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84 lines
4 KiB
TeX
84 lines
4 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
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important tools for numerical calculations in particle physics. Be it
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for validating the well established Standard Model (SM) or for making
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predictions about new theories, MC simulations are the crucial
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interface of theory and experimental data, making them directly
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comparable.
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% Furthermore horizontal scaling is almost trivial to implement in MC
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% algorithms, making them well adapted to 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 test subject here is the quark-antiquark 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~\cite{Aad:2012tfa,Chatrchyan:2012ufa}, and to a dihiggs
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decay \(HH\rightarrow b\bar{b}\gamma\gamma\), a process of recent
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interest~\cite{aaboud2018:sf} to study the higgs self coupling and
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probe the limits of the SM. All the while, the diphoton process is
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still pure QED (Quantum Electrodynamics) at leading order and thus
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calculable by hand within the scope of this thesis as is being done in
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\cref{chap:qqgg}. The obtained result is compared to the total cross
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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. After studying some basic MC integration methods, the
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\vegas\ algorithm~\cite{Lepage:19781an} is implemented and
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evaluated. Subsequently MC sampling methods, which are closely related
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to the integration methods, are explored and the output of \vegas\ is
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used to improve the sampling efficiency. Histograms of observables are
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generated and compared to histograms from \sherpa\ using the
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\rivet~\cite{Bierlich:2019rhm} analysis framework. \Cref{chap:pdf}
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deals with proton-proton scattering in the partonic picture using
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parton density functions, ending with the implementation of a simple
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event generator for \(\ppgg\) scattering at \lhc\ conditions. Some
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integration and sampling algorithms and their implementations are
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adapted to the multidimensional case and histograms of observables are
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generated with good efficiency. Because a real \(pp\) scattering event
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also entails processes like parton showers, hadronization and multiple
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interactions, a realistic simulation must 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
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\(c=1, \hbar = 1, k_B=1, \varepsilon_0 = 1\) are used unless stated
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otherwise. The fine structure constant's value \(\alpha = 1/137.036\)
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is configured in \sherpa\ and used in analytic calculations.
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\section{Source Code}%
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\label{sec:source}
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The (literate) \texttt{Python} code, used to generate most of the
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results and 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 \texttt{Python} code makes heavy
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use of \href{https://www.scipy.org/}{scipy}~\cite{2020Virtanen:Sc} and
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its component \href{https://numpy.org/}{numpy}).
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\section{Software Versions}%
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\label{sec:versions}
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In \cref{sec:compsher,chap:mc} the development version of \sherpa\ has
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been used. \Cref{chap:pdf,chap:pheno} use version \texttt{2.2.10} for
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reasons of stability.
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In the whole thesis, the version \texttt{3.1.0} of \rivet\ was used.
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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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