1002 lines
60 KiB
Markdown
1002 lines
60 KiB
Markdown
---
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author: David Leppla-Weber
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title: Search for excited quark states decaying to qW/qZ
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lang: en-GB
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abstract: |
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```{=tex}
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Abstract.
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\end{abstract}
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\begin{abstract}
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Abstract 2.
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```
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@*
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---
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\newpage
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\pagenumbering{arabic}
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# Introduction
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The Standard Model is a very successful theory in describing most of the effects on a particle level. But it still has a
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lot of shortcomings that show that it isn't yet a full "theory of everything". To solve these shortcomings, lots of
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theories beyond the standard model exist that try to explain some of them.
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One category of such theories is based on a composite quark model. They predict that quarks consist of particles unknown
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to us so far or can bind to other particles using unknown forces. This could explain some symmetries between particles
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and reduce the number of constants needed to explain the properties of the known particles. One common prediction of
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those theories are excited quark states. Those are quark states of higher energy that can decay to an unexcited quark
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under the emission of a boson. These decays are the topic of this thesis.
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In previous research, a lower limit for the mass of an excited quark has already been set using data from the 2016 run
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of the Large Hadron Collider with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$. Since then, a lot more data
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has been collected, totalling to $\SI{137.19}{\per\femto\barn}$. This thesis uses this new data as well as a new
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technique to identify decays of highly boosted particles based on a deep neural network to further improve this limit
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and therefore exclude the excited quark particle to even higher masses. It will also compare this new tagging technique
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to an older tagger based on jet substructure studies used in the previous research.
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First, a theoretical background will be presented explaining in short the Standard Model, its shortcomings and the
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theory of excited quarks. Then the Large Hadron Collider and the Compact Muon Solenoid, the detector that collected the
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data for this analysis, will be described. After that, the main analysis part follows, describing how the data was used
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to extract limits on the mass of the excited quark particle. At the very end, the results are presented and compared to
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previous research.
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\newpage
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# Theoretical background
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This chapter presents a short summary of the theoretical background relevant to this thesis. It first gives an
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introduction to the standard model itself and some of the issues it raises. It then goes on to explain the background
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processes of quantum chromodynamics and the theory of q*, which will be the main topic of this thesis.
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## Standard model
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The Standard Model of physics proofed very successful in describing three of the four fundamental interactions currently
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known: the electromagnetic, weak and strong interaction. The fourth, gravity, could not yet be successfully included in
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this theory.
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The Standard Model divides all particles into spin-$\frac{n}{2}$ fermions and spin-n bosons, where n could be any
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integer but so far is only known to be one for fermions and either one (gauge bosons) or zero (scalar bosons) for
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bosons. The fermions are further divided into quarks and leptons. Each of those exists in six so called flavours.
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Furthermore, quarks and leptons can also be divided into three generations, each of which contains two particles.
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In the lepton category, each generation has one charged lepton and one neutrino, that has no charge. Also, the mass of
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the neutrinos is not yet known, only an upper bound has been established. A full list of particles known to the
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standard model can be found in [@fig:sm]. Furthermore, all fermions have an associated anti particle with reversed
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charge. Multiple quarks can form bound states called hadrons (e.g. proton and neutron).
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{width=50% #fig:sm}
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The gauge bosons, namely the photon, $W^\pm$ bosons, $Z^0$ boson, and gluon, are mediators of the different
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forces of the standard model.
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The photon is responsible for the electromagnetic force and therefore interacts with all
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electrically charged particles. It itself carries no electromagnetic charge and has no mass. Possible interactions are
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either scattering or absorption. Photons of different energies can also be described as electromagnetic waves of
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different wavelengths.
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The $W^\pm$ and $Z^0$ bosons mediate the weak force. All quarks and leptons carry a flavour, which is a conserved value.
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Only the weak interaction breaks this conservation, a quark or lepton can therefore, by interacting with a $W^\pm$
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boson, change its flavour. The probabilities of this happening are determined by the Cabibbo-Kobayashi-Maskawa matrix:
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\begin{equation}
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V_{CKM} =
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\begin{pmatrix}
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|V_{ud}| & |V_{us}| & |V_{ub}| \\
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|V_{cd}| & |V_{cs}| & |V_{cb}| \\
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|V_{td}| & |V_{ts}| & |V_{tb}|
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\end{pmatrix}
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=
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\begin{pmatrix}
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0.974 & 0.225 & 0.004 \\
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0.224 & 0.974 & 0.042 \\
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0.008 & 0.041 & 0.999
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\end{pmatrix}
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\end{equation}
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The probability of a quark changing its flavour from $i$ to $j$ is 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 in the same generation is way more likely than
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any other flavour change.
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The quantum chromodynamics (QCD) describe the strong interaction of particles. It applies to all
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particles carrying colour (e.g. quarks). The force is mediated by the gluon. This boson carries colour as well,
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although it doesn't carry only one colour but rather a combination of a colour and an anticolour, and can therefore
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interact with itself and exists in eight different variant. As a result of this, processes, where a gluon decays into
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two gluons are possible. Furthermore the strong force, binding to colour carrying particles, increases with their
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distance r making it at a certain point more energetically efficient to form a new quark - antiquark pair than
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separating the two particles even further. This effect is known as colour confinement. Due to this effect, colour
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carrying particles can't be observed directly, but rather form so called jets that cause hadronic showers in the
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detector. An effect called Hadronisation.
