1766 lines
79 KiB
TeX
1766 lines
79 KiB
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pdftitle={Search for excited quark states decaying to qW/qZ},
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\title{Search for excited quark states decaying to qW/qZ}
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\author{David Leppla-Weber}
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\date{}
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\begin{document}
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\maketitle
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\begin{abstract}
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A search for an excited quark state, called q*, is presented using data
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recorded by the CMS experiment during the years 2016, 2017 and 2018 with
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a centre-of-mass energy of \(\sqrt{s} = \SI{13}{\tera\eV}\) and a total
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integrated luminosity of \(\SI{137.19}{\per\femto\barn}\). By analysing
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its decay channels to q + W and q + Z that further decay to
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\(q + q\bar{q}\), resulting in two jets in the final state, the q* can
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be excluded up to a mass of 6.1 (qW) TeV resp. 5.5 TeV (qZ) with a
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confidence level of 95 \%. This limit is about 1 TeV higher than the
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limits found by a previous research of data collected by CMS in 2016
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\autocite{PREV_RESEARCH}, excluding the q* particle up to a mass of 5.0
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TeV resp. 4.7 TeV. Also a comparison of the new DeepAK8
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\autocite{DEEP_BOOSTED} and the older N-subjettiness \autocite{TAU21}
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tagger is conducted, showing that the newer DeepAK8 tagger, based on a
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deep neural network, is currently approximately at the same level as the
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N-subjettiness tagger, giving a \(\SI{0.1}{\tera\eV}\) better result for
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the decay to qW but a by \(\SI{0.6}{\tera\eV}\) worse one for the decay
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to qZ. It still has the potential to further improve in performance,
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between others because of an improved training.
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\end{abstract}
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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
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q*, durchgeführt. Dafür werden Daten mit einer gesamten integrierten
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Luminosität von \(\SI{137.19}{\per\femto\barn}\) analysiert, welche über
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die Jahre 2016, 2017 und 2018 bei einer Schwerpunktsenergie von
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\(\sqrt{s} = \SI{13}{\tera\eV}\) vom CMS Experiment aufgenommen wurden.
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Indem der Zerfall des q* Teilchens zu q + W und q + Z untersucht wird,
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kann dieses mit einem Konfidenzniveau von 95 \% bis zu einer Masse von
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6.1 TeV (qW) bzw. 5.5 TeV (qZ) ausgeschlossen werden. Dieses Limit liegt
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etwa 1 TeV höher, als das anhand der Daten von 2016 gefundene von 5.0
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TeV bzw. 4.7 TeV \autocite{PREV_RESEARCH}. Dabei wird der neue DeepAK8
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Tagger \autocite{DEEP_BOOSTED}, welcher auf einem neuronalen Netzwerk
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basiert, mit dem älteren N-Subjetiness Tagger \autocite{TAU21}
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verglichen. Beim Zerfall zu qW erzielt er ein um \(\SI{0.1}{\tera\eV}\)
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besseres Ergebnis, beim Zerfall zu qZ jedoch ein um
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\(\SI{0.6}{\tera\eV}\) schlechteres. Mit einem verbesserten Training,
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welches vor kurzem veröffentlicht wurde, gibt es aber noch Potential,
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die Leistung zu steigern. \newpage
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\end{abstract}
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{
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\setcounter{tocdepth}{3}
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\tableofcontents
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}
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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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shortcomings 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}, a lower limit for the
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mass of an excited quark has already been set using data from the 2016
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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, totalling to \(\SI{137.19}{\per\femto\barn}\) of data usable
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for research. This thesis uses this new data 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 explaining in
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short the Standard Model, its shortcomings and the theory of excited
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quarks. Then, in chapter 3, the Large Hadron Collider and the Compact
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Muon Solenoid, the detector that collected the data for this analysis,
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will be described. After that, in chapters 4-7, the main analysis part
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follows, describing how the data was used to extract limits on the mass
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of the excited quark particle. At the very end, in chapter 8, the
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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 will be the main topic of 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 lepton and its
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corresponding neutrino, namely first the electron, then the muon and
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third, the tau. The three quark generations consist of first, the up and
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down, second, the charm and strange, and third, the top and bottom
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quark. So overall, their exists a total of six quark and six lepton
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flavours. A full list of particles of the standard model can be found in
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Fig.~\ref{fig:sm}. Furthermore, all fermions have an associated anti
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particle with reversed charge. Bound states of multiple quarks also
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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.}\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. Only the weak
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interaction breaks this conservation, a quark or lepton can therefore,
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by interacting with a \(W^\pm\) boson, change its flavour. The
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probabilities of this happening are determined by the
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|
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} The probability of a quark changing its flavour from
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\(i\) to \(j\) is given by the square of the absolute value of the
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matrix element \(V_{ij}\). It is easy to see, that the change of flavour
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in the same 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 essentially 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 to 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
|
|
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.
