1885 lines
85 KiB
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1885 lines
85 KiB
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\author{David Leppla-Weber}
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\date{}
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\begin{document}
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\begin{titlepage}
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\begin{center}
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\vspace*{1cm}
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\Huge
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\rule{\textwidth}{0.1cm}
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\textbf{Search for excited quark states decaying to qW/qZ with the CMS experiment}
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\rule{\textwidth}{0.1cm}
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\vspace{2.5cm}
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\Large
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von\\
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\LARGE
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David Leppla-Weber\\
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\Large
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\vspace{0.5cm}
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Geboren am\\
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18.09.1996
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\vfill
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Bachelorarbeit im Studiengang Physik\\
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Universität Hamburg\\
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November 2019
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\end{center}
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\end{titlepage}
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\newpage
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\mbox{}
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\vfill
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\begin{enumerate}
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\def\labelenumi{\arabic{enumi}.}
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\tightlist
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\item
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Gutachter: Dr.~Andreas Hinzmann
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\item
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Gutachter: Jun.-Prof.~Dr.~Gregor Kasieczka
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\end{enumerate}
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\newpage
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\begin{abstract}
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A search for an excited quark state, called q*, is presented using data of proton-proton collisions at the LHC recorded
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by the CMS experiment during the years 2016, 2017 and 2018 with a centre-of-mass energy of $\sqrt{s} =
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\SI{13}{\tera\eV}$ and an integrated luminosity of $\SI{137.19}{\per\femto\barn}$. Its decay channels to q
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+ W and q + Z with the vector bosons further decaying hadronically to $q + q\bar{q}'$ resp. $q + q\bar{q}$, resulting in
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two jets in the final state, are analysed. The dijet invariant mass spectrum of those two jets is then used to look
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for a resonance and to reconstruct the q* mass. To identify jets originating from the decay of a vector boson, a
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V-tagger is needed. For that, the new DeepAK8 tagger, based on a neural network, is compared to the older N-subjettiness
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tagger. In the result, no significant deviation from the Standard Model can be observed, therefore the q* is excluded up
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to a mass of 6.1\ TeV (qW) resp. 5.5\ TeV (qZ) with a confidence level of 95 \%. This limit is about 1\ TeV higher than
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the limits found by a previous research of data with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$ collected
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by the CMS experiment in 2016, excluding the q* particle up to a mass of 5.0\ TeV resp. 4.7\ TeV. The DeepAK8 tagger is
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found to currently be at the same level as the N-subjettiness tagger, giving a $\SI{0.1}{\tera\eV}$ better result for
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the decay to qW but a by $\SI{0.5}{\tera\eV}$ worse one for the decay to qZ. By optimising the neural network's training
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for the datasets of 2016, 2017 and 2018, the sensitivity can likely be improved.
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\end{abstract}
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\newpage
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\renewcommand{\abstractname}{Zusammenfassung}
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\begin{abstract}
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In dieser Arbeit wird eine Suche nach angeregten Quarkzuständen, genannt q*, durchgeführt. Dafür werden Daten von
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Proton-Proton Kollisionen am LHC mit einer integrierten Luminosität von $\SI{137.19}{\per\femto\barn}$ analysiert,
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welche über die Jahre 2016, 2017 und 2018 bei einer Schwerpunktsenergie von $\sqrt{s} = \SI{13}{\tera\eV}$ vom CMS
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Experiment aufgenommen wurden. Es wird der Zerfall des q* Teilchens zu q + W und q + Z untersucht, bei anschließendem
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hadronischen Zerfall des Vektorbosons zu $q\bar{q}'$ bzw. $q\bar{q}$. Der gesamte Zerfall resultiert damit in zwei Jets,
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mithilfe deren invariantem Massenspektrum die q* Masse rekonstruiert und nach einer Resonanz gesucht wird. Zur
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Identifizerung von Jets, welche durch den Zerfall eines Vektorbosons entstanden sind, wird ein V-Tagger benötigt.
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Hierfür wird der neue DeepAK8 Tagger, welcher auf einem neuronalen Netzwerk basiert, mit dem älteren N-Subjettiness
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Tagger verglichen. Im Ergebnis kann keine signifikante Abweichung vom Standardmodell beobachtet werden. Das q* Teilchen
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wird mit einem Konfidenzniveau von 95 \% bis zu einer Masse von 6.1\ TeV (qW) bzw. 5.5\ TeV (qZ) ausgeschlossen. Das Limit
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liegt etwa 1\ TeV höher, als das anhand des $\SI{35.92}{\per\femto\barn}$ großen Datensatzes von 2016 gefundene von 5.0
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TeV bzw. 4.7\ TeV. Beim Zerfall zu qW erzielt der DeepAK8 Tagger ein um $\SI{0.1}{\tera\eV}$ besseres Ergebnis, als der
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N-Subjettiness Tagger, beim Zerfall zu qZ jedoch ein um $\SI{0.5}{\tera\eV}$ schlechteres. Durch Verbesserung des
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Trainings des neuronalen Netzwerkes für die drei Datensätze von 2016, 2017 und 2018, gibt es aber noch Potential die
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Sensitivität zu verbessern.
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\end{abstract}
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\newpage
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\setcounter{tocdepth}{3}
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\tableofcontents
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\newpage
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\pagenumbering{arabic}
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\hypertarget{introduction}{%
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\section{Introduction}\label{introduction}}
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The Standard Model is a very successful theory in describing most of the
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interactions happening between particles. Still, it has a lot of
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limitations, that show that it isn't yet a full \enquote{theory of
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everything}. To solve these shortcomings, lots of theories beyond the
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standard model exist that try to expand the Standard Model in different
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ways to solve these issues.
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One category of such theories is based on a composite quark model.
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Quarks are currently considered elementary particles by the Standard
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Model. The composite quark models on the other hand predict that quarks
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consist of particles unknown to us so far or can bind to other particles
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using unknown forces. This could explain the symmetries between
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particles and reduce the number of constants needed to explain the
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properties of the known particles. One common prediction of those
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theories are excited quark states. Those are quark states of higher
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energy that can decay to an unexcited quark under the emission of a
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boson. This thesis will look for their decay to a vector boson that then
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further decays hadronically. The final state of this decay consists only
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of quarks forming two jets, making Quantum Chromodynamics the main
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background.
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In a previous research \autocite{PREV_RESEARCH}, an exclusion limit for
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the mass of an excited quark has already been set using data from the
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2016 run of the Large Hadron Collider with an integrated luminosity of
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\(\SI{35.92}{\per\femto\barn}\). Since then, a lot more data has been
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collected by the CMS experiment, totalling to
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\(\SI{137.19}{\per\femto\barn}\) of data usable for research. This
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thesis takes advantage of this larger dataset as well as a new technique
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to identify decays of highly boosted particles based on a deep neural
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network. By using more data and new tagging techniques, it aims to
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either confirm the existence of the q* particle or improve the
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previously set lower limit of 5 TeV respectively 4.7 TeV for the decay
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to qW respectively qZ on its mass to even higher values. It will also
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directly compare the performance of this new tagging technique to an
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older tagger based on jet substructure studies used in the previous
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research.
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In chapter 2, a theoretical background will be presented briefly
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explaining the Standard Model, its shortcomings and the theory of
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excited quarks. Then, in chapter 3, the Large Hadron Collider and the
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Compact Muon Solenoid, the detector that collected the data for this
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analysis, will be described. After that, in chapters 4-7, the main
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analysis part follows, describing how the data were used to extract
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limits on the mass of the excited quark particle. At the very end, in
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chapter 8, the results are presented and compared to previous research.
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\newpage
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\hypertarget{theoretical-motivation}{%
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\section{Theoretical motivation}\label{theoretical-motivation}}
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This chapter presents a short summary of the theoretical background
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relevant to this thesis. It first gives an introduction to the standard
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model itself and some of the issues it raises. It then goes on to
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explain the background processes of quantum chromodynamics and the
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theory of q*, which are the relevant phenomena for the search described
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in this thesis.
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\hypertarget{sec:sm}{%
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\subsection{Standard Model}\label{sec:sm}}
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The Standard Model of physics proved to be very successful in describing
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three of the four fundamental interactions currently known: the
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electromagnetic, weak and strong interaction. The fourth, gravity, could
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not yet be successfully included in this theory.
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The Standard Model divides all particles into spin-\(\frac{n}{2}\)
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fermions and spin-n bosons, where n could be any integer but so far is
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only known to be one for fermions and either one (gauge bosons) or zero
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(scalar bosons) for bosons. Fermions are further classified into quarks
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and leptons. Quarks and leptons can also be categorized into three
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generations, each of which contains two particles, also called flavours.
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For leptons, the three generations each consist of a charged lepton and
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its corresponding neutrino, namely the electron, the muon and the tau.
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The three quark generations consist of the up and down, the charm and
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strange, and the top and bottom quark. A full list of particles of the
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standard model can be found in Fig.~\ref{fig:sm}. Furthermore, all
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fermions have an associated anti particle with reversed charge. Bound
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states of multiple quarks also exist and are called hadrons.
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\begin{figure}
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\hypertarget{fig:sm}{%
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\centering
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\includegraphics[width=0.5\textwidth,height=\textheight]{./figures/sm_wikipedia.pdf}
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\caption{Elementary particles of the Standard Model and their mass
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charge and spin \autocite{SM}.}\label{fig:sm}
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}
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\end{figure}
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The gauge bosons, namely the photon, \(W^\pm\) bosons, \(Z^0\) boson,
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and gluon, are mediators of the different forces of the standard model.
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The photon is responsible for the electromagnetic force and therefore
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interacts with all electrically charged particles. It itself carries no
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electromagnetic charge and has no mass. Possible interactions are either
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scattering or absorption. Photons of different energies can also be
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described as electromagnetic waves of different wavelengths.
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The \(W^\pm\) and \(Z^0\) bosons mediate the weak force. All quarks and
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leptons carry a flavour, which is a conserved value in all interactions
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but the weak one. There, a quark or lepton can, by interacting with a
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\(W^\pm\) boson, change its flavour. The probabilities of this happening
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are determined by the Cabibbo-Kobayashi-Maskawa matrix:
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\begin{equation}
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V_{CKM} =
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\begin{pmatrix}
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|V_{ud}| & |V_{us}| & |V_{ub}| \\
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|V_{cd}| & |V_{cs}| & |V_{cb}| \\
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|V_{td}| & |V_{ts}| & |V_{tb}|
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\end{pmatrix}
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=
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\begin{pmatrix}
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0.974 & 0.225 & 0.004 \\
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0.224 & 0.974 & 0.042 \\
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0.008 & 0.041 & 0.999
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\end{pmatrix}
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\end{equation}
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The probability of a quark changing its flavour from \(i\) to \(j\) is
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given by the square of the absolute value of the matrix element
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\(V_{ij}\). It is easy to see, that the change of flavour in the same
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generation is way more likely than any other flavour change.