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### Quantum Chromodynamic background {#sec:qcdbg}
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In this thesis, a decay with two jets in the endstate will be analysed. Therefore it will be hard to distinguish the
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signal processes from QCD effects. Those can also produce two jets in the endstate, as can be seen in [@fig:qcdfeynman].
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They are also happening very often in a proton proton collision, as it is happening in the Large Hadron Collider. This
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is caused by the structure of the proton. It not only consists of three quarks, called valence quarks, but also of a lot
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of quark-antiquark pairs connected by gluons, called the sea quarks, that exist due to the self interaction of the
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gluons binding the three valence quarks. Therefore in a proton - proton collision, interactions of gluons and quarks are
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the main processes causing a very strong QCD background.
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\begin{figure}
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\centering
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\feynmandiagram [horizontal=v1 to v2] {
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q1 [particle=\(q\)] -- [fermion] v1 -- [gluon] g1 [particle=\(g\)],
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v1 -- [gluon] v2,
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q2 [particle=\(q\)] -- [fermion] v2 -- [gluon] g2 [particle=\(g\)],
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};
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\feynmandiagram [horizontal=v1 to v2] {
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g1 [particle=\(g\)] -- [gluon] v1 -- [gluon] g2 [particle=\(g\)],
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v1 -- [gluon] v2,
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g3 [particle=\(g\)] -- [gluon] v2 -- [gluon] g4 [particle=\(g\)],
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};
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\caption{Two examples of QCD processes resulting in two jets.} \label{fig:qcdfeynman}
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\end{figure}
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### Shortcomings of the Standard Model
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While being very successful in describing mostly all of the effects we can observe in particle colliders so far, the
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Standard Model still has several shortcomings.
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- **Gravity**: as already noted, the standard model doesn't include gravity as a force.
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- **Dark Matter**: observations of the rotational velocity of galaxies can't be explained by the known matter. Dark
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matter currently is our best theory to explain those.
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- **Matter-antimatter assymetry**: The amount of matter vastly outweights the amount of
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antimatter in the observable universe. This can't be explained by the standard model, which predicts a similar amount
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of matter and antimatter.
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- **Symmetries between particles**: Why do exactly three generations of fermions exist? Why is the charge of a quark
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exactly one third of the charge of a lepton? How are the masses of the particles related? Those and more questions
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cannot be answered by the standard model.
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- **Hierarchy problem**: The weak force is approximately $10^{24}$ times stronger than gravity and so far, there's no
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satisfactory explanation as to why that is.
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## Excited quark states {#sec:qs}
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One category of theories that try to solve some of the shortcomings of the standard model are the composite quark
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models. Those state, that quarks consist of some particles unknown to us so far. This could explain the symmetries
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between the different fermions. A common prediction of those models are excited quark states (q\*, q\*\*, q\*\*\*...).
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Similar to atoms, that can be excited by the absorption of a photon and can then decay again under emission of a photon
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with an energy corresponding to the excited state, those excited quark states could decay under the emission of some
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boson. Quarks are smaller than $10^{-18}$ m, due to that, excited states have to be of very high energy. That will cause
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the emitted boson to be highly boosted.
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\begin{figure}
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\centering
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\feynmandiagram [large, horizontal=qs to v] {
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a -- qs -- b,
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qs -- [fermion, edge label=\(q*\)] v,
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q1 [particle=\(q\)] -- v -- w [particle=\(W\)],
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q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)],
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};
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\caption{Feynman diagram showing a possible decay of a q* particle to a W boson and a quark with the W boson also
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decaying to two quarks.} \label{fig:qsfeynman}
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\end{figure}
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This thesis will search data collected by the CMS in the years 2016, 2017 and 2018 for the single excited quark state
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q\* which can decay to a quark and any boson. An example of a q\* decaying to a quark and a W boson can be seen in
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[@fig:qsfeynman]. The boson quickly further decays into for example two quarks. Because the boson is highly boosted,
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those will be very close together and therefore appear to the detector as only one jet. This means that the decay of a
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q\* particle will have two jets in the endstate (assuming the W/Z boson decays to two quarks) and will therefore be hard
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to distinguish from the QCD background described in [@sec:qcdbg].
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To reconstruct the mass of the q\* particle from an event successfully recognized to be the decay of such a particle,
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the dijet invariant mass, the mass of the two jets in the final state, can be calculated by adding their four momenta,
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vectors consisting of the energy and momentum of a particle, together. From the four momentum it's easy to derive the
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mass by solving $E=\sqrt{p^2 + m^2}$ for m.
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\newpage
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# Experimental Setup
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Following on, the experimental setup used to gather the data analysed in this thesis will be described.
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## Large Hadron Collider
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The Large Hadron Collider is the world's largest and most powerful particle accelerator [@website]. It has a perimeter
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of 27 km and can collide protons at a centre of mass energy of 13 TeV. It is home to several experiments, the biggest of
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those are ATLAS and the Compact Muon Solenoid (CMS). Both are general-purpose detectors to investigate the particles
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that form during particle collisions.