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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
|
|
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
|
|
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
|
|
\(10^{24}\) times stronger than gravity and so far, there's no
|
|
satisfactory explanation as to why that is.
|
|
\end{itemize}
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|
|
|
\hypertarget{sec:qs}{%
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|
\subsection{Excited quark states}\label{sec:qs}}
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|
|
|
One category of theories that try to explain the symmetries between
|
|
particles of the standard model are the composite quark models. Those
|
|
state, that quarks consist of some particles unknown so far. This could
|
|
explain the symmetries between the different fermions. A common
|
|
prediction of those models are excited quark states (q*, q**,
|
|
q***\ldots). Similar to atoms, that can be excited by the absorption of
|
|
a photon and can then decay again under emission of a photon with an
|
|
energy corresponding to the excited state, those excited quark states
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|
could decay under the emission of any boson. Quarks are measured to be
|
|
smaller than \(10^{-18}\) m. This corresponds to an energy scale of
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|
approximately 1 TeV. Therefore the excited quark states are expected to
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|
be in that region. That will cause the emitted boson to be highly
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boosted.
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|
\begin{figure}
|
|
\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}
|
|
\end{figure}
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|
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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
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|
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
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|
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
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|
bosons is motivated by the branching ratios calculated for the decay
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|
\autocite{QSTAR_THEORY}:
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|
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|
\begin{longtable}[]{@{}llll@{}}
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|
\caption{Branching ratios of the decaying q* particle.}\tabularnewline
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|
\toprule
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decay mode & br. ratio {[}\%{]} & decay mode & br. ratio
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{[}\%{]}\tabularnewline
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|
\midrule
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|
\endfirsthead
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\toprule
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decay mode & br. ratio {[}\%{]} & decay mode & br. ratio
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{[}\%{]}\tabularnewline
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|
\midrule
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|
\endhead
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|
\(U^* \rightarrow ug\) & 83.4 & \(D^* \rightarrow dg\) &
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83.4\tabularnewline
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|
\(U^* \rightarrow dW\) & 10.9 & \(D^* \rightarrow uW\) &
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|
10.9\tabularnewline
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|
\(U^* \rightarrow u\gamma\) & 2.2 & \(D^* \rightarrow d\gamma\) &
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0.5\tabularnewline
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|
\(U^* \rightarrow uZ\) & 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 obvious 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.
|
|
|
|
This theory has already been investigated in \autocite{PREV_RESEARCH}
|
|
analysing data recorded by CMS 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 the higher center of mass energy of the LHC as well as 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 25 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, the biggest of those are ATLAS and the
|
|
Compact Muon Solenoid (CMS). Both are general-purpose detectors 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
|
|
\(\SI{63.67}{\per\femto\barn}\). Because of eventual inconsistencies in
|
|
the setup, some data have to be discarded. The amount of usable data is
|
|
\(\SI{34.92}{\per\femto\barn}\), \(\SI{41.53}{\per\femto\barn}\) 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 has to be 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. Taken from
|
|
https://inspirehep.net/record/1236817/plots}\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
|
|
reconstruct the tracks of charged particles, measuring their charge
|
|
sign, direction and momentum. 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 are of higher energy 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 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 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 of the CMS. 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 detection 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.