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Due to their high masses of 80.39 GeV resp. 91.19 GeV, the \(W^\pm\) and
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\(Z^0\) bosons themselves decay very quickly. Either in the leptonic or
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hadronic decay channel. In the leptonic channel, the \(W^\pm\) decays to
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a lepton and the corresponding anti-lepton neutrino, in the hadronic
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channel it decays to a quark and an anti-quark of a different flavour.
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Due to the \(Z^0\) boson having no charge, it always decays to a fermion
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and its anti-particle, in the leptonic channel this might be for example
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an electron - positron pair, in the hadronic channel an up and anti-up
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quark pair. This thesis examines the hadronic decay channel, where both
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vector bosons decay to two quarks.
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The quantum chromodynamics (QCD) describes the strong interaction of
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particles. It applies to all particles carrying colour (e.g.~quarks).
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The force is mediated by gluons. These bosons carry colour as well,
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although they don't carry only one colour but rather a combination of a
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colour and an anticolour, and can therefore interact with themselves and
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exist in eight different variants. As a result of this, processes where
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a gluon decays into two gluons are possible. Furthermore the strength of
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the strong force, binding colour carrying particles, increases with
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their distance making it at a certain point more energetically efficient
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to form a new quark - antiquark pair than separating the two particles
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even further. This effect is known as colour confinement. Due to this
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effect, colour carrying particles can't be observed directly, but rather
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form so called jets that cause hadronic showers in the detector. Those
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jets are cone like structures made of hadrons and other particles. The
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effect is called hadronisation \autocite{HADRONIZATION}.
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\hypertarget{shortcomings-of-the-standard-model}{%
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\subsubsection{Shortcomings of the Standard
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Model}\label{shortcomings-of-the-standard-model}}
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|
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|
While being very successful in describing the effects observed in
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particle colliders or the particles reaching earth from cosmological
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sources, the Standard Model still has several shortcomings.
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\begin{itemize}
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\tightlist
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|
\item
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\textbf{Gravity}: as already noted, the standard model doesn't include
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gravity as a force.
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\item
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\textbf{Dark Matter}: observations of the rotational velocity of
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galaxies can't be explained by the known matter. Dark matter currently
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|
the most popular theory to explain those.
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|
\item
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\textbf{Matter-antimatter asymmetry}: The amount of matter vastly
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|
outweights the amount of antimatter in the observable universe. This
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can't be explained by the standard model, which predicts a similar
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|
amount of matter and antimatter.
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|
\item
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\textbf{Symmetries between particles}: Why do exactly three
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|
generations of fermions exist? Why is the charge of a quark exactly
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|
one third of the charge of a lepton? How are the masses of the
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|
particles related? Those and more questions cannot be answered by the
|
|
standard model.
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|
\item
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|
\textbf{Hierarchy problem}: The weak force is approximately
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|
\(10^{24}\) times stronger than gravity and so far, there's no
|
|
satisfactory explanation as to why that is.
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|
\end{itemize}
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|
\hypertarget{sec:qs}{%
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\subsection{Excited quark states}\label{sec:qs}}
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|
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|
One category of theories that try to explain the symmetries between
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particles of the standard model are the composite quark models. Those
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state, that quarks consist of some particles unknown so far. This could
|
|
explain the symmetries between the different fermions. A common
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|
prediction of those models are excited quark states (q*, q**,
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|
q***\ldots) \autocite{QSTAR_THEORY}. Similar to atoms, that can be
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excited by the absorption of a photon and can then decay again under
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emission of a photon with an energy corresponding to the excited state,
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those excited quark states could decay under the emission of any boson.
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Quarks are measured to be smaller than \(10^{-18}\) m. This corresponds
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to an energy scale of approximately 1 TeV. Therefore the excited quark
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states are expected to be in that energy region. That will cause the
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emitted boson to be highly boosted.
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\begin{figure}
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\centering
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\feynmandiagram [large, horizontal=qs to v] {
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a -- qs -- b,
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qs -- [fermion, edge label=\(q*\)] v,
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q1 [particle=\(q\)] -- v -- w [particle=\(W\)],
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q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)],
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};
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\caption{Feynman diagram showing the decay of a q* particle to a W boson and a quark with the W boson decaying
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hadronically.} \label{fig:qsfeynman}
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\end{figure}
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|
|
This thesis will search data collected by the CMS in the years 2016,
|
|
2017 and 2018 for the decay of a single excited quark state q* to a
|
|
quark and a vector boson . An example of a q* decaying to a quark and a
|
|
W boson can be seen in Fig.~\ref{fig:qsfeynman}. As explained in
|
|
Sec.~\ref{sec:sm}, the vector boson can then decay either in the
|
|
hadronic or leptonic decay channel. This research investigates only the
|
|
hadronic channel with two quarks in the final state. Because the boson
|
|
is highly boosted, those will be very close together and therefore
|
|
appear to the detector as only one jet. This means that the investigated
|
|
decay of a q* particle will have two jets in the final state and will
|
|
therefore be hard to distinguish from the QCD background described in
|
|
Sec.~\ref{sec:qcdbg}.
|
|
|
|
The choice of only examining the decay of the q* particle to the vector
|
|
bosons is motivated by the branching ratios calculated for the decay
|
|
\autocite{QSTAR_THEORY}:
|
|
|
|
\begin{longtable}[]{@{}llll@{}}
|
|
\caption{Branching ratios of the decaying q* particle.}\tabularnewline
|
|
\toprule
|
|
decay mode & br. ratio {[}\%{]} & decay mode & br. ratio
|
|
{[}\%{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
decay mode & br. ratio {[}\%{]} & decay mode & br. ratio
|
|
{[}\%{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
\(U^* \rightarrow ug\) & 83.4 & \(D^* \rightarrow dg\) &
|
|
83.4\tabularnewline
|
|
\(U^* \rightarrow dW\) & 10.9 & \(D^* \rightarrow uW\) &
|
|
10.9\tabularnewline
|
|
\(U^* \rightarrow u\gamma\) & 2.2 & \(D^* \rightarrow d\gamma\) &
|
|
0.5\tabularnewline
|
|
\(U^* \rightarrow uZ\) & 3.5 & \(D^* \rightarrow dZ\) &
|
|
5.1\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
The decay to the vector bosons have the second highest branching ratio.
|
|
The decay to a gluon and a quark is the dominant decay, but virtually
|
|
impossible to distinguish from the QCD background described in the next
|
|
section. This makes the decay to the vector bosons the most promising
|
|
choice.
|
|
|
|
To reconstruct the mass of the q* particle from an event successfully
|
|
recognized to be the decay of such a particle, the dijet invariant mass
|
|
has to be calculated. This can be achieved by adding the four momenta of
|
|
the two jets in the final state, vectors consisting of the energy and
|
|
momentum of a particle, together. From the four momentum it's easy to
|
|
derive the mass by solving \(E=\sqrt{p^2 + m^2}\) for m.
|
|
|
|
A search for the excited quark predicted by this theory has already been
|
|
investigated in \autocite{PREV_RESEARCH} analysing data with an
|
|
integrated luminosity of \(\SI{35.92}{\per\femto\barn}\) recorded by the
|
|
CMS experiment in 2016, excluding the q* particle up to a mass of 5 TeV
|
|
resp. 4.7 TeV for the decay to qW resp. qZ analysing the hadronic decay
|
|
of the vector boson. This thesis aims to either exclude the particle to
|
|
higher masses or find a resonance showing its existence using more data
|
|
that is available now.
|
|
|
|
\hypertarget{sec:qcdbg}{%
|
|
\subsubsection{Quantum Chromodynamic background}\label{sec:qcdbg}}
|
|
|
|
In this thesis, a decay with two jets in the final state will be
|
|
analysed. Therefore it will be hard to distinguish the signal processes
|
|
from QCD effects. Those can also produce two jets in the final state, as
|
|
can be seen in Fig.~\ref{fig:qcdfeynman}. They are also happening very
|
|
often in a proton proton collision, as it is happening in the Large
|
|
Hadron Collider. This is caused by the structure of the proton. It not
|
|
only consists of three quarks, called valence quarks, but also of a lot
|
|
of quark-antiquark pairs connected by gluons, called the sea quarks,
|
|
that exist due to the self interaction of the gluons binding the three
|
|
valence quarks. Therefore the QCD multijet backgroubd is the dominant
|
|
background of the signal described in Sec.~\ref{sec:qs}.
|
|
|
|
\begin{figure}
|
|
\centering
|
|
\feynmandiagram [horizontal=v1 to v2] {
|
|
q1 [particle=\(q\)] -- [fermion] v1 -- [gluon] g1 [particle=\(g\)],
|
|
v1 -- [gluon] v2,
|
|
q2 [particle=\(q\)] -- [fermion] v2 -- [gluon] g2 [particle=\(g\)],
|
|
};
|
|
\feynmandiagram [horizontal=v1 to v2] {
|
|
g1 [particle=\(g\)] -- [gluon] v1 -- [gluon] g2 [particle=\(g\)],
|
|
v1 -- [gluon] v2,
|
|
g3 [particle=\(g\)] -- [gluon] v2 -- [gluon] g4 [particle=\(g\)],
|
|
};
|
|
\caption{Two examples of QCD processes resulting in two jets.} \label{fig:qcdfeynman}
|
|
\end{figure}
|
|
|
|
\newpage
|
|
|
|
\hypertarget{experimental-setup}{%
|
|
\section{Experimental Setup}\label{experimental-setup}}
|
|
|
|
Following on, the experimental setup used to gather the data analysed in
|
|
this thesis will be described.
|
|
|
|
\hypertarget{large-hadron-collider}{%
|
|
\subsection{Large Hadron Collider}\label{large-hadron-collider}}
|
|
|
|
The Large Hadron Collider \autocite{LHC_MACHINE} is the world's largest
|
|
and most powerful particle accelerator. It has a circumference of 27 km
|
|
and can accelerate two beams of protons to an energy of 6.5 TeV
|
|
resulting in a collision with a centre of mass energy of 13 TeV. It is
|
|
home to several experiments, between others the Compact Muon Solenoid
|
|
(CMS), which is the one used for the search presented in this thesis. It
|
|
is a general-purpose detector to investigate the particles that form
|
|
during particle collisions. The LHC may also be used for colliding ions
|
|
but this ability is to no interest for this research.
|
|
|
|
Because of the collision of two beams with particles of the same charge,
|
|
it is not possible to use the same magnetic field for both beams.
|
|
Therefore opposite magnetic-dipole fields exist in both rings to be able
|
|
to accelerate the beams in opposite directions.
|
|
|
|
Particle colliders are characterized by their luminosity L. It is a
|
|
quantity to be able to calculate the number of events per second
|
|
generated in a collision by \(\dot{N}_{event} = L\sigma_{event}\) with
|
|
\(\sigma_{event}\) being the cross section of the event. The LHC aims
|
|
for a peak luminosity of \(10^{34}\si{\per\square\centi\metre\per\s}\).
|
|
This is achieved by colliding two bunches of protons every
|
|
\(\SI{25}{ns}\). Each proton beam thereby consists of 2'808 bunches.