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Particle colliders are characterized by their luminosity L. It is a quantity to be able to calculate the number of
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events per second generated in a collision by $N_{event} = L\sigma_{event}$ with $\sigma_{event}$ being the cross
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section of the event. The luminosity of the LHC for a Gaussian beam distribution can be described as follows:
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\begin{equation}
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L = \frac{N_b^2 n_b f_{rev} \gamma_r}{4 \pi \epsilon_n \beta^*}F
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\end{equation}
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Where $N_b$ is the number of particles per bunch, $n_b$ the number of bunches per beam, $f_{rev}$ the revolution
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frequency, $\gamma_r$ the relativistic gamma factor, $\epsilon_n$ the normalised transverse beam emittance, $\beta^*$
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the beta function at the collision point and F the geometric luminosity reduction factor due to the crossing angle at
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the interaction point:
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\begin{equation}
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F = \left(1+\left( \frac{\theta_c\sigma_z}{2\sigma^*}\right)^2\right)^{-1/2}
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\end{equation}
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At the maximum luminosity of $10^{34}\si{\per\square\centi\metre\per\s}$, $N_b = 1.15 \cdot 10^{11}$, $n_b = 2808$,
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$f_{rev} = \SI{11.2}{\kilo\Hz}$, $\beta^* = \SI{0.55}{\m}$, $\epsilon_n = \SI{3.75}{\micro\m}$ and $F = 0.85$.
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To quantify the amount of data collected by one of the experiments at LHC, the integrated luminosity is introduced as
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$L_{int} = \int L dt$.
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## Compact Muon Solenoid
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The data used in this thesis was captured by the Compact Muon Solenoid (CMS). It is one of the biggest experiments at
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the Large Hadron Collider. It can detect all elementary particles of the standard model except neutrinos. For that, it
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has an onion like setup. The particles produced in a collision first go through a tracking system. They then pass an
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electromegnetic as well as a hadronic calorimeter. This part is surrounded by a superconducting solenoid that generates
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a magenetic field of 3.8 T. Outside of the solenoid are big muon chambers. In 2016 the CMS captured data of a integrated
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luminosity of $\SI{35.92}{\per\femto\barn}$. In 2017 it collected $\SI{41.53}{\per\femto\barn}$ and in 2018
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$\SI{59.74}{\per\femto\barn}$. Therefore the combined dataset of all three years has a total integrated luminosity of
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$\SI{137.19}{\per\femto\barn}$.
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### Coordinate conventions
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Per convention, the z axis points along the beam axis, the y axis upwards and the x axis horizontal towards the LHC
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centre. Furthermore, the azimuthal angle $\phi$, which describes the angle in the x - y plane, the polar angle $\theta$,
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which describes the angle in the y - z plane and the pseudorapidity $\eta$, which is defined as $\eta =
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-ln\left(tan\frac{\theta}{2}\right)$ are introduced. The coordinates are visualised in [@fig:cmscoords]. Furthermore,
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to describe a particles momentum, often the transverse momentum, $p_t$ is used. It is the component of the momentum
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transversal to the beam axis. It is a useful quantity, because the sum of all transverse momenta has to be zero.
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Missing transverse momentum implies particles that weren't detected such as neutrinos.
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{#fig:cmscoords width=60%}
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### The tracking system
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The tracking system is built of two parts, first a pixel detector and then silicon strip sensors. It is used to
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reconstruct the tracks of charged particles, measuring their charge sign, direction and momentum. It is as close to the
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collision as possible to be able to identify secondary vertices.
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### The electromagnetic calorimeter
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The electromagnetic calorimeter measures the energy of photons and electrons. It is made of tungstate crystal.
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When passed by particles, it produces light in proportion to the particle's energy. This light is measured by
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photodetectors that convert this scintillation light to an electrical signal. To measure a particles energy, it has to
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leave its whole energy in the ECAL, which is true for photons and electrons, but not for other particles such as
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hadrons and muons. They too leave some energy in the ECAL.
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### The hadronic calorimeter
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The hadronic calorimeter (HCAL) is used to detect high energy hadronic particles. It surrounds the ECAL and is made of
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alternating layers of active and absorber material. While the absorber material with its high density causes the hadrons
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to shower, the active material then detects those showers and measures their energy, similar to how the ECAL works.
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### The solenoid
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The solenoid, giving the detector its name, is one of the most important features. It creates a magnetic field of 3.8 T
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and therefore makes it possible to measure momentum of charged particles by bending their tracks.
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### The muon system
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Outside of the solenoid there is only the muon system. It consists of three types of gas detectors, the drift tubes,
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cathode strip chambers and resistive plate chambers. The system is divided into a barrel part and two endcaps. Together
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they cover $0 < |\eta| < 2.4$. The muons are the only detected particles, that can pass all the other systems
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without a significant energy loss.
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### The Trigger system
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The CMS features a two level trigger system. It is necessary because the detector is unable to process all the events
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due to limited bandwidth. The Level 1 trigger reduces the event rate from 40 MHz to 100 kHz, the software based High
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Level trigger is then able to further reduce the rate to 1 kHz. The Level 1 trigger uses the data from the
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electromagnetic and hadronic calorimeters as well as the muon chambers to decide whether to keep an event. The High
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Level trigger uses a streamlined version of the CMS offline reconstruction software for its decision making.
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### The Particle Flow algorithm
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The particle flow algorithm is used to identify and reconstruct all the particles arising from the proton - proton
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collision by using all the information available from the different sub-detectors of the CMS. It does so by
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extrapolating the tracks through the different calorimeters and associating clusters they cross with them. The set of
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the track and its clusters is then no more used for the detection of other particles. This is first done for muons and
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then for charged hadrons, so a muon can't give rise to a wrongly identified charged hadron. Due to Bremsstrahlung photon
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emission, electrons are harder to reconstruct. For them a specific track reconstruction algorithm is used.