|
|
After identifying charged hadrons, muons and electrons, all remaining
|
|
clusters within the HCAL correspond to neutral hadrons and within ECAL
|
|
to photons. If 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-\(k_t\) 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}. Taken from
|
|
\autocite{ANTIKT}}\label{fig:antiktcomparison}
|
|
}
|
|
\end{figure}
|
|
|
|
Furthermore, to approximate the mass of a heavy particle that caused a
|
|
jet, the soft-drop mass can be used. It is calculated by removing wide
|
|
angle soft particles from the jet to counter the effects of
|
|
contamination from initial state radiation, underlying event and
|
|
multiple hadron scattering. 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 the LHC
|
|
and 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, which is identical to the mass of the q*
|
|
particle, is reconstructed. The only background considered is the QCD
|
|
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 with two different sets of data. First,
|
|
only the data collected by CMS in 2016 will be used to compare the
|
|
results to the previous analysis \autocite{PREV_RESEARCH}. Then the
|
|
combined data from 2016, 2017 and 2018 will be used to improve the
|
|
previously set limits for the mass of the q* particle. Also, two
|
|
different V-tagging mechanisms 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}}
|
|
|
|
To make sure the setup is working as intended, at first simulated
|
|
samples of background and signal are used. In those Monte Carlo
|
|
simulations, 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. 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 \(\SI{1}{\per\pico\barn}\). The simulation
|
|
was done using MadGraph. 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.
|
|
|
|
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 and a simulated signal
|
|
cross section of \(\SI{1}{\per\pico\barn}\). The resulting coefficients
|
|
of said combination then show the expected signal rate for the simulated
|
|
cross section. 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
|
|
the actual analysis a 1 GeV binning will be used. 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 extremely close to the expected 3000 GeV mean. Those numbers
|
|
clearly show that the method in use is able to successfully describe the
|
|
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 by different variables is introduced. It is divided
|
|
into two stages. The first one (the preselection) adds some general
|
|
physics motivated selections using kinematic variables and is also used
|
|
to ensure a high trigger efficiency. In the second part, the
|
|
discriminators 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 results in studies of the semi or
|
|
all-leptonic decay channels.
|
|
|
|
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}.
|
|
|
|
\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}
|
|
\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 \(\Delta\eta\) as they mainly
|
|
form from less heavy resonances. To maintain comparability, the same
|
|
selection as in previous research of \(\Delta\eta \le 1.3\) is used. A
|
|
comparison of the \(\Delta\eta\) distribution before and after the
|
|
selection can be seen in Fig.~\ref{fig:deta}.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{\textwidth}
|
|
\centering\textbf{Comparison for 2016}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Njet_deta_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/2016/v1_Eta_deta_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_Njet_deta_stack.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/combined/v1_Eta_deta_stack.eps}
|
|
\end{minipage}
|
|
\caption{Comparison of the $\Delta\eta$ distribution before and after the cut at $\Delta\eta \le 1.3$. \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: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 its 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, wheres 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 high data quality, 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 year 2016 and for the combined
|
|
dataset. In Fig.~\ref{fig:data-mc}, this comparison can be seen for the
|
|
distributions of the variables used during the preselection. 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, 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 published by the CMS group. {[}cite todo{]}
|
|
|
|
\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}{%
|
|
\subsubsection{Sideband}\label{sideband}}
|
|
|
|
The sideband region is introduced to make sure no bias in the data and
|
|
Monte Carlo simulation is introduced. 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. As in
|
|
Fig.~\ref{fig:data-mc}, the histograms are rescaled, so that the dijet
|
|
invariant mass distributions of data and simulation have the same
|
|
integral. 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
|
|
\(\SI{34}{\giga\eV}\) 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 discriminator value to choose whether an event
|
|
originates in the decay of a vector boson or from QCD effects. This
|
|
value will be optimized afterwards to make sure the maximum efficiency
|
|
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 because of the high mass of the vector bosons, the particles
|
|
are highly boosted and appear, after applying a clustering algorithm, as
|
|
just one. 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. Experiments showed, that
|
|
rather than using \(\tau_N\) directly, the ratio
|
|
\(\tau_{21} = \tau_2/\tau_1\) is a better discriminator between QCD
|
|
events 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 optimization 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 claims to
|
|
reduce 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 supported by
|
|
Fig.~\ref{fig:ak8_eff}, showing a comparison of background and signal
|
|
efficiency of the DeepAK8-MD (MD being short for mass decorrelated)
|
|
tagger, with, between others, the \(\tau_{20}\) tagger that are 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-MD (which stands for mass decorrelated and is the one used for
|
|
this research) and \(\tau_{21}\) tagger used in this analysis. Taken
|
|
from \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 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. As the mass variable is already in use for
|
|
the soft-drop mass selection, this version of the tagger is to be
|
|
preferred.
