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\hypersetup{
  pdftitle={Search for excited quark states decaying to qW/qZ},
  pdfauthor={David Leppla-Weber},
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  hidelinks,
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\title{Search for excited quark states decaying to qW/qZ}
\author{David Leppla-Weber}
\date{}

\begin{document}
\maketitle
\begin{abstract}
This is my very long abstract.

Blubb
\end{abstract}

{
\setcounter{tocdepth}{3}
\tableofcontents
}
\newpage
\pagenumbering{arabic}

\hypertarget{introduction}{%
\section{Introduction}\label{introduction}}

\newpage

\hypertarget{theoretical-background}{%
\section{Theoretical background}\label{theoretical-background}}

This chapter presents a short summary of the theoretical background
relevant to this thesis. It first gives introduction to the standard
model itself and some of the issues it raises. It then goes on to
explain the processes of quantum chromodynamics and the theory of q*,
which will be the main topic of this thesis.

\hypertarget{standard-model}{%
\subsection{Standard model}\label{standard-model}}

The Standard Model of physics proofed very successful in describing
three of the four fundamental interactions currently known: the
electromagnetic, weak and strong interaction. The fourth, gravity, could
not yet be successfully included in this theory.

The Standard Model divides all particles into spin-\(\frac{n}{2}\)
fermions and spin-n bosons, where n could be any integer but so far is
only known to be one for fermions and either one (gauge bosons) or zero
(scalar bosons) for bosons. The fermions are further divided into quarks
and leptons, both of which exist in three generations.

\begin{itemize}
\tightlist
\item
  issues
\end{itemize}

\hypertarget{quantum-chromodynamics}{%
\subsection{Quantum Chromodynamics}\label{quantum-chromodynamics}}

The quantum chromodynamics (QCD) describe the strong interaction of
particles. It applies to all particles carrying colour (e.g.~quarks).
The force is mediated by the gluons. Those bosons carry colour as well
and can therefore interact with themselves. As a result of this,
processes, where a gluon decays into two gluons are possible.
Furthermore the strong force, binding to colour carrying particles,
increases with their distance r making it impossible to separate two
bound particles and causing the effect of hadronisation, which describes
the process of hadrons forming out of individual, colour carrying,
particles.

\hypertarget{excited-quark-states}{%
\subsection{Excited quark states}\label{excited-quark-states}}

One category of theories that try to solve some of the shortcomings of
the standard model are the composite quark models. Those state, that
quarks consist of some particles unknown to us so far. A common
prediction of those models are excited quark states (q*, q**,
q***\ldots). This thesis will search data of the years 2016, 2017 and
2018 for the single excited quark state q* which decays to a quark and
any boson. As the boson will also quickly decay to for example two
quarks, those events will be hard to distinguish from the QCD background
described in \ldots.

\feynmandiagram [horizontal=a to b] {
  i1 -- [fermion] a -- [fermion] i2,
  a -- [photon] b,
  f1 -- [fermion] b -- [fermion] f2,
};

\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 is the world's largest and most powerful
particle accelerator \autocite{website}. It has a perimeter of 27 km and
can collide protons at a centre of mass energy of 13 TeV. It is home to
several experiments, the biggest of those are ATLAS and CMS. Both are
general-purpose detectors to investigate the particles that form during
particle collisions.

\hypertarget{cms}{%
\subsection{CMS}\label{cms}}

\hypertarget{the-particle-flow-algorithm}{%
\subsubsection{The Particle Flow
algorithm}\label{the-particle-flow-algorithm}}

\hypertarget{jet-clustering}{%
\subsubsection{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-\(k_t\) 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 hard particles with
their soft 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. A softer particles jet will
change its shape more than a harder particles. A visual comparision of
four different clustering algorithms can be seen in \ldots.