|
|
Furthermore, the integrated Luminosity, defined as \(\int Ldt\), can be
|
|
used to describe the amount of data collected over a specific time
|
|
interval.
|
|
|
|
\hypertarget{compact-muon-solenoid}{%
|
|
\subsection{Compact Muon Solenoid}\label{compact-muon-solenoid}}
|
|
|
|
The data used in this thesis was recorded by the Compact Muon Solenoid
|
|
(CMS) \autocite{CMS_REPORT}. It is one of the four main experiments at
|
|
the Large Hadron Collider. It can detect all elementary particles of the
|
|
standard model except neutrinos. For that, it has an onion like setup,
|
|
as can be seen in Fig.~\ref{fig:cms_setup}. The particles produced in a
|
|
collision first go through a tracking system. They then pass an
|
|
electromagnetic as well as a hadronic calorimeter. This part is
|
|
surrounded by a superconducting solenoid that generates a magenetic
|
|
field of 3.8 T. Outside of the solenoid are big muon chambers. In 2016
|
|
the CMS captured data of an integrated luminosity of
|
|
\(\SI{37.80}{\per\femto\barn}\). In 2017 it collected
|
|
\(\SI{44.98}{\per\femto\barn}\) and in 2018
|
|
\(\SI{63.67}{\per\femto\barn}\) \autocite{CMS_LUMI}. The amount of data
|
|
usable for research is \(\SI{35.92}{\per\femto\barn}\),
|
|
\(\SI{41.53}{\per\femto\barn}\) and \(\SI{59.74}{\per\femto\barn}\) for
|
|
the years 2016, 2017 and 2018, totalling to
|
|
\(\SI{137.19}{\per\femto\barn}\) of data.
|
|
|
|
\begin{figure}
|
|
\hypertarget{fig:cms_setup}{%
|
|
\centering
|
|
\includegraphics{./figures/cms_setup.png}
|
|
\caption{The setup of the Compact Muon Solenoid showing its onion like
|
|
structure, the different detector parts and where different particles
|
|
are detected \autocite{CMS_PLOT}.}\label{fig:cms_setup}
|
|
}
|
|
\end{figure}
|
|
|
|
\hypertarget{coordinate-conventions}{%
|
|
\subsubsection{Coordinate conventions}\label{coordinate-conventions}}
|
|
|
|
Per convention, the z axis points along the beam axis in the direction
|
|
of the magnetic fields of the solenoid, the y axis upwards and the x
|
|
axis horizontal towards the LHC centre. The azimuthal angle \(\phi\),
|
|
which describes the angle in the x - y plane, the polar angle
|
|
\(\theta\), which describes the angle in the y - z plane and the
|
|
pseudorapidity \(\eta\), which is defined as
|
|
\(\eta = -ln\left(tan\frac{\theta}{2}\right)\) are also introduced. The
|
|
coordinates are visualised in Fig.~\ref{fig:cmscoords}. Furthermore, to
|
|
describe a particle's momentum, often the transverse momentum, \(p_t\)
|
|
is used. It is the component of the momentum transversal to the beam
|
|
axis. Before the collision, the transverse momentum is zero, therefore,
|
|
due to conservation of energy, the sum of all transverse momenta after
|
|
the collision has to be zero, too. If this is not the case for the
|
|
detected events, it implies particles that weren't detected such as
|
|
neutrinos.
|
|
|
|
\begin{figure}
|
|
\hypertarget{fig:cmscoords}{%
|
|
\centering
|
|
\includegraphics[width=0.6\textwidth,height=\textheight]{./figures/cms_coordinates.png}
|
|
\caption{Coordinate conventions of the CMS illustrating the use of
|
|
\(\eta\) and \(\phi\). The Z axis is in beam direction
|
|
\autocite{COORD_PLOT}.}\label{fig:cmscoords}
|
|
}
|
|
\end{figure}
|
|
|
|
\hypertarget{the-tracking-system}{%
|
|
\subsubsection{The tracking system}\label{the-tracking-system}}
|
|
|
|
The tracking system is built of two parts, closest to the collision is a
|
|
pixel detector and around that silicon strip sensors. They are used to
|
|
measure their charge sign, direction and momentum to be later able to
|
|
reconstruct the tracks of charged particles. They are as close to the
|
|
collision as possible to be able to identify secondary vertices.
|
|
|
|
\hypertarget{the-electromagnetic-calorimeter}{%
|
|
\subsubsection{The electromagnetic
|
|
calorimeter}\label{the-electromagnetic-calorimeter}}
|
|
|
|
The electromagnetic calorimeter measures the energy of photons and
|
|
electrons. It is made of tungstate crystal and photodetectors. When
|
|
passed by particles, the crystal produces scintillation light in
|
|
proportion to the particle's energy. This light is measured by the
|
|
photodetectors that convert it to an electrical signal. To measure a
|
|
particles energy, it has to leave its whole energy in the ECAL, which is
|
|
true for photons and electrons, but not for other particles such as
|
|
hadrons and muons. Those interact with matter differently and therefore
|
|
only leave some energy in the ECAL but are not stopped by it.
|
|
|
|
\hypertarget{the-hadronic-calorimeter}{%
|
|
\subsubsection{The hadronic
|
|
calorimeter}\label{the-hadronic-calorimeter}}
|
|
|
|
The hadronic calorimeter (HCAL) is used to detect high energy hadronic
|
|
particles. It surrounds the ECAL and is made of alternating layers of
|
|
active and absorber material. While the absorber material with its high
|
|
density causes the hadrons to shower, the active material then detects
|
|
those showers and measures their energy, similar to how the ECAL works.
|
|
|
|
\hypertarget{the-solenoid}{%
|
|
\subsubsection{The solenoid}\label{the-solenoid}}
|
|
|
|
The solenoid, giving the detector its name, is one of the most important
|
|
features. It creates a magnetic field of 3.8 T and therefore makes it
|
|
possible to measure momentum of charged particles by bending their
|
|
tracks.
|
|
|
|
\hypertarget{the-muon-system}{%
|
|
\subsubsection{The muon system}\label{the-muon-system}}
|
|
|
|
Outside of the solenoid, but still in its return yoke, there is only the
|
|
muon system. It consists of three types of gas detectors, the drift
|
|
tubes, cathode strip chambers and resistive plate chambers. It covers a
|
|
total of \(0 < |\eta| < 2.4\). The muons are the only detected
|
|
particles, that can pass all the other systems without a significant
|
|
energy loss.
|
|
|
|
\hypertarget{the-trigger-system}{%
|
|
\subsubsection{The Trigger system}\label{the-trigger-system}}
|
|
|
|
The CMS features a two level trigger system. It is necessary because the
|
|
detector is unable to process all the events due to limited bandwidth.
|
|
The Level 1 trigger reduces the event rate from 40 MHz to 100 kHz, the
|
|
software based High Level trigger is then able to further reduce the
|
|
rate to 1 kHz. The Level 1 trigger uses the data from the
|
|
electromagnetic and hadronic calorimeters as well as the muon chambers
|
|
to decide whether to keep an event. The High Level trigger uses a
|
|
streamlined version of the CMS offline reconstruction software for its
|
|
decision making.
|
|
|
|
\hypertarget{the-particle-flow-algorithm}{%
|
|
\subsubsection{The Particle Flow
|
|
algorithm}\label{the-particle-flow-algorithm}}
|
|
|
|
The particle flow algorithm \autocite{PARTICLE_FLOW} is used to identify
|
|
and reconstruct all the particles arising from the proton - proton
|
|
collision by using all the information available from the different
|
|
sub-detectors. It does so by extrapolating the tracks through the
|
|
different calorimeters and associating clusters they cross with them.
|
|
The set of clusters already associated to a track is then no more used
|
|
for the reconstruction of other particles. This is first done for muons
|
|
and then for charged hadrons, so a muon can't give rise to a wrongly
|
|
identified charged hadron. Due to Bremsstrahlung photon emission,
|
|
electrons are harder to reconstruct. For them a specific track
|
|
reconstruction algorithm is used \autocite{ERECO}. After identifying
|
|
charged hadrons, muons and electrons, all remaining clusters within the
|
|
HCAL correspond to neutral hadrons and within ECAL to photons. When the
|
|
list of particles and their corresponding deposits is established, it
|
|
can be used to determine the particles four momenta. From that, the
|
|
missing transverse energy can be calculated and tau particles can be
|
|
reconstructed by their decay products.
|
|
|
|
\hypertarget{jet-clustering}{%
|
|
\subsection{Jet clustering}\label{jet-clustering}}
|
|
|
|
Because of the hadronisation it is not possible to uniquely identify the
|
|
originating particle of a jet. Nonetheless, several algorithms exist to
|
|
help with this problem. The algorithm used in this thesis is the
|
|
anti-\(k_t\) \autocite{ANTIKT} clustering algorithm. It arises from a
|
|
generalization of several other clustering algorithms, namely the
|
|
\(k_t\), Cambridge/Aachen and SISCone clustering algorithms.
|
|
|
|
The anti-\(k_t\) clustering algorithm associates high \(p_t\) particles
|
|
with the lower \(p_t\) particles surrounding them within a radius R in
|
|
the \(\eta\) - \(\phi\) plane forming cone like jets. If two jets
|
|
overlap, the jets shape is changed according to its hardness in regards
|
|
to the transverse momentum. A softer particles jet will change its shape
|
|
more than a harder particles. A visual comparison of four different
|
|
clustering algorithms can be seen in Fig.~\ref{fig:antiktcomparison}. It
|
|
shows, that the jets reconstructed using the anti-\(k_t\) algorithm have
|
|
the clearest cone like shape and is therefore chosen for this thesis.
|
|
For this analysis, a radius of 0.8 is used.
|
|
|
|
\begin{figure}
|
|
\hypertarget{fig:antiktcomparison}{%
|
|
\centering
|
|
\includegraphics{./figures/antikt-comparision.png}
|
|
\caption{Comparison of the \(k_t\), Cambridge/Aachen, SISCone and
|
|
anti-\(k_t\) algorithms clustering a sample parton-level event with many
|
|
random soft \enquote{ghosts}
|
|
\autocite{ANTIKT}.}\label{fig:antiktcomparison}
|
|
}
|
|
\end{figure}
|
|
|
|
Furthermore, to approximate the mass of a heavy particle that caused a
|
|
jet, the soft-drop mass \autocite{SDM} can be used. In its calculation,
|
|
to reduce the contamination from initial state radiation, underlying
|
|
event and multiple hadron scattering, wide angle soft particles are
|
|
removed from the jet. It therefore is more accurate in determining the
|
|
mass of a particle causing a jet than taking the mass of all constituent
|
|
particles of the jet combined.
|
|
|
|
\newpage
|
|
|
|
\hypertarget{sec:moa}{%
|
|
\section{Method of analysis}\label{sec:moa}}
|
|
|
|
This section gives an overview over how the data collected by CMS is
|
|
going to be analysed to be able to either exclude the q* particle to
|
|
even higher masses than already done or confirm its existence.