|
|
|
|
The higher the discriminator value, called WvsQCD resp. ZvsQCD, of the
|
|
deep boosted 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 WvsQCD/ZvsQCD value greater than some
|
|
value determined by the optimization presented next.
|
|
|
|
\hypertarget{sec:opt}{%
|
|
\subsection{Optimization}\label{sec:opt}}
|
|
|
|
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. It follows from the central limit theorem
|
|
that states, that for identical distributed random variables, their sum
|
|
converges to a gaussian distribution. The significance 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 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 deep
|
|
boosted resp. the N-subjettiness tagger.
|
|
|
|
The optimization 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 deep boosted (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 deep boosted 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. The
|
|
significance for the \(\tau_{21}\) cut is 14, and for the deep boosted
|
|
tagger 26.
|
|
|
|
For both taggers also a low purity category is introduced for high TeV
|
|
regions. 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. As low purity category
|
|
for the N-subjettiness tagger, a cut at \(0.35 < \tau_{21} < 0.75\) is
|
|
used. For the deep boosted tagger the opposite cut from the high purity
|
|
category is used: \(VvsQCD < 0.95\).
|
|
|
|
\hypertarget{sec:extr}{%
|
|
\section{Signal extraction}\label{sec:extr}}
|
|
|
|
After the optimization, now the optimal selection for the N-subjettiness
|
|
as well as the deep boosted tagger is found and applied to the simulated
|
|
samples as well as the data collected by the CMS. The fit described in
|
|
Sec.~\ref{sec:moa} is performed for all masspoints of the decay to qW
|
|
and qZ and for both datasets used, the one from 2016 und the combined
|
|
one of years 2016, 2017 and 2018.
|
|
|
|
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 calculator 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 on the data recorded by
|
|
the CMS, 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 \%.
|
|
|
|
If there's no resonance of the q* particle in the data, the observed
|
|
limit should 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.
|
|
The crossing of the theory line with the observed limit is then
|
|
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{uncertainties}{%
|
|
\subsection{Uncertainties}\label{uncertainties}}
|
|
|
|
For calculating the cross section of the signal, four sources of
|
|
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 is not perfect 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 of the LHC of 2.5 \% is also
|
|
taken into account for the final results.
|
|
|
|
\hypertarget{results}{%
|
|
\section{Results}\label{results}}
|
|
|
|
This chapter will start by presenting the results for the data of year
|
|
2016 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, again using both taggers comparing their performances.
|
|
|
|
\hypertarget{section}{%
|
|
\subsection{2016}\label{section}}
|
|
|
|
Using the data collected by the CMS experiment on 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:res2016} it can be
|
|
seen, that the observed limit 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 earlier, which results in lower
|
|
exclusion limits on the mass of the q* particle causing the deep boosted
|
|
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 very flat 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 data collected
|
|
in 2016}\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 & deep boosted & 4.96 & 5.19 & 4.84\tabularnewline
|
|
qZ & \(\tau_{21}\) & 4.86 & 4.96 & 4.70\tabularnewline
|
|
qZ & deep boosted & 4.49 & 4.61 & 4.40\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqW_2016tau_13TeV.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqW_2016db_13TeV.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqZ_2016tau_13TeV.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf}
|
|
\end{minipage}
|
|
\caption{Results of the cross section limits for 2016 using the $\tau_{21}$ tagger (left) and the deep boosted tagger
|
|
(right).}
|
|
\label{fig:res2016}
|
|
\end{figure}
|
|
|
|
\hypertarget{previous-research}{%
|
|
\subsubsection{Previous research}\label{previous-research}}
|
|
|
|
The limit established by using the N-subjettiness tagger on the 2016
|
|
data is already slightly 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. This is likely caused by a newer detector
|
|
calibration as well as updated reconstruction algorithms used for this
|
|
analysis. 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).