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After identifying charged hadrons, muons and electrons, all remaining clusters within the HCAL correspond to neutral
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hadrons and within ECAL to photons. If the list of particles and their corresponding deposits is established, it can be
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used to determine the particles four momenta. From that, the missing transverse energy can be calculated and tau
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particles can be reconstructed by their decay products.
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## Jet clustering
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Because of the hadronisation it is not possible to uniquely identify the originating particle of a jet. Nonetheless,
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several algorithms exist to help with this problem. The algorithm used in this thesis is the anti-$k_t$ clustering
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algorithm. It arises from a generalization of several other clustering algorithms, namely the $k_t$, Cambridge/Aachen
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and SISCone clustering algorithms.
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The anti-$k_t$ clustering algorithm associates hard particles with their soft particles surrounding them within a radius
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R in the $\eta$ - $\phi$ plane forming cone like jets. If two jets overlap, the jets shape is changed according to its
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hardness. A softer particles jet will change its shape more than a harder particles. A visual comparison of four
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different clustering algorithms can be seen in [@fig:antiktcomparision]. For this analysis, a radius of 0.8 is used.
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Furthermore, to approximate the mass of a heavy particle that caused a jet, the softdropmass can be used. It is
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calculated by removing wide angle soft particles from the jet to counter the effects of contamination from initial state
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radiation, underlying event and multiple hadron scattering. It therefore is more accurate in determining the mass of a
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particle causing a jet than taking the mass of all constituent particles of the jet combined.
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{#fig:antiktcomparision}
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\newpage
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# Method of analysis
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This section gives an overview over how the data gathered by the LHC and CMS is going to be analysed to be able to
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either exclude the q\* particle to even higher masses than already done or maybe confirm its existence.
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As described in [@sec:qs], an excited quark q\* can decay to a quark and any boson. The branching ratios are calculated
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to be as follows [@QSTAR_THEORY]:
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: Branching ratios of the decaying q\* particle.
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| decay mode | br. ratio [%] | decay mode | br. ratio [%] |
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|---------------------------|---------------|---------------------------|---------------|
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| $U^* \rightarrow ug$ | 83.4 | $D^* \rightarrow dg$ | 83.4 |
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| $U^* \rightarrow dW$ | 10.9 | $D^* \rightarrow uW$ | 10.9 |
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| $U^* \rightarrow u\gamma$ | 2.2 | $D^* \rightarrow d\gamma$ | 0.5 |
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| $U^* \rightarrow uZ$ | 3.5 | $D^* \rightarrow dZ$ | 5.1 |
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The majority of excited quarks will decay to a quark and a gluon, but as this is virtually impossible to distinguish
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from QCD effects (for example from the qg $\rightarrow$ qg processes), this analysis will focus on the processes q\*
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$\rightarrow$ qW and q\* $\rightarrow$ qZ. In this case, due to jet substructure studies, it is possible to establish a
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discriminator between QCD background and jets originating in a W/Z decay. They still make up roughly 20 % of the signal
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events to study and therefore seem like a good choice.
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The data studied was collected by the CMS experiment in the years 2016, 2017 and 2018. It is analysed with the Particle
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Flow algorithm to reconstruct jets and all the other particles forming during the collision. The jets are then clustered
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using the anti-$k_t$ algorithm with the distance parameter R being 0.8. Furthermore, the calorimeters of the CMS
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detector have to be calibrated. For that, jet energy corrections published by the CMS working group are applied to the
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data.
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To find signal events in the data, this thesis looks at the dijet invariant mass distribution. The data is assumed to
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only consist of QCD background and signal events, other backgrounds are neglected. Cuts on several distributions are
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introduced to reduce the background and improve the sensitivity for the signal. If the q\* particle exists, the dijet
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invariant mass distribution should show a resonance at its invariant mass. This resonance will be looked for with
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statistical methods explained later on.
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The analysis will be conducted with two different sets of data. First, only the data collected by CMS in 2016 will be
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used to compare the results to the previous analysis [@PREV_RESEARCH]. Then the combined data from 2016, 2017 and 2018
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will be used to improve the previously set limits for the mass of the q\* particle. Also, two different tagging
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mechanisms will be used. One based on the N-subjettiness variable used in the previous research, the other being a novel
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approach using a deep neural network.
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## Signal and Background modelling
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To make sure the setup is working as intended, at first simulated samples of background and signal are used. In those
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Monte Carlo simulations, the different particle interactions that take place in a proton - proton
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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 [@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:
|
|
|
|
- mean: the functions mean, in this case the resonance mass
|
|
- sigma: the functions width, in this case the resolution of the detector
|
|
- n1, n2, alpha1, alpha2: parameters influencing the shape of the left and right tail
|
|
|
|
A gaussian and a poisson have also been studied but found to not fit the signal sample very well as they aren't able to
|
|
fit the tail on both sides of the peak.
|
|
|
|
An example of a fit of these functions to a toy dataset with gaussian errors can be seen in [@fig:cb_fit]. In this
|
|
figure, a binning of 200 GeV is used. For the actual analysis a 1 GeV binning will be used.
|
|
|
|
{#fig:cb_fit}
|
|
|
|
\newpage
|
|
|
|
# Preselection and data quality
|
|
|
|
To separate the background from the signal, cuts on several distributions have to be introduced. The selection of events
|
|
is divided into
|
|
two parts. The first one (the preselection) adds some general physics motivated cuts and is also used to make sure a
|
|
good trigger efficiency is achieved. It is not expected to already provide a good separation of background and signal.