|
|
|
|
As described in Sec.~\ref{sec:qs}, the decay of the q* particle to a
|
|
quark and a vector boson with the vector boson then decaying
|
|
hadronically will be investigated. This is the second most probable
|
|
decay of the q* particle and easier to analyse than the dominant decay
|
|
to a quark and a gluon. Therefore it is a good choice for this research.
|
|
It results in two jets, because the decay products of the heavy vector
|
|
boson are highly boosted, causing them to be very close together and
|
|
therefore be reconstructed as one jet. The dijet invariant mass of the
|
|
two jets in the final state is then used to reconstruct the mass of the
|
|
q* particle. The only background considered is the QCD multijet
|
|
background described in Sec.~\ref{sec:qcdbg}. A selection using
|
|
different kinematic variables as well as a tagger to identify jets from
|
|
the decay of a vector boson is introduced to reduce the background and
|
|
increase the sensitivity for the signal. After that, it will be looked
|
|
for a peak in the dijet invariant mass distribution at the resonance
|
|
mass of the q* particle.
|
|
|
|
The data studied were collected by the CMS experiment in the years 2016,
|
|
2017 and 2018. They are analysed with the Particle Flow algorithm to
|
|
reconstruct jets and all the other particles forming during the
|
|
collision. The jets are then clustered using the anti-\(k_t\) algorithm
|
|
with the distance parameter R being 0.8.
|
|
|
|
The analysis will be conducted in two steps. First, only the data
|
|
collected by the CMS experiment in 2016 with an integrated luminosity of
|
|
\(\SI{35.92}{\per\femto\barn}\) will be used to compare the results to
|
|
the previous analysis \autocite{PREV_RESEARCH}. Then the combined data
|
|
from 2016, 2017 and 2018 with an integrated luminosity of
|
|
\(\SI{137.19}{\per\femto\barn}\) will be used to improve the previously
|
|
set limits for the mass of the q* particle. Also, two different
|
|
V-tagging methods will be used to compare their performance. One based
|
|
on the N-subjettiness variable used in the previous research
|
|
\autocite{PREV_RESEARCH}, the other being a novel approach using a deep
|
|
neural network, that will be explained in the following.
|
|
|
|
\hypertarget{signal-and-background-modelling}{%
|
|
\subsection{Signal and Background
|
|
modelling}\label{signal-and-background-modelling}}
|
|
|
|
Before looking at the data collected by the CMS experiment, Monte Carlo
|
|
simulations \autocite{MONTECARLO} of background and signal are used to
|
|
understand how the data is expected to look like. To replicate the QCD
|
|
background processes, the different particle interactions that take
|
|
place in a proton - proton collision are simulated using the
|
|
probabilities provided by the Standard Model by calculating the cross
|
|
sections of the different Feynman diagrams. This was done using MadGraph
|
|
\autocite{MADGRAPH} and Pythia 8 \autocite{PYTHIA8}. Later on, also
|
|
detector effects (like its limited resolution) are applied to make sure,
|
|
they look like real data coming from the CMS detector.
|
|
|
|
The q* signal samples are simulated by the probabilities given by the q*
|
|
theory \autocite{QSTAR_THEORY} and assuming a cross section of
|
|
\(\SI{1}{\pico\barn}\). The simulation was done using MadGraph
|
|
\autocite{MADGRAPH} for eleven masspoints between 1.6 TeV and 7 TeV.
|
|
Because of the expected high mass, the signal width will be dominated by
|
|
the resolution of the detector, not by the natural resonance width.
|
|
|
|
The dijet invariant mass distribution of the QCD background is expected
|
|
to smoothly fall with higher masses. It is therefore fitted using the
|
|
following smooth falling function with three parameters p0, p1, p2:
|
|
\begin{equation}
|
|
\frac{dN}{dm_{jj}} = \frac{p_0 \cdot ( 1 - m_{jj} / \sqrt{s} )^{p_2}}{ (m_{jj} / \sqrt{s})^{p_1}}
|
|
\end{equation} Whereas \(m_{jj}\) is the invariant mass of the dijet and
|
|
\(p_0\) is a normalisation parameter. It is the same function as used in
|
|
the previous research studying 2016 data only but was also found to
|
|
reliably reproduce the background shape of the other years.
|
|
|
|
The signal is fitted using a double sided crystal ball function. It has
|
|
six parameters:
|
|
|
|
\begin{itemize}
|
|
\tightlist
|
|
\item
|
|
mean: the functions mean, in this case the resonance mass
|
|
\item
|
|
sigma: the functions width, in this case the resolution of the
|
|
detector due to the very small resonance width expected
|
|
\item
|
|
n1, n2, alpha1, alpha2: parameters influencing the shape of the left
|
|
and right tail
|
|
\end{itemize}
|
|
|
|
A gaussian and a poisson function have also been studied but found to be
|
|
not able to reproduce the signal shape as they couldn't model the tails
|
|
on both sides of the peak.
|
|
|
|
A linear combination of the signal and background function is then
|
|
fitted to a toy dataset with gaussian errors obtained by adding
|
|
simulated background and signal. The resulting coefficients of said
|
|
combination then show the expected signal rate for the simulated signal
|
|
cross section of \(\SI{1}{\pico\barn}\). An example of such a fit can be
|
|
seen in Fig.~\ref{fig:cb_fit}. In this figure, a binning of 200 GeV is
|
|
used for presentational purposes. The analysis itself is conducted using
|
|
a 1 GeV binning. It can be seen that the fit works very well and
|
|
therefore confirms the functions chosen to model signal and background.
|
|
This is supported by a \(\chi^2 /\) ndof of 0.5 and a found mean for the
|
|
signal at 2999 \(\pm\) 23 \(\si{\giga\eV}\) which is in very good
|
|
agreement with the expected 3000 GeV mean. Those numbers clearly show
|
|
that the method in use is able to successfully describe the simulated
|
|
toy data.
|
|
|
|
\begin{figure}
|
|
\hypertarget{fig:cb_fit}{%
|
|
\centering
|
|
\includegraphics{./figures/cb_fit.pdf}
|
|
\caption{Combined fit of signal and background on a toy dataset with
|
|
gaussian errors and a simulated resonance mass of 3
|
|
TeV.}\label{fig:cb_fit}
|
|
}
|
|
\end{figure}
|
|
|
|
\newpage
|
|
|
|
\hypertarget{preselection-and-data-quality}{%
|
|
\section{Preselection and data
|
|
quality}\label{preselection-and-data-quality}}
|
|
|
|
To reduce the background and increase the signal sensitivity, a
|
|
selection of events that satisfy certain requirements is introduced.
|
|
This is done taking into account different variables. The selection is
|
|
divided into two stages. The first one (the preselection) introduces
|
|
some general physics motivated selections using kinematic variables and
|
|
is also used to ensure a high trigger efficiency. In the second part,
|
|
the discriminants introduced by different taggers will be used to
|
|
identify jets originating from the decay of a vector boson. After the
|
|
preselection, it is made sure, that the simulated samples represent the
|
|
real data well by comparing the data with the simulation in the signal
|
|
as well as a sideband region, where no signal events are expected.
|
|
|
|
\hypertarget{preselection}{%
|
|
\subsection{Preselection}\label{preselection}}
|
|
|
|
First, all events are cleaned of jets with a
|
|
\(p_t < \SI{200}{\giga\eV}\) and a pseudorapidity \(|\eta| > 2.4\). This
|
|
is to discard soft background and to make sure the particles are in the
|
|
barrel region of the detector for an optimal track reconstruction.
|
|
Furthermore, all events with one of the two highest \(p_t\) jets having
|
|
an angular separation smaller than 0.8 from any electron or muon are
|
|
discarded to allow future use of the data in studies investigating the
|
|
leptonic decay channel of the vector boson.
|
|
|
|
From a decaying q* particle, two jets are expected in the final state.
|
|
The dijet invariant mass of those two jets will be used to reconstruct
|
|
the mass of the q* particle. Therefore a cut is added to have at least 2
|
|
jets, accounting for the possibility of more jets, for example caused by
|
|
gluon radiation of a quark or other QCD effects. If this is the case,
|
|
the two jets with the highest \(p_t\) are used for the reconstruction of
|
|
the q* mass. The distributions of the number of jets before and after
|
|
the selection can be seen in Fig.~\ref{fig:njets}. The light blue filled
|
|
histogram shows the QCD background, the green and red line show the
|
|
expected signal for a decay of the q* particle to qW with a mass of 2
|
|
TeV (green) and 5 TeV (red). By comparing the left to the right
|
|
distributions, it is clear that the requirement of at least 2 jets
|
|
reduces the background significantly while keeping mostly all signal
|
|
events.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{\textwidth}
|
|
\centering\textbf{Comparison for 2016}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Cleaner_N_jets_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Njet_N_jets_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{\textwidth}
|
|
\vspace{0.1cm}
|
|
\centering\textbf{Comparison for the combined dataset}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_Cleaner_N_jets_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_Njet_N_jets_stack.eps}
|
|
\end{minipage}
|
|
\caption{Comparison of the number of jet distribution before and after the cut at number of jets $\ge$ 2. \newline
|
|
Left: distribution before the cut. Right: distribution after the cut. \newline
|
|
The signal curves are amplified by a factor of 10'000 to be visible.}
|
|
\label{fig:njets}
|
|
\end{figure}
|
|
|
|
The next selection is done using \(\Delta\eta = |\eta_1 - \eta_2|\),
|
|
with \(\eta_1\) and \(\eta_2\) being the \(\eta\) of the two jets with
|
|
the highest transverse momentum. The q* particle is expected to be very
|
|
heavy in regards to the center of mass energy of the collision and will
|
|
therefore be almost stationary. Its decay products should therefore be
|
|
close to back to back, which means the \(\Delta\eta\) distribution is
|
|
expected to peak at zero. At the same time, particles originating from
|
|
QCD effects are expected to have a higher \(\Delta\eta\). To maintain
|
|
comparability, the same selection as in previous research of
|
|
\(\Delta\eta \le 1.3\) is used. In the top two distributions of
|
|
Fig.~\ref{fig:deta}, this cut is marked by a vertical black line. The
|
|
difference in the \(m_{jj}\) distribution shows the strong reduction of
|
|
the background by this cut.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{\textwidth}
|
|
\centering\textbf{$\Delta\eta$ cut with signal amplified by 10'000}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Njet_deta_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_Njet_deta_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{\textwidth}
|
|
\vspace{0.1cm}
|
|
\centering\textbf{$m_{jj}$ distribution before the cut}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Njet_invMass_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_Njet_invMass_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{\textwidth}
|
|
\vspace{0.1cm}
|
|
\centering\textbf{$m_{jj}$ distribution after the cut}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Eta_invMass_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_Eta_invMass_stack.eps}
|
|
\end{minipage}
|
|
\caption{Demonstration of the effect of the $\Delta\eta$ cut at $\Delta\eta \le 1.3$ on the $m_{jj}$ distribution.