|
|
Taken from \cite{PREV_RESEARCH}.}
|
|
\label{fig:prev}
|
|
\end{figure}
|
|
|
|
\hypertarget{combined-dataset}{%
|
|
\subsection{Combined dataset}\label{combined-dataset}}
|
|
|
|
Using the combined data, the cross section limits seen in
|
|
Fig.~\ref{fig:resCombined} were obtained. The cross section limits are,
|
|
compared to only using the 2016 dataset, almost cut in half. 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 as follows:
|
|
|
|
\begin{longtable}[]{@{}lllll@{}}
|
|
\caption{Mass limits found using the data collected in 2016 -
|
|
2018}\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 & deep boosted & 6.11 & 6.31 & 5.39\tabularnewline
|
|
qZ & \(\tau_{21}\) & 5.49 & 5.76 & 5.29\tabularnewline
|
|
qZ & deep boosted & 4.92 & 5.02 & 4.80\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}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqW_Combinedtau_13TeV.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqW_Combineddb_13TeV.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqZ_Combinedtau_13TeV.pdf}
|
|
\end{minipage}
|
|
\begin{minipage}{0.5\textwidth}
|
|
\includegraphics{./figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf}
|
|
\end{minipage}
|
|
\caption{Results of the cross section limits for the three combined years using the $\tau_{21}$ tagger (left) and the
|
|
deep boosted tagger (right).}
|
|
\label{fig:resCombined}
|
|
\end{figure}
|
|
|
|
\hypertarget{comparison-of-taggers}{%
|
|
\subsection{Comparison of taggers}\label{comparison-of-taggers}}
|
|
|
|
The previously shown results already show, that the deep boosted 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 deep boosted 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. Apparently, doing the
|
|
optimization only on data of the year 2018, was not a good choice. 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 deep boosted tagger are a bit
|
|
lower than with the N-subjettiness tagger, showing, that the method used
|
|
for optimisation was working but should have been applied to the
|
|
combined dataset.
|
|
|
|
Recently, some issues with the training of the deep boosted tagger used
|
|
in this analysis were also found, which might explain, why it didn't
|
|
perform better in general.
|
|
|
|
\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=0.6\textwidth,height=\textheight]{./figures/limit_comp_2018.pdf}
|
|
\caption{Comparision of deep boosted 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 limit on the mass of the q* particle has been
|
|
successfully established. This was done searching for its decay to qW
|
|
and qW with the vector boson then decaying hadronically. By combining
|
|
the data from the years 2016, 2017 and 2018, collected by the CMS
|
|
experiment, the previously set limit could be significantly improved.
|
|
|
|
For the analysis, the following selection was applied to the data:
|
|
|
|
\begin{itemize}
|
|
\tightlist
|
|
\item
|
|
\#jets \(\ge\) 2
|
|
\item
|
|
\(\Delta\eta < 1.4\)
|
|
\item
|
|
\(m_{jj} \ge \SI{1050}{\giga\eV}\)
|
|
\item
|
|
\(\SI{35}{\giga\eV} < m_{SDM} < \SI{105}{\giga\eV}\)
|
|
\end{itemize}
|
|
|
|
For the deep boosted 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 optimizing for the highest possible significance of the
|
|
signal.
|
|
|
|
A combined fit of background and 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 and new exclusion
|
|
limits for the mass of the q* particle 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.
|
|
|
|
Two different taggers were used to compare the result. The newer deep
|
|
boosted tagger was found to not improve the result over the older
|
|
N-subjettiness tagger. This was rather unexpected but might be caused by
|
|
some training issues, that were identified lately.
|
|
|
|
The optimization process used to find the optimal values for the
|
|
discriminant provided by the taggers, was found to not be optimal. It
|
|
was only done using 2018 data, with which the deep boosted tagger showed
|
|
a higher significance than the N-subjettiness tagger. Apparently, the
|
|
assumption, that the same optimization would apply to the data of the
|
|
other years as well, did not hold. Using the combined dataset, the deep
|
|
boosted tagger showed no better cross section limits than the
|
|
N-subjettiness tagger, which are directly related to the significance
|
|
used for the optimization. Therefore, with a better optimization and the
|
|
fixed training issues of the deep boosted tagger, it is very likely,
|
|
that the result presented could be further improved.