|
|
In the second part, different taggers will be used as a discriminator between QCD background and signal events. After
|
|
the preselection, it is made sure, that the simulated samples represent the real data well.
|
|
|
|
## 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 detector
|
|
resolution. 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, we expect two jets in the endstate. Therefore a cut is added to have at least 2 jets.
|
|
More jets are also possible, for example caused by gluon radiation of a quark causing another jet. The cut can be seen
|
|
in [@fig:njets].
|
|
|
|
\begin{figure}
|
|
\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}{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{Number of jet distribution showing the cut at number of jets $\ge$ 2. Left: distribution before the cut. Right:
|
|
distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves
|
|
are amplified by a factor of 10,000, to be visible.}
|
|
\label{fig:njets}
|
|
\end{figure}
|
|
|
|
Another cut is on $\Delta\eta$. 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 0. 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 cut as in previous research of $\Delta\eta \le 1.3$ is used as can be seen in [@fig:deta].
|
|
|
|
\begin{figure}
|
|
\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}{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{$\Delta\eta$ distribution showing the cut at $\Delta\eta \le 1.3$. Left: distribution before the cut. Right:
|
|
distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves
|
|
are amplified by a factor of 10,000, to be visible.}
|
|
\label{fig:deta}
|
|
\end{figure}
|
|
|
|
The last cut in the preselection is on the dijet invariant mass: $m_{jj} \ge \SI{1050}{\giga\eV}$. It is important for a
|
|
high trigger efficiency and can be seen in [@fig:invmass]. Also, it has a huge impact on the background because it
|
|
usually consists of way lighter particles. The q\* on the other hand is expected to have a very high invariant mass of
|
|
more than 1 TeV. The 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}{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}{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{Invariant mass distribution showing 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.
|
|
Left: distribution before the
|
|
cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018.}
|
|
\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. Still, as can be seen in [@fig:njets] to [@fig:invmass], the amount of signal is very low and, without
|
|
logarithmic scale, even has to be amplified to be visible.
|
|
|
|
## Data - Monte Carlo Comparison
|
|
|
|
To ensure high data quality, the simulated QCD background sample is now being compared to the actual data of the
|
|
corresponding year collected by the CMS detector. This is done for the year 2016 and for the combined data of years
|
|
2016, 2017 and 2018. The distributions are rescaled so the integral over the invariant mass distribution of data and
|
|
simulation are the same. In [@fig:data-mc], the three distributions that cuts were applied on can be seen for year 2016
|
|
and the combined data of years 2016 to 2018.
|
|
|
|
\begin{figure}
|
|
\begin{minipage}{0.33\textwidth}
|
|
\includegraphics{./figures/2016/DATA/v1_invmass_N_jets.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.33\textwidth}
|
|
\includegraphics{./figures/2016/DATA/v1_invmass_deta.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.33\textwidth}
|
|
\includegraphics{./figures/2016/DATA/v1_invmass_invMass.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.33\textwidth}
|
|
\includegraphics{./figures/combined/DATA/v1_invmass_N_jets.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.33\textwidth}
|
|
\includegraphics{./figures/combined/DATA/v1_invmass_deta.eps}
|
|
\end{minipage}
|
|
\begin{minipage}{0.33\textwidth}
|
|
\includegraphics{./figures/combined/DATA/v1_invmass_invMass.eps}
|
|
\end{minipage}
|
|
\caption{Comparision of data with the Monte Carlo simulation.
|
|
1st row: data from 2016.
|
|
2nd row: combined data from 2016, 2017 and 2018.}
|
|
\label{fig:data-mc}
|
|
\end{figure}
|
|
|
|
The shape of the real data matches the simulation well. The $\Delta\eta$ distributions shows some offset between data
|
|
and simulation.
|
|
|
|
### Sideband
|
|
|
|
The sideband is introduced to make sure there are no unwanted side effects of the used cuts. It is a region in which no
|
|
data is used for the actual analysis. Again, data and the Monte Carlo simulation are compared. For this analysis, the
|
|
region where the softdropmass of both of the two jets with the highest transverse momentum ($p_t$) is more than 105 GeV
|
|
was chosen. Because the decay of a q\* to a vector boson is being investigated, later on, a selection is applied that
|
|
one of those particles has to have a mass between 105 GeV and 35 GeV. Therefore events with jets with a softdropmass
|
|
higher than 105 GeV will not be used for this analysis which makes them a good sideband to use.
|
|
|
|
In [@fig:sideband], the comparison of data with simulation in the sideband region can be seen for the softdropmass
|
|
distribution as well as the dijet invariant mass distribution. As in [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}{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}{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. 1st row: data from 2016. 2nd row:
|
|
combined data from 2016, 2017 and 2018.}
|
|
\label{fig:sideband}
|
|
\end{figure}
|
|
|
|
\newpage
|
|
|
|
# Jet substructure selection
|
|
|
|
So far it was made sure, that the actual data and the simulation match well 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 extract the hypothetical signal events from the actual 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 the results. 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 cut on the
|
|
softdropmass of a jet. The softdropmass of at least one of the two leading jets is expected to be within
|
|
$\SI{35}{\giga\eV}$ and $\SI{105}{\giga\eV}$. This cut already provides a good separation of QCD and signal events, on
|
|
which the two taggers presented next can build.
|
|
|
|
Both taggers provide a 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.
|
|
|
|
## N-Subjettiness
|
|
|
|
The N-subjettiness $\tau_n$ 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 an
|
|
optimization process described in the next chapter. As candidate jet the one of the two highest $p_t$ jets passing the
|
|
softdropmass window is used. If both of them pass, the one with higher $p_t$ is chosen.