|
|
\newline
|
|
Left: Partial dataset of $\SI{35.92}{\per\femto\barn}$ Right: Full dataset of $\SI{137.19}{\per\femto\barn}$.
|
|
}
|
|
\label{fig:deta}
|
|
\end{figure}
|
|
|
|
The last selection in the preselection is on the dijet invariant mass:
|
|
\(m_{jj} \ge \SI{1050}{\giga\eV}\). It is important for a trigger
|
|
efficiency higher than 99 \% with a soft-drop mass cut of
|
|
\(m_{SDM} > \SI{65}{\giga\eV}\) applied to the jet with the highest
|
|
transverse momentum. A comparison of the \(m_{jj}\) distribution before
|
|
and after the selection can be seen in Fig.~\ref{fig:invmass}. Also, it
|
|
has a huge impact on the background because it usually consists of
|
|
lighter particles. The q* on the other hand is expected to have a very
|
|
high invariant mass of more than 1 TeV. The \(m_{jj}\) distribution
|
|
should be a smoothly falling function for the QCD background and peak at
|
|
the simulated resonance mass for the signal events.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{\textwidth}
|
|
\centering\textbf{Comparison for 2016}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Eta_invMass_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_invmass_invMass_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{\textwidth}
|
|
\centering\textbf{Comparison for the combined dataset}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_Eta_invMass_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_invmass_invMass_stack.eps}
|
|
\end{minipage}
|
|
\caption{Comparison of the invariant mass distribution before and after the cut at $m_{jj} \ge \SI{1050}{\giga\eV}$. It
|
|
shows the expected smooth falling functions of the background whereas the signal peaks at the simulated resonance mass.
|
|
\newline
|
|
Left: distribution before the cut. Right: distribution after the cut.}
|
|
\label{fig:invmass}
|
|
\end{figure}
|
|
|
|
After the preselection, the signal efficiency for q* decaying to qW of
|
|
2016 ranges from 48 \% for 1.6 TeV to 49 \% for 7 TeV. Decaying to qZ,
|
|
the efficiencies are between 45 \% (1.6 TeV) and 50 \% (7 TeV). The
|
|
amount of background after the preselection is reduced to 5 \% of the
|
|
original events. For the combined data of the three years those values
|
|
look similar. Decaying to qW signal efficiencies between 49 \% (1.6 TeV)
|
|
and 56 \% (7 TeV) are reached, whereas the efficiencies when decaying to
|
|
qZ are in the range of 46 \% (1.6 TeV) to 50 \% (7 TeV). Here, the
|
|
background could be reduced to 8 \% of the original events. So while
|
|
keeping around 50 \% of the signal, the background was already reduced
|
|
to less than a tenth.
|
|
|
|
\hypertarget{data---monte-carlo-comparison}{%
|
|
\subsection{Data - Monte Carlo
|
|
Comparison}\label{data---monte-carlo-comparison}}
|
|
|
|
To ensure that the simulation reproduces the data well, the simulated
|
|
QCD background sample is now being compared to the data of the
|
|
corresponding year collected by the CMS detector. This is done for the
|
|
partial dataset of year 2016 and for the full dataset separately. In
|
|
Fig.~\ref{fig:data-mc}, this comparison can be seen for the
|
|
distributions of the variables used during the preselection. To
|
|
compensate for the simulation overpredicting the scale of the QCD
|
|
background, histograms are rescaled, so that the dijet invariant mass
|
|
distributions of data and simulation have the same integral. The
|
|
invariant mass distribution of the data of 2016 falls slightly faster
|
|
than the simulated one, apart from that, the distributions are in very
|
|
good agreement.
|
|
|
|
For analysing the data from the CMS experiment, jet energy corrections
|
|
have to be applied. Those are to calibrate the ECAL and HCAL parts of
|
|
the CMS, so the energy of the detected particles can be measured
|
|
correctly. The corrections used were recommended by the CMS group for
|
|
internal use \autocite{JEC}.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\centering\textbf{2016}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\centering\textbf{Combined}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/DATA/v1_invmass_N_jets.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/DATA/v1_invmass_N_jets.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/DATA/v1_invmass_deta.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/DATA/v1_invmass_deta.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/DATA/v1_invmass_invMass.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/DATA/v1_invmass_invMass.eps}
|
|
\end{minipage}
|
|
\caption{Comparison of data with the Monte Carlo simulation.}
|
|
\label{fig:data-mc}
|
|
\end{figure}
|
|
|
|
\hypertarget{sideband-region}{%
|
|
\subsubsection{Sideband region}\label{sideband-region}}
|
|
|
|
The sideband region is introduced to make sure no bias in the data and
|
|
Monte Carlo simulation is introduced and also to verify the agreement of
|
|
data and simulation. It is a region in which no signal event is
|
|
expected. Again, data and the Monte Carlo simulation are compared. For
|
|
this analysis, the region where the soft-drop mass of both of the two
|
|
jets with the highest transverse momentum is more than 105 GeV is
|
|
chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the
|
|
heavier vector boson. Therefore it is very unlikely, that an event with
|
|
a particle heavier than that originates from the decay of a vector
|
|
boson. In Fig.~\ref{fig:sideband}, the comparison of data with
|
|
simulation in the sideband region can be seen for the soft-drop mass
|
|
distribution as well as the dijet invariant mass distribution. It can be
|
|
seen, that in the sideband region data and simulation match very well.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{\textwidth}
|
|
\centering\textbf{2016}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/sideband/v1_SDM_SoftDropMass_1.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/sideband/v1_SDM_invMass.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{\textwidth}
|
|
\centering\textbf{Combined dataset}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/sideband/v1_SDM_SoftDropMass_1.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/sideband/v1_SDM_invMass.eps}
|
|
\end{minipage}
|
|
\caption{Comparison of data with the Monte Carlo simulation in the sideband region.}
|
|
\label{fig:sideband}
|
|
\end{figure}
|
|
|
|
\newpage
|
|
|
|
\hypertarget{jet-substructure-selection}{%
|
|
\section{Jet substructure selection}\label{jet-substructure-selection}}
|
|
|
|
So far it was made sure, that the data collected by the CMS and the
|
|
simulation are in good agreement after the preselection and no unwanted
|
|
side effects are introduced in the data by the used cuts. Now another
|
|
selection has to be introduced, to further reduce the background to be
|
|
able to look for the hypothetical signal events in the data.
|
|
|
|
This is done by distinguishing between QCD and signal events using a
|
|
tagger to identify jets coming from a vector boson. Two different
|
|
taggers will be used to later compare their performance. The decay
|
|
analysed includes either a W or Z boson, which are, compared to the
|
|
particles in QCD effects, very heavy. This can be used by adding a
|
|
selection using the soft-drop mass of a jet. The soft-drop mass of at
|
|
least one of the two leading jets is expected to be within
|
|
\(\SI{35}{\giga\eV}\) and \(\SI{105}{\giga\eV}\). This cut already
|
|
provides a good separation of QCD and signal events, on which the two
|
|
taggers presented next can build.
|
|
|
|
Both taggers provide a discriminant to choose whether an event can be
|
|
classified as the decay of a vector boson or originates from QCD
|
|
effects. This value will be optimized afterwards to make sure the
|
|
maximum signal significance possible is achieved.
|
|
|
|
\hypertarget{n-subjettiness}{%
|
|
\subsection{N-Subjettiness}\label{n-subjettiness}}
|
|
|
|
The N-subjettiness \autocite{TAU21} \(\tau_N\) is a jet shape parameter
|
|
designed to identify boosted hadronically-decaying objects. When a
|
|
vector boson decays hadronically, it produces two quarks each causing a
|
|
jet. But in the case of the decay of a q* particle, the vector boson is
|
|
highly boosted and so are its decay products. They therefore appear,
|
|
after applying a clustering algorithm, as just one jet. This algorithm
|
|
now tries to figure out, whether one jet might consist of two subjets by
|
|
using the kinematics and positions of the constituent particles of this
|
|
jet. The N-subjettiness is defined as
|
|
|
|
\begin{equation} \tau_N = \frac{1}{d_0} \sum_k p_{T,k} \cdot \text{min}\{ \Delta R_{1,k}, \Delta R_{2,k}, …, \Delta
|
|
R_{N,k} \} \end{equation}
|
|
|
|
with k going over the constituent particles in a given jet, \(p_{T,k}\)
|
|
being their transverse momenta and
|
|
\(\Delta R_{J,k} = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}\) being the
|
|
distance of a candidate subjet J and a constituent particle k in the
|
|
\(\eta\) - \(\phi\) plane. It quantifies to what degree a jet can be
|
|
regarded as a jet composed of \(N\) subjets. In the hadronic decay of a
|
|
highly boosted vector boson, two subjets are expected. Therefore it
|
|
seems that \(\tau_2\) would be a good choice for a discriminant.
|
|
However, experiments showed, that rather than using \(\tau_2\) directly,
|
|
the ratio \(\tau_{21} = \tau_2/\tau_1\) is a better discriminant between
|
|
QCD effects and events originating from the decay of a boosted vector
|
|
boson.
|
|
|
|
The lower the \(\tau_{21}\) is, the more likely a jet is caused by the
|
|
decay of a vector boson. Therefore a selection will be introduced, so
|
|
that \(\tau_{21}\) of one candidate jet is smaller then some value that
|
|
will be determined by the optimisation process described in the next
|
|
chapter. As candidate jet the one of the two highest \(p_t\) jets
|
|
passing the soft-drop mass window is used. If both of them pass, the one
|
|
with higher \(p_t\) is chosen.
|
|
|
|
\hypertarget{deepak8}{%
|
|
\subsection{DeepAK8}\label{deepak8}}
|
|
|
|
The DeepAK8 tagger \autocite{DEEP_BOOSTED} uses a deep neural network
|
|
(DNN) to identify decays originating in a vector boson. It reduces the
|
|
background rate by up to a factor of \textasciitilde10 with the same
|
|
signal efficiency compared to non-machine-learning approaches like the
|
|
N-Subjettiness method. This is shown by Fig.~\ref{fig:ak8_eff}, showing
|
|
a comparison of background and signal efficiency of the DeepAK8 tagger
|
|
with, between others, the \(\tau_{20}\) tagger that is also used in this
|
|
analysis.
|
|
|
|
\begin{figure}
|
|
\hypertarget{fig:ak8_eff}{%
|
|
\centering
|
|
\includegraphics[width=0.6\textwidth,height=\textheight]{./figures/deep_ak8.pdf}
|
|
\caption{Comparison of tagger efficiencies, showing, between others, the
|
|
DeepAK8 and \(\tau_{21}\) tagger used in this analysis
|
|
\autocite{DEEP_BOOSTED}.}\label{fig:ak8_eff}
|
|
}
|
|
\end{figure}
|
|
|
|
The DNN has two input lists for each jet. The first is a list of up to
|
|
100 constituent particles of the jet, sorted by decreasing \(p_t\). A
|
|
total of 42 properties of the particles such es \(p_t\), energy deposit,
|
|
charge and the angular momentum between the particle and the jet or
|
|
subjet axes are included. The second input list is a list of up to seven
|
|
secondary vertices, each with 15 features, such as the kinematics,
|
|
displacement and quality criteria. To process those inputs, a customised
|
|
DNN architecture has been developed. It consists of two convolutional
|
|
neural networks (CNN) that each process one of the input lists. The
|
|
outputs of the two CNNs are then combined and processed by a
|
|
fully-connected network to identify the jet. The network was trained
|
|
with a sample of 40 million jets, another 10 million jets were used for
|
|
development and validation.
