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73 lines
3.5 KiB
TeX
73 lines
3.5 KiB
TeX
\chapter{Introduction}%
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\label{chap:intro}
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Monte Carlo (MC) methods have been and still are one of the most important
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tools for numerical calculations in particle physics. Be it for
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validating the well established standard model or for making
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predictions about new theories, Monte Carlo simulations are the
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crucial interface of theory and experimental data, making them
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directly comparable. Furthermore horizontal scaling is almost trivial
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to implement in Monte Carlo algorithms, making them well adapted to
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modern parallel computing. In this thesis, the use of Monte Carlo
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methods will be traced through from simple integration to the
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simulation of proton-proton scattering.
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The ``Drosophila'' of this thesis is the quark annihilation into two
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photons \(\qqgg\), henceforth called the diphoton process. It forms an
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important background to the higgs decay channel
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\(H\rightarrow \gamma\gamma\) and to a dihiggs decay
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\(HH\rightarrow b\bar{b}\gamma\gamma\)~\cite{aaboud2018:sf}, while
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still being a pure QED process and thus calculable by hand within the
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scope of this thesis. The differential and total cross section of this
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process is being calculated in leading order in \cref{chap:qqgg} and
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the obtained result is compared to the total cross section obtained
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with the \sherpa~\cite{Gleisberg:2008ta} event generator, used as
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matrix element integrator. In \cref{chap:mc} some simple Monte Carlo
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methods are discussed, implemented and their results
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compared. Beginning with a study of Monte Carlo integration the
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\vegas\ algorithm~\cite{Lepage:19781an} is implemented and
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evaluated. Subsequently Monte Carlo sampling methods are explored and
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the output of \vegas\ is used to improve the sampling
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efficiency. Histograms of observables are generated and compared to
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histograms from \sherpa\ using the \rivet~\cite{Bierlich:2019rhm}
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analysis framework. \Cref{chap:pdf} deals with proton-proton
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scattering in the partonic picture using parton density functions,
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ending with the implementation of a simple event generator for
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\(\ppgg\) scattering at \lhc\ conditions. Some integration and
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sampling algorithms and their implementation are adapted to the
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multidimensional case and histograms of observables are generated with
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good efficiency. Because a real \(pp\) scattering event also
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incorporates processes like parton showers, hadronization and multiple
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interactions, a realistic simulation should account for those
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effects. The impact of those effects on observables is studied in
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\cref{chap:pheno} using the \sherpa\ event generator.
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\section{Conventions}%
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\label{sec:convent}
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Throughout natural units with \(c=1, \hbar = 1, k_B=1, \varepsilon_0
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= 1\) are used unless stated otherwise. Histograms without label on
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the y-axis are normalized to unity and to be interpreted as
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probability densities.
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\section{Source Code}%
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\label{sec:source}
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The (literate) python code, used to generate most of the results and
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figures can be found on under
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\url{https://github.com/vale981/bachelor_thesis/} and more
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specifically in the subdirectory \texttt{prog/python/qqgg}.
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The file \texttt{monte\_carlo.py} implements all the monte-carlo
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algorithm related functionality as a module. The file
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\texttt{analytical\_xs.org} contains a literate computation notebook
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that generates all the results of \cref{chap:mc}. The file
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\texttt{parton\_density\_function\_stuff.org} contains all the
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computations for \cref{chap:pdf}. The python code makes heavy use of
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\href{https://www.scipy.org/}{scipy} (and of course
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\href{https://numpy.org/}{numpy}).
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%%% Local Variables: ***
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%%% mode: latex ***
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%%% TeX-master: "../document.tex" ***
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%%% End: ***
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