|
|
|
|
## DeepAK8
|
|
|
|
The DeepAK8 tagger uses a deep neural network (DNN) to identify decays originating in a vector boson. It is supposed
|
|
to give better efficiencies than the older N-Subjettiness method.
|
|
|
|
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 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 softdropmass selection, this version of the tagger is to be preferred.
|
|
|
|
The higher the discriminator value of the deep boosted tagger, the more likely is the jet to be caused by 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.
|
|
|
|
## Optimization
|
|
|
|
To figure out the best value to cut on the discriminators introduced by the two taggers, a value to quantify how good a
|
|
cut is has to be introduced. For that, the significance calculated by $\frac{S}{\sqrt{B}}$ will be used. S stands for
|
|
the amount of signal events and B for the amount of background events in a given interval. This value assumes a gaussian
|
|
error on the background so it will be calculated for the 2 TeV masspoint where enough background events exist to justify
|
|
this assumption. 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 masspoint is chosen.
|
|
|
|
\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 14.08, and for the deep boosted tagger 25.61.
|
|
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: $VvsQCD < 0.95$.
|
|
|
|
# Signal extraction
|
|
|
|
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: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 2016,
|
|
2017 and 2018.
|
|
|
|
To extract the signal from the background, its cross section limit is calculated using a frequentist asymptotic limit
|
|
calculator. It uses the fit that was performed to the simulated samples to calculate expected limits for all the
|
|
available masspoints and then a fit to the actual data to determine an observed limit. If there's no resonance of the
|
|
q\* particle in the data, the observed limit should lie within the $2\sigma$ environment of the expected limit. After
|
|
that, the crossing of the theory line, representing the cross section limits expected, if the q\* particle would exist,
|
|
and the observed data is calculated, to have a limit of mass up to which the existence of the q\* particle can be
|
|
excluded. To find the uncertainty of this result, the crossing of the theory line plus, respectively minus, its
|
|
uncertainty with the observed limit is also calculated.
|
|
|
|
## Uncertainties
|
|
|
|
The following uncertainties are considered:
|
|
|
|
- *Luminosity*: the integrated luminosity of the LHC has an uncertainty of 2.5 %.
|
|
- *Jet Energy Corrections*: for the Jet Energy Corrections, an uncertainty of 2 % is assumed.
|
|
- *Tagger Efficiency(?)*: 6 % (TODO!)
|
|
- *Parameter Uncertainty of the fit*: The CombinedLimit program used for determining the cross section varies the
|
|
parameters used for the fit and therefore includes their uncertainties to calculate the final result.
|
|
|
|
# Results
|
|
|
|
In this chapter the results and a comparison to previous research will be shown as well as a comparison between the two
|
|
different taggers used.
|
|
|
|
## 2016
|
|
|
|
Using the data collected by the CMS experiment on 2016, the cross section limits seen in [@fig:res2016] were obtained.
|
|
The extracted cross section limits are:
|
|
|
|
|
|
: Cross Section limits using 2016 data and the N-subjettiness tagger for the decay to qW
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.10406 | 0.14720 | 0.07371 | 0.08165 |
|
|
| 1.8 | 0.07656 | 0.10800 | 0.05441 | 0.04114 |
|
|
| 2.0 | 0.05422 | 0.07605 | 0.03879 | 0.04043 |
|
|
| 2.5 | 0.02430 | 0.03408 | 0.01747 | 0.04052 |
|
|
| 3.0 | 0.01262 | 0.01775 | 0.00904 | 0.02109 |
|
|
| 3.5 | 0.00703 | 0.00992 | 0.00502 | 0.00399 |
|
|
| 4.0 | 0.00424 | 0.00603 | 0.00300 | 0.00172 |
|
|
| 4.5 | 0.00355 | 0.00478 | 0.00273 | 0.00249 |
|
|
| 5.0 | 0.00269 | 0.00357 | 0.00211 | 0.00240 |
|
|
| 6.0 | 0.00103 | 0.00160 | 0.00068 | 0.00062 |
|
|
| 7.0 | 0.00063 | 0.00105 | 0.00039 | 0.00086 |
|
|
|
|
|
|
: Cross Section limits using 2016 data and the deep boosted tagger for the decay to qW
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.17750 | 0.25179 | 0.12572 | 0.38242 |
|
|
| 1.8 | 0.11125 | 0.15870 | 0.07826 | 0.11692 |
|
|
| 2.0 | 0.08188 | 0.11549 | 0.05799 | 0.09528 |
|
|