|
|
|
|
In this thesis, the mass decorrelated version of the DeepAK8 tagger,
|
|
called DeepAK8-MD but further referred to as only DeepAK8, is used. It
|
|
adds an additional mass predictor layer, that is trained to quantify how
|
|
strongly the output of the non-decorrelated tagger is correlated to the
|
|
mass of a particle. Its output is fed back to the network as a penalty
|
|
so it avoids using features of the particles correlated to their mass.
|
|
The result is a largely mass decorrelated tagger of heavy resonances,
|
|
that doesn't introduce a bias in the jet mass shape. As can be seen in
|
|
Fig.~\ref{fig:ak8_eff}, it performs not as good as the
|
|
non-mass-decorrelated version, but still better than the other taggers
|
|
it was compared to.
|
|
|
|
The higher the discriminant value, called WvsQCD resp. ZvsQCD (further
|
|
referred to as only VvsQCD), of the DeepAK8 tagger, the more likely is
|
|
the jet to be caused by the decay of a vector boson. Therefore, using
|
|
the same way to choose a candidate jet as for the N-subjettiness tagger,
|
|
a selection is applied so that this candidate jet has a VvsQCD value
|
|
greater than some value determined by the optimisation presented next.
|
|
|
|
\hypertarget{sec:opt}{%
|
|
\subsection{Optimisation}\label{sec:opt}}
|
|
|
|
To figure out the best value to cut on the discriminants introduced by
|
|
the two taggers, a value to quantify how good a cut is has to be
|
|
introduced. For that, the significance calculated by
|
|
\(\frac{S}{\sqrt{B}}\) will be used. S stands for the amount of signal
|
|
events and B for the amount of background events in a given interval.
|
|
This value assumes a gaussian error on the background so it will be
|
|
calculated for the 2 TeV masspoint of the decay to qW where enough
|
|
background events exist to justify this assumption, which follows from
|
|
the central limit theorem \autocite{CLT} that states, that for identical
|
|
distributed random variables, their sum converges to a gaussian
|
|
distribution. The significance represents how good the signal can be
|
|
distinguished from the background in units of the standard deviation of
|
|
the background. As interval, a 10 \% margin around the resonance nominal
|
|
mass is chosen. The significance is then calculated for different
|
|
selections on the discriminant of the two taggers and then plotted in
|
|
dependence on the minimum resp. maximum allowed value of the
|
|
discriminant to pass the selection for the DeepAK8 resp. the
|
|
N-subjettiness tagger.
|
|
|
|
The optimisation process is done using only the data from year 2018,
|
|
assuming the taggers have similar performances on the data of the
|
|
different years.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/sig-db.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/sig-tau.pdf}
|
|
\end{minipage}
|
|
\caption{Significance plots for the DeepAK8 (left) and N-subjettiness (right) tagger at the 2 TeV masspoint.}
|
|
\label{fig:sig}
|
|
\end{figure}
|
|
|
|
As a result, the \(\tau_{21}\) cut is placed at \(\le 0.35\), confirming
|
|
the value previous research chose and the deep boosted cut is placed at
|
|
\(\ge 0.95\). For the DeepAK8 tagger, 0.97 would give a slightly higher
|
|
significance but as it is very close to the edge where the significance
|
|
drops very low and the higher the cut the less background will be left
|
|
to calculate the cross section limits, especially at higher resonance
|
|
masses, the slightly less strict cut is chosen.
|
|
|
|
For both taggers also a low purity category is introduced. Using the
|
|
cuts optimized for 2 TeV, there are very few background events left for
|
|
higher resonance masses, but to reliably calculate cross section limits,
|
|
those are needed. Therefore in the final cross section calculation, the
|
|
two categories are combined to have a high signal sensitivity for all
|
|
masspoints between 1.6 TeV and 7 TeV that were simulated. As low purity
|
|
category for the N-subjettiness tagger, a cut at
|
|
\(0.35 < \tau_{21} < 0.75\) is used. For the DeepAK8 tagger the opposite
|
|
cut from the high purity category is used: \(VvsQCD < 0.95\).
|
|
|
|
\newpage
|
|
|
|
\hypertarget{sec:extr}{%
|
|
\section{Signal extraction}\label{sec:extr}}
|
|
|
|
After the optimisation, now the optimal selection for the N-subjettiness
|
|
as well as the DeepAK8 tagger is found and applied to the simulated
|
|
samples as well as the data collected by the CMS experiment. The fit
|
|
described in Sec.~\ref{sec:moa} is performed for all masspoints of the
|
|
decay to qW and qZ and for the partial dataset of
|
|
\(\SI{35.92}{\per\femto\barn}\) as well as the complete dataset of
|
|
\(\SI{137.19}{\per\femto\barn}\) separately.
|
|
|
|
To test for the presence of a resonance in the data, the cross section
|
|
limits of the signal event are calculated using a frequentist asymptotic
|
|
limit criterion described in \autocite{ASYMPTOTIC_LIMIT}. Using the
|
|
parameters and signal rate obtained by the method described in
|
|
Sec.~\ref{sec:moa} as well as a shape analysis of the data recorded by
|
|
the CMS experiment, it determines an expected and an observed cross
|
|
section limit by doing a signal + background versus background-only
|
|
hypothesis test. It also calculates upper and lower limits of the
|
|
expected cross section corresponding to a confidence level of 95 \%.
|
|
|
|
In the absence of the q* particle in the data, the observed limits lie
|
|
within the \(2\sigma\) environment, meaning a 95 \% confidence level, of
|
|
the expected limit. This observed limit is plotted together with a
|
|
theory line, representing the cross section limits expected, if the q*
|
|
predicted by \autocite{QSTAR_THEORY} would exist. Since no significant
|
|
deviation from the Standard Model is found while looking for the
|
|
resonance, the crossing of the theory line with the observed limit is
|
|
calculated, to have a limit of mass up to which the existence of the q*
|
|
particle can be excluded. To find the uncertainty of this result, the
|
|
crossing of the theory line plus, respectively minus, its uncertainty
|
|
with the observed limit is also calculated.
|
|
|
|
\hypertarget{systematic-uncertainties}{%
|
|
\subsection{Systematic Uncertainties}\label{systematic-uncertainties}}
|
|
|
|
The variables used in this analysis are affected by systematic
|
|
uncertainties. For calculating the cross section of the signal, four
|
|
sources of such uncertainties are considered.
|
|
|
|
First, the uncertainty of the Jet Energy Corrections. When measuring a
|
|
particle's energy with the ECAL or HCAL part of the CMS, the electronic
|
|
signals send by the photodetectors in the calorimeters have to be
|
|
converted to actual energy values. Therefore an error in this
|
|
calibration causes the energy measured to be shifted to higher or lower
|
|
values causing also the position of the signal peak in the \(m_{jj}\)
|
|
distribution to vary. The uncertainty is approximated to be 2 \%.
|
|
|
|
Second, the tagger does not work perfectly and therefore some events,
|
|
that don't originate from a V boson are wrongly chosen and on the other
|
|
hand sometimes events that do originate from one are not. It influences
|
|
the events chose for analysis and is therefore also considered as an
|
|
uncertainty, which is approximated to be 6 \%.
|
|
|
|
Third, the uncertainty of the parameters of the background fit is also
|
|
considered, as it might change the background shape a little and
|
|
therefore influence how many signal and background events are
|
|
reconstructed from the data.
|
|
|
|
Fourth, the uncertainty on the luminosity influences the normalization
|
|
of the processes. Its value is 2.5 \% \autocite{LUMI_UNC}. \newpage
|
|
|
|
\hypertarget{results}{%
|
|
\section{Results}\label{results}}
|
|
|
|
This chapter will start by presenting the results for the partial
|
|
dataset of year 2016 with an integrated luminosity of
|
|
\(\SI{35.92}{\per\femto\barn}\) using both taggers and comparing it to
|
|
the previous research \autocite{PREV_RESEARCH}. It will then go on
|
|
showing the results for the combined dataset with an integrated
|
|
luminosity of \(\SI{137.19}{\per\femto\barn}\), again using both taggers
|
|
comparing their performances.
|
|
|
|
\hypertarget{partial-dataset}{%
|
|
\subsection{Partial dataset}\label{partial-dataset}}
|
|
|
|
Using the \(\SI{35.92}{\per\femto\barn}\) of data collected by the CMS
|
|
experiment during 2016, the cross section limits seen in
|
|
Fig.~\ref{fig:res2016} were obtained.
|
|
|
|
As described in Sec.~\ref{sec:extr}, the calculated cross section limits
|
|
are used to then calculate a mass limit, meaning the lowest possible
|
|
mass of the q* particle, by finding the crossing of the theory line with
|
|
the observed cross section limit. In Fig.~\ref{fig:res2016dw} it can be
|
|
seen, that the observed limit using the DeepAK8 tagger in the region
|
|
where theory and observed limit cross is very high compared to when
|
|
using the N-subjettiness tagger. Therefore the two lines cross at lower
|
|
resonance masses, which results in lower exclusion limits on the mass of
|
|
the q* particle causing the DeepAK8 tagger to perform worse than the
|
|
N-subjettiness tagger in regards of establishing those limits as can be
|
|
seen in Table~\ref{tbl:res2016}. The table also shows the upper and
|
|
lower limits on the mass found by calculating the crossing of the theory
|
|
plus resp. minus its uncertainty. Due to the theory and the observed
|
|
limits line being slowly falling in the high TeV region, even a small
|
|
uncertainty of the theory can cause a high difference of the mass limit.