|
|
|
|
\newpage
|
|
|
|
\nocite{*}
|
|
|
|
\printbibliography
|
|
|
|
\newpage
|
|
\hypertarget{appendix}{%
|
|
\section*{Appendix}\label{appendix}}
|
|
|
|
\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 & 0.10406 & 0.14720 & 0.07371 & 0.08165\tabularnewline
|
|
1.8 & 0.07656 & 0.10800 & 0.05441 & 0.04114\tabularnewline
|
|
2.0 & 0.05422 & 0.07605 & 0.03879 & 0.04043\tabularnewline
|
|
2.5 & 0.02430 & 0.03408 & 0.01747 & 0.04052\tabularnewline
|
|
3.0 & 0.01262 & 0.01775 & 0.00904 & 0.02109\tabularnewline
|
|
3.5 & 0.00703 & 0.00992 & 0.00502 & 0.00399\tabularnewline
|
|
4.0 & 0.00424 & 0.00603 & 0.00300 & 0.00172\tabularnewline
|
|
4.5 & 0.00355 & 0.00478 & 0.00273 & 0.00249\tabularnewline
|
|
5.0 & 0.00269 & 0.00357 & 0.00211 & 0.00240\tabularnewline
|
|
6.0 & 0.00103 & 0.00160 & 0.00068 & 0.00062\tabularnewline
|
|
7.0 & 0.00063 & 0.00105 & 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 & 0.17750 & 0.25179 & 0.12572 & 0.38242\tabularnewline
|
|
1.8 & 0.11125 & 0.15870 & 0.07826 & 0.11692\tabularnewline
|
|
2.0 & 0.08188 & 0.11549 & 0.05799 & 0.09528\tabularnewline
|
|
2.5 & 0.03328 & 0.04668 & 0.02373 & 0.03653\tabularnewline
|
|
3.0 & 0.01648 & 0.02338 & 0.01181 & 0.01108\tabularnewline
|
|
3.5 & 0.00840 & 0.01195 & 0.00593 & 0.00683\tabularnewline
|
|
4.0 & 0.00459 & 0.00666 & 0.00322 & 0.00342\tabularnewline
|
|
4.5 & 0.00276 & 0.00412 & 0.00190 & 0.00366\tabularnewline
|
|
5.0 & 0.00177 & 0.00271 & 0.00118 & 0.00401\tabularnewline
|
|
6.0 & 0.00110 & 0.00175 & 0.00071 & 0.00155\tabularnewline
|
|
7.0 & 0.00065 & 0.00108 & 0.00041 & 0.00108\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 & 0.08687 & 0.12254 & 0.06174 & 0.06987\tabularnewline
|
|
1.8 & 0.06719 & 0.09477 & 0.04832 & 0.03424\tabularnewline
|
|
2.0 & 0.04734 & 0.06640 & 0.03405 & 0.03310\tabularnewline
|
|
2.5 & 0.01867 & 0.02619 & 0.01343 & 0.03214\tabularnewline
|
|
3.0 & 0.01043 & 0.01463 & 0.00744 & 0.01773\tabularnewline
|
|
3.5 & 0.00596 & 0.00840 & 0.00426 & 0.00347\tabularnewline
|
|
4.0 & 0.00353 & 0.00500 & 0.00250 & 0.00140\tabularnewline
|
|
4.5 & 0.00233 & 0.00335 & 0.00164 & 0.00181\tabularnewline
|
|
5.0 & 0.00157 & 0.00231 & 0.00110 & 0.00188\tabularnewline
|
|
6.0 & 0.00082 & 0.00126 & 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 & 0.16687 & 0.23805 & 0.11699 & 0.35999\tabularnewline
|
|
1.8 & 0.12750 & 0.17934 & 0.09138 & 0.12891\tabularnewline
|
|
2.0 & 0.09062 & 0.12783 & 0.06474 & 0.09977\tabularnewline
|
|
2.5 & 0.03391 & 0.04783 & 0.02422 & 0.03754\tabularnewline
|
|
3.0 & 0.01781 & 0.02513 & 0.01277 & 0.01159\tabularnewline
|
|
3.5 & 0.00949 & 0.01346 & 0.00678 & 0.00741\tabularnewline
|
|
4.0 & 0.00494 & 0.00711 & 0.00349 & 0.00362\tabularnewline
|
|
4.5 & 0.00293 & 0.00429 & 0.00203 & 0.00368\tabularnewline