| 2.5 | 0.03328 | 0.04668 | 0.02373 | 0.03653 |
|
|
| 3.0 | 0.01648 | 0.02338 | 0.01181 | 0.01108 |
|
|
| 3.5 | 0.00840 | 0.01195 | 0.00593 | 0.00683 |
|
|
| 4.0 | 0.00459 | 0.00666 | 0.00322 | 0.00342 |
|
|
| 4.5 | 0.00276 | 0.00412 | 0.00190 | 0.00366 |
|
|
| 5.0 | 0.00177 | 0.00271 | 0.00118 | 0.00401 |
|
|
| 6.0 | 0.00110 | 0.00175 | 0.00071 | 0.00155 |
|
|
| 7.0 | 0.00065 | 0.00108 | 0.00041 | 0.00108 |
|
|
|
|
|
|
: Cross Section limits using 2016 data and the N-subjettiness tagger for the decay to qZ
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.08687 | 0.12254 | 0.06174 | 0.06987 |
|
|
| 1.8 | 0.06719 | 0.09477 | 0.04832 | 0.03424 |
|
|
| 2.0 | 0.04734 | 0.06640 | 0.03405 | 0.03310 |
|
|
| 2.5 | 0.01867 | 0.02619 | 0.01343 | 0.03214 |
|
|
| 3.0 | 0.01043 | 0.01463 | 0.00744 | 0.01773 |
|
|
| 3.5 | 0.00596 | 0.00840 | 0.00426 | 0.00347 |
|
|
| 4.0 | 0.00353 | 0.00500 | 0.00250 | 0.00140 |
|
|
| 4.5 | 0.00233 | 0.00335 | 0.00164 | 0.00181 |
|
|
| 5.0 | 0.00157 | 0.00231 | 0.00110 | 0.00188 |
|
|
| 6.0 | 0.00082 | 0.00126 | 0.00054 | 0.00049 |
|
|
| 7.0 | 0.00050 | 0.00083 | 0.00031 | 0.00066 |
|
|
|
|
|
|
: Cross Section limits using 2016 data and deep boosted tagger for the decay to qZ
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.16687 | 0.23805 | 0.11699 | 0.35999 |
|
|
| 1.8 | 0.12750 | 0.17934 | 0.09138 | 0.12891 |
|
|
| 2.0 | 0.09062 | 0.12783 | 0.06474 | 0.09977 |
|
|
| 2.5 | 0.03391 | 0.04783 | 0.02422 | 0.03754 |
|
|
| 3.0 | 0.01781 | 0.02513 | 0.01277 | 0.01159 |
|
|
| 3.5 | 0.00949 | 0.01346 | 0.00678 | 0.00741 |
|
|
| 4.0 | 0.00494 | 0.00711 | 0.00349 | 0.00362 |
|
|
| 4.5 | 0.00293 | 0.00429 | 0.00203 | 0.00368 |
|
|
| 5.0 | 0.00188 | 0.00284 | 0.00127 | 0.00426 |
|
|
| 6.0 | 0.00102 | 0.00161 | 0.00066 | 0.00155 |
|
|
| 7.0 | 0.00053 | 0.00085 | 0.00034 | 0.00085 |
|
|
|
|
|
|
As can be seen in [@fig:res2016], 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.
|
|
|
|
|
|
: Mass limits found using the data collected in 2016
|
|
|
|
| Decay | Tagger | Limit [TeV] | Upper Limit [TeV] | Lower Limit [TeV] |
|
|
|-------|--------------|-------------|-------------------|-------------------|
|
|
| qW | $\tau_{21}$ | 5.39 | 6.01 | 4.99 |
|
|
| qW | deep boosted | 4.96 | 5.19 | 4.84 |
|
|
| qZ | $\tau_{21}$ | 4.86 | 4.96 | 4.70 |
|
|
| qZ | deep boosted | 4.49 | 4.61 | 4.40 |
|
|
|
|
|
|
|
|
\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}
|
|
|
|
### Previous research
|
|
|
|
The limit 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:res2016]. This could be
|
|
caused by small differences of the setup used or slightly differently processed data. In general, the results appear to
|
|
be very similar to the previous research, seen in [@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}
|
|
|
|
## 2016 + 2017 + 2018
|
|
|
|
Using the combined data, the cross section limits seen in [@fig:resCombined] were obtained. It is quite obvious, that
|
|
the limits are already significantly lower than when only using the data of 2016. The extracted cross section limits are
|
|
the following:
|
|
|
|
|
|
: Cross Section limits using the combined data and the N-subjettiness tagger for the decay to qW
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.05703 | 0.07999 | 0.04088 | 0.03366 |
|
|
| 1.8 | 0.03953 | 0.05576 | 0.02833 | 0.04319 |
|
|
| 2.0 | 0.02844 | 0.03989 | 0.02045 | 0.04755 |
|
|
| 2.5 | 0.01270 | 0.01781 | 0.00913 | 0.01519 |
|
|
| 3.0 | 0.00658 | 0.00923 | 0.00473 | 0.01218 |
|
|
| 3.5 | 0.00376 | 0.00529 | 0.00269 | 0.00474 |
|
|
| 4.0 | 0.00218 | 0.00309 | 0.00156 | 0.00114 |
|
|
| 4.5 | 0.00132 | 0.00188 | 0.00094 | 0.00068 |
|
|
| 5.0 | 0.00084 | 0.00122 | 0.00060 | 0.00059 |
|
|
| 6.0 | 0.00044 | 0.00066 | 0.00030 | 0.00041 |
|
|
| 7.0 | 0.00022 | 0.00036 | 0.00014 | 0.00043 |
|
|
|
|
|
|
: Cross Section limits using the combined data and the deep boosted tagger for the decay to qW
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.06656 | 0.09495 | 0.04698 | 0.12374 |
|
|
| 1.8 | 0.04281 | 0.06141 | 0.03001 | 0.05422 |
|
|
| 2.0 | 0.03297 | 0.04650 | 0.02363 | 0.04658 |
|
|
| 2.5 | 0.01328 | 0.01868 | 0.00950 | 0.01109 |
|
|
| 3.0 | 0.00650 | 0.00917 | 0.00464 | 0.00502 |
|
|
| 3.5 | 0.00338 | 0.00479 | 0.00241 | 0.00408 |
|
|
| 4.0 | 0.00182 | 0.00261 | 0.00129 | 0.00127 |
|
|
| 4.5 | 0.00107 | 0.00156 | 0.00074 | 0.00123 |
|
|