|
|
|
|
\hypertarget{tbl:res2016}{}
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{\label{tbl:res2016}Mass limits found using the partial dataset
|
|
of \(\SI{35.92}{\per\femto\barn}\)}\tabularnewline
|
|
\toprule
|
|
Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
|
|
{[}TeV{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
|
|
{[}TeV{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
qW & \(\tau_{21}\) & 5.39 & 6.01 & 4.99\tabularnewline
|
|
qW & DeepAK8 & 4.96 & 5.19 & 4.84\tabularnewline
|
|
qZ & \(\tau_{21}\) & 4.86 & 4.96 & 4.70\tabularnewline
|
|
qZ & DeepAK8 & 4.62 & 4.71 & 4.49\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{figure}%
|
|
\centering
|
|
\subfloat[Decay to qW, using N-subjettiness tagger]{%
|
|
\label{fig:res2016tw}%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_2016tau_13TeV.pdf}}
|
|
\subfloat[Decay to qW, using DeepAK8 tagger]{%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_2016db_13TeV.pdf}%
|
|
\label{fig:res2016dw}}\\
|
|
\subfloat[Decay to qZ, using N-subjettiness tagger]{%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_2016tau_13TeV.pdf}%
|
|
\label{fig:res2016tz}}%
|
|
\subfloat[Decay to qZ, using DeepAK8 tagger]{%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf}%
|
|
\label{fig:res2016dz}}%
|
|
\caption{Results of the cross section limits for the partial dataset of 2016 using the $\tau_{21}$ tagger and the deep
|
|
boosted tagger.}
|
|
\label{fig:res2016}
|
|
\end{figure}
|
|
|
|
\hypertarget{comparison-with-existing-results}{%
|
|
\subsubsection{Comparison with existing
|
|
results}\label{comparison-with-existing-results}}
|
|
|
|
The result will now be compared to an existing result using the same
|
|
dataset. This research, however, uses a newer detector calibration as
|
|
well as an improved reconstruction so slight variations in the results
|
|
are to be expected.
|
|
|
|
The limit established by using the N-subjettiness tagger with the
|
|
partial dataset is \(\SI{0.39}{\tera\eV}\) (decay to qW) resp.
|
|
\(\SI{0.16}{\tera\eV}\) (decay to qZ) higher than the one from previous
|
|
research, which was found to be 5 TeV for the decay to qW and 4.7 TeV
|
|
for the decay to qZ. This is mainly due to the fact, that in our data,
|
|
the observed limit at the intersection point happens to be in the lower
|
|
region of the expected limit interval and therefore causing a very late
|
|
crossing with the theory line when using the N-subjettiness tagger (as
|
|
can be seen in Fig.~\ref{fig:res2016}). Comparing the expected limits,
|
|
there is a difference between 2 \% and 30 \%, between the values
|
|
calculated by this thesis compared to the previous research. It is not,
|
|
however, that one of the two results was constantly lower or higher but
|
|
rather fluctuating. As already noted, a slight variations in the results
|
|
was expected, therefore it can be said, that the results are in good
|
|
agreement. The cross section limits of the previous research can be seen
|
|
in Fig.~\ref{fig:prev}.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/prev_qW.png}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/prev_qZ.png}
|
|
\end{minipage}
|
|
\caption{Previous results of the cross section limits for q\* decaying to qW (left) and q\* decaying to qZ (right)
|
|
\cite{PREV_RESEARCH}.}
|
|
\label{fig:prev}
|
|
\end{figure}
|
|
|
|
\hypertarget{combined-dataset}{%
|
|
\subsection{Combined dataset}\label{combined-dataset}}
|
|
|
|
Using the full available dataset of \(\SI{137.19}{\per\femto\barn}\),
|
|
the cross section limits seen in Fig.~\ref{fig:resCombined} were
|
|
obtained. The cross section limits are, compared to only using the 2016
|
|
dataset, reduced to about 50 \%. This shows the big improvement achieved
|
|
by using more than three times the amount of data.
|
|
|
|
The results for the mass limits of the combined years are presented in
|
|
the following table.
|
|
|
|
\hypertarget{tbl:resCombined}{}
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{\label{tbl:resCombined}Mass limits found using
|
|
\(\SI{137.19}{\per\femto\barn}\) of data}\tabularnewline
|
|
\toprule
|
|
Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
|
|
{[}TeV{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
|
|
{[}TeV{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
qW & \(\tau_{21}\) & 6.00 & 6.26 & 5.74\tabularnewline
|
|
qW & DeepAK8 & 6.11 & 6.31 & 5.39\tabularnewline
|
|
qZ & \(\tau_{21}\) & 5.49 & 5.76 & 5.29\tabularnewline
|
|
qZ & DeepAK8 & 4.95 & 5.13 & 4.85\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
The combination of the three years not just improved the cross section
|
|
limits, but also the limit for the mass of the q* particle. The final
|
|
result is 1 TeV higher for the decay to qW and almost 0.8 TeV higher for
|
|
the decay to qZ than what was concluded by the previous research
|
|
\autocite{PREV_RESEARCH}.
|
|
|
|
\begin{figure}%
|
|
\centering
|
|
\subfloat[Decay to qW, using N-subjettiness tagger]{%
|
|
\label{fig:resCombinedtw}%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_Combinedtau_13TeV.pdf}}
|
|
\subfloat[Decay to qW, using DeepAK8 tagger]{%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_Combineddb_13TeV.pdf}%
|
|
\label{fig:resCombineddw}}\\
|
|
\subfloat[Decay to qZ, using N-subjettiness tagger]{%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_Combinedtau_13TeV.pdf}%
|
|
\label{fig:resCombinedtz}}%
|
|
\subfloat[Decay to qZ, using DeepAK8 tagger]{%
|
|
\includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf}%
|
|
\label{fig:resCombineddz}}%
|
|
\caption{Results of the cross section limits for the combined dataset using the $\tau_{21}$ tagger and the DeepAK8
|
|
tagger.}
|
|
\label{fig:resCombined}
|
|
\end{figure}
|
|
|
|
\hypertarget{comparison-of-taggers}{%
|
|
\subsection{Comparison of taggers}\label{comparison-of-taggers}}
|
|
|
|
The results presented in Table~\ref{tbl:res2016} show, that the DeepAK8
|
|
tagger was not able to significantly improve the results compared to the
|
|
N-subjettiness tagger. For further comparison, in
|
|
Fig.~\ref{fig:limit_comp} the expected limits of the different taggers
|
|
for the q* \(\rightarrow\) qW and the q* \(\rightarrow\) qZ decay are
|
|
shown. It can be seen, that the DeepAK8 is at best as good as the
|
|
N-subjettiness tagger. This was not the expected result, as the deep
|
|
neural network was already found to provide a higher significance in the
|
|
optimisation done in Sec.~\ref{sec:opt}. The higher significance should
|
|
also result in lower cross section limits. To make sure, there is no
|
|
mistake in the setup, also the expected cross section limits using only
|
|
the high purity category of the two taggers with 2018 data are compared
|
|
in Fig.~\ref{fig:comp_2018}. There, the cross section limits calculated
|
|
using the DeepAK8 tagger are a bit lower than with the N-subjettiness
|
|
tagger, showing, that the method used for optimisation is working but
|
|
the assumption of it also applying to the combined dataset did not hold.
|
|
|
|
This can be explained by some training issues identified lately. The
|
|
training of the DeepAK8 tagger was done for the data of year 2016. It
|
|
therefore performs differently for the data of the other years. This
|
|
caused the DeepAK8 tagger to perform significantly worse than it could
|
|
have for several reasons. First, the optimisation done for the data of
|
|
year 2018 could therefore not be applied to the other datasets. Second,
|
|
even for the data of 2016, a newer version of the background simulation
|
|
was used, that, in combination with the samples used for the signal,
|
|
turned out to be the worst case scenario for the used training.
|
|
Recently, the training was improved to better perform across all
|
|
datasets, but those changes could not be incorporated into this thesis
|
|
due to it not being possible to do this in a reasonable timeframe.
|
|
\newpage
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/limit_comp_w.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/limit_comp_z.pdf}
|
|
\end{minipage}
|
|
\caption{Comparison of expected limits of the different taggers using different datasets. Left: decay to qW. Right:
|
|
decay to qZ}
|
|
\label{fig:limit_comp}
|
|
\end{figure}
|
|
|
|
\begin{figure}
|
|
\hypertarget{fig:comp_2018}{%
|
|
\centering
|
|
\includegraphics[width=0.55\textwidth,height=\textheight]{./figures/limit_comp_2018.pdf}
|
|
\caption{Comparison of DeepAK8 and N-subjettiness tagger in the high
|
|
purity category using the data from year 2018.}\label{fig:comp_2018}
|
|
}
|
|
\end{figure}
|
|
|
|
\clearpage
|
|
\newpage
|
|
|
|
\hypertarget{summary}{%
|
|
\section{Summary}\label{summary}}
|
|
|
|
In this thesis, a search for the q* particle decaying to q + W and q + Z
|
|
was presented. Data of proton - proton collisions at the LHC of an
|
|
integrated luminosity of \(\SI{137.19}{\per\femto\barn}\) collected by
|
|
the CMS experiment at a centre-of-mass energy of
|
|
\(\sqrt{s} = \SI{13}{\tera\eV}\) has been searched. Also a partial
|
|
dataset of \(\SI{35.92}{\per\femto\barn}\) was analysed, to be able to
|
|
compare the results to previous research. Monte Carlo simulations were
|
|
used to model the QCD multijet background and signal shapes.
|
|
|
|
A selection was introduced to reduce background events and enhance
|
|
signal sensitivity. This selection required at least two jets, a
|
|
\(\Delta\eta \ge 1.3\) between the two highest \(p_t\) jets, an
|
|
invariant mass of the two highest \(p_t\) jets greater than
|
|
\(\SI{1050}{\giga\eV}\) and a soft-drop mass of at least one jet between
|
|
\(\SI{35}{\giga\eV}\) and \(\SI{105}{\giga\eV}\).
|
|
|
|
Two taggers, the DeepAK8 and the N-subjettiness tagger, have been used
|
|
to identify jets originating from the decay of a vector boson. For both
|
|
of them, two categories were introduced. A high purity category, aiming
|
|
for maximal signal sensitivity in the low TeV region of the invariant
|
|
mass spectrum and a low purity category, aiming for better statistics in
|
|
the high TeV region. For the DeepAK8 tagger, a high purity category of
|
|
\(VvsQCD > 0.95\) and a low purity category of \(VvsQCD \le 0.95\) was
|
|
used. For the N-subjettiness tagger the high purity category was
|
|
\(\tau_{21} < 0.35\) and the low purity category
|
|
\(0.35 < \tau_{21} < 0.75\). These values were obtained by optimising
|
|
for the highest possible significance of the signal.
|
|
|
|
A combined fit to the dijet invariant mass distribution of background
|
|
plus signal has been used to determine their shape parameters and the
|
|
expected signal rate. With those results, the cross section limits were
|
|
extracted from the data. Because no significant deviation from the
|
|
Standard Model was observed, new exclusion limits for the mass of the q*
|
|
particle were set. These are 6.1 TeV by analyzing the decay to qW,
|
|
respectively 5.5 TeV for the decay to qZ. Those limits are about 1 TeV
|
|
higher than the ones found in previous research, that found them to be 5
|
|
TeV resp. 4.7 TeV.
|
|
|
|
The performance of the two taggers used have been compared and found to
|
|
produce similar results. This was unexpected, as the DeepAK8 tagger was
|
|
supposed to perform better than the N-subjettiness tagger. The result
|
|
analysing the decay to qW was \(\SI{0.1}{\tera\eV}\) better using the
|
|
DeepAK8 than with the N-subjettiness tagger, but analysing the decay to
|
|
qZ it was \(\SI{0.5}{\tera\eV}\) worse. The performance of the DeepAK8
|
|
tagger is likely to significantly improve with an updated training that
|
|
was not yet available in the framework used by this thesis.
