. Plus 135, 497 (2020). https://doi.org/10.1140/epjp/s13360-020-00499-1

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