| 5.0 | 0.00068 | 0.00102 | 0.00046 | 0.00149 |
|
|
| 6.0 | 0.00038 | 0.00060 | 0.00024 | 0.00034 |
|
|
| 7.0 | 0.00021 | 0.00035 | 0.00013 | 0.00046 |
|
|
|
|
|
|
|
|
: Cross Section limits using the combined data and the N-subjettiness tagger for the decay to qZ
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.05125 | 0.07188 | 0.03667 | 0.02993 |
|
|
| 1.8 | 0.03547 | 0.04989 | 0.02551 | 0.03614 |
|
|
| 2.0 | 0.02523 | 0.03539 | 0.01815 | 0.04177 |
|
|
| 2.5 | 0.01059 | 0.01485 | 0.00761 | 0.01230 |
|
|
| 3.0 | 0.00576 | 0.00808 | 0.00412 | 0.01087 |
|
|
| 3.5 | 0.00327 | 0.00460 | 0.00234 | 0.00425 |
|
|
| 4.0 | 0.00190 | 0.00269 | 0.00136 | 0.00097 |
|
|
| 4.5 | 0.00119 | 0.00168 | 0.00084 | 0.00059 |
|
|
| 5.0 | 0.00077 | 0.00110 | 0.00054 | 0.00051 |
|
|
| 6.0 | 0.00039 | 0.00057 | 0.00026 | 0.00036 |
|
|
| 7.0 | 0.00019 | 0.00031 | 0.00013 | 0.00036 |
|
|
|
|
|
|
: Cross Section limits using the combined data and deep boosted tagger for the decay to qZ
|
|
|
|
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
|
|------------|-----------------|------------------|------------------|-----------------|
|
|
| 1.6 | 0.07719 | 0.10949 | 0.05467 | 0.14090 |
|
|
| 1.8 | 0.05297 | 0.07493 | 0.03752 | 0.06690 |
|
|
| 2.0 | 0.03875 | 0.05466 | 0.02768 | 0.05855 |
|
|
| 2.5 | 0.01512 | 0.02126 | 0.01080 | 0.01160 |
|
|
| 3.0 | 0.00773 | 0.01088 | 0.00554 | 0.00548 |
|
|
| 3.5 | 0.00400 | 0.00565 | 0.00285 | 0.00465 |
|
|
| 4.0 | 0.00211 | 0.00301 | 0.00149 | 0.00152 |
|
|
| 4.5 | 0.00118 | 0.00172 | 0.00082 | 0.00128 |
|
|
| 5.0 | 0.00073 | 0.00108 | 0.00050 | 0.00161 |
|
|
| 6.0 | 0.00039 | 0.00060 | 0.00025 | 0.00036 |
|
|
| 7.0 | 0.00021 | 0.00034 | 0.00013 | 0.00045 |
|
|
|
|
|
|
The results for the mass limits of the combined years are as follows:
|
|
|
|
|
|
: Mass limits found using the data collected in 2016 - 2018
|
|
|
|
| Decay | Tagger | Limit [TeV] | Upper Limit [TeV] | Lower Limit [TeV] |
|
|
|-------|--------------|-------------|-------------------|-------------------|
|
|
| qW | $\tau_{21}$ | 6.00 | 6.26 | 5.74 |
|
|
| qW | deep boosted | 6.11 | 6.31 | 5.39 |
|
|
| qZ | $\tau_{21}$ | 5.49 | 5.76 | 5.29 |
|
|
| qZ | deep boosted | 4.92 | 5.02 | 4.80 |
|
|
|
|
|
|
|
|
\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}
|
|
|
|
The combination of the three years has a big impact on the result. The final limit is 1 TeV higher than what could
|
|
previously be concluded.
|
|
|
|
## 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: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 supposed to provide better
|
|
separation between signal and background events than the older N-subjettiness tagger. Recently, some issues with the
|
|
training of the deep boosted tagger used in this analysis were found, so those might explain the bad performance.
|
|
|
|
\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}
|
|
|
|
\newpage
|
|
|
|
# Summary
|
|
|
|
In this thesis, a limit on the mass of the q\* particle has been successfully established. 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 that, a combined fit to the QCD background and signal had to be performed and the cross section limits
|
|
extracted. Also, the new deep boosted tagger, using a deep neural network, was compared to the older N-subjettiness
|
|
tagger and found to not significantly change the result, neither to the better nor to the worse. Due to some training
|
|
issues identified lately, there is still a good chance, that, with that issue fixed, it will be able to further improve
|
|
the results.
|
|
Also previously research of the 2016 data was repeated and the results compared. The previous research arrived at a
|
|
exclusion limit up to 5 TeV resp. 4.7 TeV for the decay to qW resp. qZ, this thesis at 5.4 TeV resp. 4.9 TeV. The
|
|
difference can be explained by small differences in the data used and the setup itself. After that, using the combined
|
|
data, the limit could be significantly improved to exclude the q\* particle up to a mass of 6.2 TeV resp. 5.5 TeV.
|
|
With the research presented in this thesis, it would also be possible to test other theories of the q\* particle that
|
|
predict its existence at lower masses, than the one used, by overlaying the different theory curves in the plots shown
|
|
in [@fig:res2016] and [@fig:resCombined].
|
|
|
|
\newpage
|
|
|
|
\nocite{*}
|