|
|
|
|
\newpage
|
|
|
|
\nocite{*}
|
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\printbibliography
|
|
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|
\newpage
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|
\appendix
|
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\hypertarget{expected-and-observed-cross-section-limits}{%
|
|
\section{Expected and observed cross section
|
|
limits}\label{expected-and-observed-cross-section-limits}}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using 2016 data and the N-subjettiness
|
|
tagger for the decay to qW}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.10 & 0.15 & 0.074 & 0.082\tabularnewline
|
|
1.8 & 0.077 & 0.11 & 0.054 & 0.041\tabularnewline
|
|
2.0 & 0.054 & 0.076 & 0.039 & 0.040\tabularnewline
|
|
2.5 & 0.024 & 0.034 & 0.017 & 0.041\tabularnewline
|
|
3.0 & 0.013 & 0.018 & 0.009 & 0.021\tabularnewline
|
|
3.5 & 0.0070 & 0.0099 & 0.005 & 0.004\tabularnewline
|
|
4.0 & 0.0042 & 0.0060 & 0.003 & 0.0017\tabularnewline
|
|
4.0 & 0.0042 & 0.0060 & 0.003 & 0.0017\tabularnewline
|
|
4.5 & 0.0035 & 0.0048 & 0.0027 & 0.0025\tabularnewline
|
|
5.0 & 0.0027 & 0.0036 & 0.0021 & 0.0024\tabularnewline
|
|
6.0 & 0.0010 & 0.0016 & 0.00068 & 0.00062\tabularnewline
|
|
7.0 & 0.00063 & 0.0010 & 0.00039 & 0.00086\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using 2016 data and the deep boosted
|
|
tagger for the decay to qW}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.18 & 0.25 & 0.13 & 0.38\tabularnewline
|
|
1.8 & 0.11 & 0.16 & 0.078 & 0.12\tabularnewline
|
|
2.0 & 0.082 & 0.12 & 0.058 & 0.095\tabularnewline
|
|
2.5 & 0.033 & 0.047 & 0.024 & 0.037\tabularnewline
|
|
3.0 & 0.016 & 0.023 & 0.012 & 0.011\tabularnewline
|
|
3.5 & 0.0084 & 0.012 & 0.0059 & 0.0068\tabularnewline
|
|
4.0 & 0.0046 & 0.0067 & 0.0032 & 0.0034\tabularnewline
|
|
4.5 & 0.0028 & 0.0041 & 0.0019 & 0.0037\tabularnewline
|
|
5.0 & 0.0018 & 0.0027 & 0.0012 & 0.0040\tabularnewline
|
|
6.0 & 0.0011 & 0.0017 & 0.00071 & 0.0016\tabularnewline
|
|
7.0 & 0.00065 & 0.0011 & 0.00041 & 0.0011\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using 2016 data and the N-subjettiness
|
|
tagger for the decay to qZ}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.087 & 0.12 & 0.062 & 0.07\tabularnewline
|
|
1.8 & 0.067 & 0.095 & 0.048 & 0.034\tabularnewline
|
|
2.0 & 0.047 & 0.066 & 0.034 & 0.033\tabularnewline
|
|
2.5 & 0.019 & 0.026 & 0.013 & 0.032\tabularnewline
|
|
3.0 & 0.010 & 0.015 & 0.0074 & 0.018\tabularnewline
|
|
3.5 & 0.0060 & 0.0084 & 0.0043 & 0.0035\tabularnewline
|
|
4.0 & 0.0035 & 0.0050 & 0.0025 & 0.0014\tabularnewline
|
|
4.5 & 0.0023 & 0.0034 & 0.0016 & 0.0018\tabularnewline
|
|
5.0 & 0.0016 & 0.0023 & 0.0011 & 0.0019\tabularnewline
|
|
6.0 & 0.00082 & 0.0013 & 0.00054 & 0.00049\tabularnewline
|
|
7.0 & 0.00050 & 0.00083 & 0.00031 & 0.00066\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using 2016 data and deep boosted tagger
|
|
for the decay to qZ}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.15 & 0.22 & 0.11 & 0.33\tabularnewline
|
|
1.8 & 0.10 & 0.14 & 0.072 & 0.085\tabularnewline
|
|
2.0 & 0.077 & 0.11 & 0.056 & 0.064\tabularnewline
|
|
2.5 & 0.027 & 0.038 & 0.019 & 0.041\tabularnewline
|
|
3.0 & 0.015 & 0.021 & 0.010 & 0.0087\tabularnewline
|
|
3.5 & 0.0084 & 0.012 & 0.006 & 0.0066\tabularnewline
|
|
4.0 & 0.0049 & 0.0071 & 0.0035 & 0.0045\tabularnewline
|
|
4.5 & 0.0032 & 0.0046 & 0.0022 & 0.0026\tabularnewline
|
|
5.0 & 0.0022 & 0.0033 & 0.0015 & 0.0041\tabularnewline
|
|
6.0 & 0.0012 & 0.0019 & 0.00081 & 0.0018\tabularnewline
|
|
7.0 & 0.00057 & 0.00092 & 0.00037 & 0.00093\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using the combined data and the
|
|
N-subjettiness tagger for the decay to qW}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.057 & 0.08 & 0.041 & 0.034\tabularnewline
|
|
1.8 & 0.040 & 0.056 & 0.028 & 0.043\tabularnewline
|
|
2.0 & 0.028 & 0.040 & 0.020 & 0.048\tabularnewline
|
|
2.5 & 0.013 & 0.018 & 0.0091 & 0.015\tabularnewline
|
|
3.0 & 0.0066 & 0.0092 & 0.0047 & 0.012\tabularnewline
|
|
3.5 & 0.0038 & 0.0053 & 0.0027 & 0.0047\tabularnewline
|
|
4.0 & 0.0022 & 0.0031 & 0.0016 & 0.0011\tabularnewline
|
|
4.5 & 0.0013 & 0.0019 & 0.00094 & 0.00068\tabularnewline
|
|
5.0 & 0.00084 & 0.0012 & 0.00060 & 0.00059\tabularnewline
|
|
6.0 & 0.00044 & 0.00066 & 0.00030 & 0.00041\tabularnewline
|
|
7.0 & 0.00022 & 0.00036 & 0.00014 & 0.00043\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using the combined data and the deep
|
|
boosted tagger for the decay to qW}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.067 & 0.095 & 0.047 & 0.12\tabularnewline
|
|
1.8 & 0.043 & 0.061 & 0.030 & 0.054\tabularnewline
|
|
2.0 & 0.033 & 0.047 & 0.024 & 0.047\tabularnewline
|
|
2.5 & 0.013 & 0.019 & 0.0095 & 0.011\tabularnewline
|
|
3.0 & 0.0065 & 0.0092 & 0.0046 & 0.0050\tabularnewline
|
|
3.5 & 0.0034 & 0.0048 & 0.0024 & 0.0041\tabularnewline
|
|
4.0 & 0.0018 & 0.0026 & 0.0013 & 0.0013\tabularnewline
|
|
4.5 & 0.0011 & 0.0016 & 0.00074 & 0.0012\tabularnewline
|
|
5.0 & 0.00068 & 0.0010 & 0.00046 & 0.0015\tabularnewline
|
|
6.0 & 0.00038 & 0.00060 & 0.00024 & 0.00034\tabularnewline
|
|
7.0 & 0.00021 & 0.00035 & 0.00013 & 0.00046\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using the combined data and the
|
|
N-subjettiness tagger for the decay to qZ}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.051 & 0.072 & 0.037 & 0.030\tabularnewline
|
|
1.8 & 0.035 & 0.050 & 0.026 & 0.036\tabularnewline
|
|
2.0 & 0.025 & 0.035 & 0.018 & 0.042\tabularnewline
|
|
2.5 & 0.011 & 0.015 & 0.0076 & 0.012\tabularnewline
|
|
3.0 & 0.0058 & 0.0081 & 0.0041 & 0.011\tabularnewline
|
|
3.5 & 0.0033 & 0.0046 & 0.0023 & 0.0042\tabularnewline
|
|
4.0 & 0.0019 & 0.0027 & 0.0014 & 0.00097\tabularnewline
|
|
4.5 & 0.0012 & 0.0017 & 0.00084 & 0.00059\tabularnewline
|
|
5.0 & 0.00077 & 0.0011 & 0.00054 & 0.00051\tabularnewline
|
|
6.0 & 0.00039 & 0.00057 & 0.00026 & 0.00036\tabularnewline
|
|
7.0 & 0.00019 & 0.00031 & 0.00013 & 0.00036\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Cross Section limits using the combined data and deep boosted
|
|
tagger for the decay to qZ}\tabularnewline
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endfirsthead
|
|
\toprule
|
|
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
|
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
|
\midrule
|
|
\endhead
|
|
1.6 & 0.067 & 0.095 & 0.047 & 0.095\tabularnewline
|
|
1.8 & 0.044 & 0.063 & 0.032 & 0.048\tabularnewline
|
|
2.0 & 0.032 & 0.045 & 0.023 & 0.045\tabularnewline
|
|
2.5 & 0.012 & 0.017 & 0.0088 & 0.013\tabularnewline
|
|
3.0 & 0.0064 & 0.009 & 0.0046 & 0.0032\tabularnewline
|
|
3.5 & 0.0036 & 0.0051 & 0.0026 & 0.0039\tabularnewline
|
|
4.0 & 0.0021 & 0.0029 & 0.0015 & 0.0027\tabularnewline
|
|
4.5 & 0.0013 & 0.0018 & 0.00088 & 0.00094\tabularnewline
|
|
5.0 & 0.00083 & 0.0012 & 0.00057 & 0.00150\tabularnewline
|
|
6.0 & 0.00046 & 0.00072 & 0.00031 & 0.00043\tabularnewline
|
|
7.0 & 0.00023 & 0.00037 & 0.00015 & 0.00049\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\newpage
|
|
\section*{Erklärung}
|
|
|
|
Hiermit bestätige ich, dass die vorliegende Bachelorarbeit von mir
|
|
selbstständig verfasst wurde und ich keine anderen als die angegebenen
|
|
Hilfsmittel - insbesondere keine im Quellenverzeichnis nicht benannten
|
|
Internet-Quellen - benutzt habe. Die Arbeit wurde bisher weder gesamt
|
|
noch in Teilen einer anderen Prüfungsbehörde vorgelegt. Die eingereichte
|
|
schriftliche Fassung entspricht der auf dem elekronischen
|
|
Speichermedium. Ich bin damit einverstanden, dass die Bachelorarbeit
|
|
veröffentlicht wird.
|
|
|
|
\vspace{5cm}
|
|
|
|
\parbox{5cm}{\hrule
|
|
\strut \footnotesize Ort, Datum} \hspace{1cm}\parbox{5cm}{\hrule
|
|
\strut \footnotesize David Leppla-Weber}
|
|
|
|
\end{document}
|