\hypertarget{method-of-analysis}{%
\section{Method of analysis}\label{method-of-analysis}}

As described in \ldots, an excited quark q* can decay to a quark and any
boson. The branching ratios are calculated to be as follows:

The majority of excited quarks will decay to a quark and a gluon, but as
this is virtually impossible to distinguish from QCD effects (for
example from the qg-\textgreater qg processes), this analysis will focus
on the processes q\emph{-\textgreater qW and q}-\textgreater qZ. As the
vector bosons quickly decay mainly into two quarks, it will still be
hard to discriminate between signal and qcd background events, but due
to jet substructure studies it is well possible to establish a
discriminator.

\begin{itemize}
\tightlist
\item
  dominant background: QCD (gg-gg e.g.~- two jets)
\item
  division in QCD bg and signal
\end{itemize}

\hypertarget{signalbackground-modelling}{%
\subsection{Signal/Background
modelling}\label{signalbackground-modelling}}

Following on, as background a QCD Monte Carlo sample will be used and as
signal a Monte Carlo sample of q* decaying to qW/qZ.

The background is fitted using the following 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. Two and four parameter functions have also been
studied but found to not fit the background as good as this one.

The signal is fitted using a double sided crystal ball function. A
gaussian and a poisson have also been studied but found to not fit the
signal sample very well.

\hypertarget{event-selection}{%
\section{Event selection}\label{event-selection}}

The selection of events is divided in two parts. First, the preselection
is optimized for high trigger efficiency and makes some physically
motivated cuts. After that, a jet substructure selection uses different
taggers to discriminate between QCD and signal events.

\hypertarget{preselection}{%
\subsection{Preselection}\label{preselection}}

The preselection introduces the following cuts:

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  Number of jets \(\ge\) 2
\item
  \(\Delta\eta \le 1.3\)
\item
  \(m_{jj} \ge \SI{1050}{\giga\eV}\)
\end{enumerate}

In the final state, at least two jets are expected. One directly
originating from the decaying q* particle, the other one from the
decaying vector boson. The resonance mass of the q* particle is expected
to be very high, therefore it will be almost stationary and decay into
two particles that are approximately back to back. That is ensured by
the \(\Delta\eta\) cut. The last cut of the invariant dijet mass is to
improve trigger efficiency.

\hypertarget{datamc-comparision}{%
\subsection{Data/MC Comparision}\label{datamc-comparision}}

To ensure high data quality, the MC QCD background sample is now being
compared to the actual data of the corresponding data. This is done for
all three years of data available in Run2.

\hypertarget{event-substructure-selection}{%
\section{Event substructure
selection}\label{event-substructure-selection}}

This selection is responsible for distinguishing between QCD and signal
events by using a tagger to identify jets coming from a vector boson.
Two taggers different taggers will be used to later compare the results.
For each tagger, a softdropmass is introduced.

\hypertarget{sideband}{%
\subsection{Sideband}\label{sideband}}

The sideband is introduced to make sure there are no unwanted side
effects of the used cut. It adds a cut, that makes sure, no data in the
sideband is used for the actual analysis. Later on, a cut on the
softdropmass will be used. The sideband is the softdropmass cut
reversed.

\hypertarget{n-subjettiness}{%
\subsection{N-Subjettiness}\label{n-subjettiness}}

The N-subjettiness \(\tau_n\) 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
rapidity-azimuth plane. It has been shown, that
\(\tau_{21} = \tau_2/\tau_1\) is a good discriminator between QCD events
and events originating from the decay of a boosted vector boson.

\hypertarget{deepboosted}{%
\subsection{DeepBoosted}\label{deepboosted}}

The deep boosted tagger uses a trained neural network to identify decays
originitating in a vector boson. It is supposed to give better
efficiencies than the older N-Subjettiness method.

\hypertarget{optimization}{%
\subsection{Optimization}\label{optimization}}

To figure out the best value to cut on the discriminators 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 where enough background events exist
to justify this assumption. The value therefore 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
masspoint is chosen.

As a result, the \(\tau_{21}\) cut is placed at \(\le 0.35\) and the
VvsQCD cut is placed at \(\ge 0.83\).

\hypertarget{signal-extraction}{%
\section{Signal extraction}\label{signal-extraction}}

\hypertarget{uncertainties}{%
\subsection{Uncertainties}\label{uncertainties}}

\hypertarget{results}{%
\section{Results}\label{results}}

\hypertarget{section}{%
\subsection{2016}\label{section}}

\hypertarget{previous-research}{%
\subsubsection{previous research}\label{previous-research}}

\hypertarget{section-1}{%
\subsection{2016 + 2017 + 2018}\label{section-1}}

\printbibliography[title=Summary]

\end{document}