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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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MC (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, MC 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 MC algorithms, making them well adapted to
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% modern parallel computing.
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In this thesis, the use of MC methods will be traced through from
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simple integration to the simulation of proton-proton scattering.
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The ``Guinea Pig'' 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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\(H\rightarrow \gamma\gamma\) (which was instrumental in its
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discovery) 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 at leading order and thus calculable by
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hand within the scope of this thesis. The differential and total cross
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section of this process is being calculated in leading order in
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\cref{chap:qqgg} and the obtained result is compared to the total
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cross section obtained with the \sherpa~\cite{Gleisberg:2008ta} event
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generator, used as matrix element integrator. In \cref{chap:mc} some
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simple MC methods are discussed, implemented and their results
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compared. Beginning with a study of MC integration the \vegas\
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algorithm~\cite{Lepage:19781an} is implemented and
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evaluated. Subsequently MC sampling methods are explored and the
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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. The QED coupling constant was
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set to the value \(\alpha = 1/137.036\) in \sherpa.
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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 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}~\cite{2020Virtanen:Sc} (and of
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course \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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