|
|
5.0 & 0.00188 & 0.00284 & 0.00127 & 0.00426\tabularnewline
|
|
6.0 & 0.00102 & 0.00161 & 0.00066 & 0.00155\tabularnewline
|
|
7.0 & 0.00053 & 0.00085 & 0.00034 & 0.00085\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 & 0.05703 & 0.07999 & 0.04088 & 0.03366\tabularnewline
|
|
1.8 & 0.03953 & 0.05576 & 0.02833 & 0.04319\tabularnewline
|
|
2.0 & 0.02844 & 0.03989 & 0.02045 & 0.04755\tabularnewline
|
|
2.5 & 0.01270 & 0.01781 & 0.00913 & 0.01519\tabularnewline
|
|
3.0 & 0.00658 & 0.00923 & 0.00473 & 0.01218\tabularnewline
|
|
3.5 & 0.00376 & 0.00529 & 0.00269 & 0.00474\tabularnewline
|
|
4.0 & 0.00218 & 0.00309 & 0.00156 & 0.00114\tabularnewline
|
|
4.5 & 0.00132 & 0.00188 & 0.00094 & 0.00068\tabularnewline
|
|
5.0 & 0.00084 & 0.00122 & 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 & 0.06656 & 0.09495 & 0.04698 & 0.12374\tabularnewline
|
|
1.8 & 0.04281 & 0.06141 & 0.03001 & 0.05422\tabularnewline
|
|
2.0 & 0.03297 & 0.04650 & 0.02363 & 0.04658\tabularnewline
|
|
2.5 & 0.01328 & 0.01868 & 0.00950 & 0.01109\tabularnewline
|
|
3.0 & 0.00650 & 0.00917 & 0.00464 & 0.00502\tabularnewline
|
|
3.5 & 0.00338 & 0.00479 & 0.00241 & 0.00408\tabularnewline
|
|
4.0 & 0.00182 & 0.00261 & 0.00129 & 0.00127\tabularnewline
|
|
4.5 & 0.00107 & 0.00156 & 0.00074 & 0.00123\tabularnewline
|
|
5.0 & 0.00068 & 0.00102 & 0.00046 & 0.00149\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 & 0.05125 & 0.07188 & 0.03667 & 0.02993\tabularnewline
|
|
1.8 & 0.03547 & 0.04989 & 0.02551 & 0.03614\tabularnewline
|
|
2.0 & 0.02523 & 0.03539 & 0.01815 & 0.04177\tabularnewline
|
|
2.5 & 0.01059 & 0.01485 & 0.00761 & 0.01230\tabularnewline
|
|
3.0 & 0.00576 & 0.00808 & 0.00412 & 0.01087\tabularnewline
|
|
3.5 & 0.00327 & 0.00460 & 0.00234 & 0.00425\tabularnewline
|
|
4.0 & 0.00190 & 0.00269 & 0.00136 & 0.00097\tabularnewline
|
|
4.5 & 0.00119 & 0.00168 & 0.00084 & 0.00059\tabularnewline
|
|
5.0 & 0.00077 & 0.00110 & 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 & 0.07719 & 0.10949 & 0.05467 & 0.14090\tabularnewline
|
|
1.8 & 0.05297 & 0.07493 & 0.03752 & 0.06690\tabularnewline
|
|
2.0 & 0.03875 & 0.05466 & 0.02768 & 0.05855\tabularnewline
|
|
2.5 & 0.01512 & 0.02126 & 0.01080 & 0.01160\tabularnewline
|
|
3.0 & 0.00773 & 0.01088 & 0.00554 & 0.00548\tabularnewline
|
|
3.5 & 0.00400 & 0.00565 & 0.00285 & 0.00465\tabularnewline
|
|
4.0 & 0.00211 & 0.00301 & 0.00149 & 0.00152\tabularnewline
|
|
4.5 & 0.00118 & 0.00172 & 0.00082 & 0.00128\tabularnewline
|
|
5.0 & 0.00073 & 0.00108 & 0.00050 & 0.00161\tabularnewline
|
|
6.0 & 0.00039 & 0.00060 & 0.00025 & 0.00036\tabularnewline
|
|
7.0 & 0.00021 & 0.00034 & 0.00013 & 0.00045\tabularnewline
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\end{document}
|