This commit is contained in:
david 2019-10-28 15:16:30 +01:00
parent 7b4be2a193
commit f5c4bff66c
57 changed files with 188182 additions and 2619 deletions

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@ -753,21 +753,6 @@ can also collide heavy (Pb) ions with an energy of 2.8 TeV per nucleon
and a peak luminosity of 1027 cm2 s1. In this paper, the machine
design is described.}
}
@ARTICLE{LHC,
author = {{Apollinari}, G. and {Bruening}, O. and {Nakamoto}, T. and {Rossi}, L.},
title = "{High Luminosity Large Hadron Collider HL-LHC}",
journal = {arXiv e-prints},
keywords = {Physics - Accelerator Physics},
year = "2017",
month = "May",
eid = {arXiv:1705.08830},
pages = {arXiv:1705.08830},
archivePrefix = {arXiv},
eprint = {1705.08830},
primaryClass = {physics.acc-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2017arXiv170508830A},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@techreport{DEEP_BOOSTED,
title = "{Machine learning-based identification of highly
Lorentz-boosted hadronically decaying particles at the CMS

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@ -2,7 +2,7 @@
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thesis.md
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@ -20,8 +20,9 @@ abstract: |
previous research of data collected by CMS in 2016 [@PREV_RESEARCH], excluding the q\* particle up to a mass of 5.0
TeV resp. 4.7 TeV. Also a comparison of the new DeepAK8 [@DEEP_BOOSTED] and the older N-subjettiness [@TAU21] tagger
is conducted, showing that the newer DeepAK8 tagger, based on a deep neural network, is currently approximately at
the same level as the N-subjettiness tagger, but has the potential to further improve in performance, between others
because of an improved training that was just published.
the same level as the N-subjettiness tagger, giving a $\SI{0.1}{\tera\eV}$ better result for the decay to qW but a
by $\SI{0.6}{\tera\eV}$ worse one for the decay to qZ. It still has the potential to further improve in performance,
between others because of an improved training.
```{=tex}
@ -35,11 +36,12 @@ abstract: |
2017 und 2018 bei einer Schwerpunktsenergie von $\sqrt{s} = \SI{13}{\tera\eV}$ vom CMS Experiment aufgenommen
wurden. Indem der Zerfall des q\* Teilchens zu q + W und q + Z untersucht wird, kann dieses mit einem
Konfidenzniveau von 95 % bis zu einer Masse von 6.1 TeV (qW) bzw. 5.5 TeV (qZ) ausgeschlossen werden. Dieses Limit
liegt etwa 1 TeV höher, als das von vorhergegangener Forschung [@PREV_RESEARCH] gesetzte von 5.0 TeV bzw. 4.7 TeV.
Dabei wird der neue DeepAK8 Tagger [@DEEP_BOOSTED], welcher auf einem neuronalen Netzwerk basiert, mit dem älteren
N-Subjetiness Tagger [@TAU21] verglichen. Das Endergebnis der beiden Tagger unterscheidet sich kaum, jedoch gibt es
beim DeepAK8 Tagger noch potential zur Verbesserung, unter anderem durch ein verbessertes Traininig, welches vor
kurzem veröffentlicht wurde.
liegt etwa 1 TeV höher, als das anhand der Daten von 2016 gefundene von 5.0 TeV bzw. 4.7 TeV [@PREV_RESEARCH]. Dabei
wird der neue DeepAK8 Tagger [@DEEP_BOOSTED], welcher auf einem neuronalen Netzwerk basiert, mit dem älteren
N-Subjetiness Tagger [@TAU21] verglichen. Beim Zerfall zu qW erzielt er ein um $\SI{0.1}{\tera\eV}$ besseres
Ergebnis, beim Zerfall zu qZ jedoch ein um $\SI{0.6}{\tera\eV}$ schlechteres. Mit einem verbesserten Training,
welches vor kurzem veröffentlicht wurde, gibt es aber noch Potential, die Leistung zu steigern.
\newpage
documentclass: article
geometry:
@ -53,24 +55,29 @@ fontsize: 12pt
toc: true
nocite: |
@*
figPrefix: "Fig."
tblPrefix: "Table"
secPrefix: "Sec."
eqnPrefix: "Eq."
---
\newpage
\pagenumbering{arabic}
# Introduction
The Standard Model is a very successful theory in describing most of the effects on a particle level. But it still has a
lot of shortcomings that show that it isn't yet a full "theory of everything". To solve these shortcomings, lots of
theories beyond the standard model exist that try to explain some of them.
The Standard Model is a very successful theory in describing most of the interactions happening between particles.
Still, it has a lot of shortcomings that show that it isn't yet a full "theory of everything". To solve these
shortcomings, lots of theories beyond the standard model exist that try to expand the Standard Model in different ways
to solve these issues.
One category of such theories is based on a composite quark model. Quarks are currently considered elementary particles
by the Standard Model. The composite quark models on the other hand predict that quarks consist of particles unknown
to us so far or can bind to other particles using unknown forces. This could explain the symmetries between particles
and reduce the number of constants needed to explain the properties of the known particles. One common prediction of
those theories are excited quark states. Those are quark states of higher energy that can decay to an unexcited quark
under the emission of a boson. This thesis will search for their decay to a quark and a W/Z boson. The W/Z boson then
decays in the hadronic channel, to two more quarks. The endstate of this decay has only quarks, making Quantum
Chromodynamics effects the main background.
under the emission of a boson. This thesis will look for their decay to a vector boson that then further decays
hadronically. The final state of this decay consists only of quarks forming two jets, making Quantum Chromodynamics the
main background.
In a previous research [@PREV_RESEARCH], a lower limit for the mass of an excited quark has already been set using data
from the 2016 run of the Large Hadron Collider with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$. Since
@ -95,7 +102,7 @@ This chapter presents a short summary of the theoretical background relevant to
introduction to the standard model itself and some of the issues it raises. It then goes on to explain the background
processes of quantum chromodynamics and the theory of q*, which will be the main topic of this thesis.
## Standard model {#sec:sm}
## Standard Model {#sec:sm}
The Standard Model of physics proved to be very successful in describing three of the four fundamental interactions
currently known: the electromagnetic, weak and strong interaction. The fourth, gravity, could not yet be successfully
@ -108,11 +115,8 @@ Quarks and leptons can also be categorized into three generations, each of which
flavours. For leptons, the three generations each consist of a lepton and its corresponding neutrino, namely first the
electron, then the muon and third, the tau. The three quark generations consist of first, the up and down, second, the
charm and strange, and third, the top and bottom quark. So overall, their exists a total of six quark and six lepton
flavours. A full list of particles known to the standard model can be found in [@fig:sm]. Furthermore, all fermions have
an associated anti particle with reversed charge.
The matter around us, is built from so called hadrons, that are bound states of quarks, for example protons and
neutrons. Long lived hadrons consist of up and down quarks, as the heavier ones over time decay to those.
flavours. A full list of particles of the standard model can be found in [@fig:sm]. Furthermore, all fermions have an
associated anti particle with reversed charge. Bound states of multiple quarks also exist and are called hadrons.
![
Elementary particles of the Standard Model and their mass charge and spin.
@ -152,8 +156,8 @@ Due to their high masses of 80.39 GeV resp. 91.19 GeV, the $W^\pm$ and $Z^0$ bos
Either in the leptonic or hadronic decay channel. In the leptonic channel, the $W^\pm$ decays to a lepton and the
corresponding anti-lepton neutrino, in the hadronic channel it decays to a quark and an anti-quark of a different
flavour. Due to the $Z^0$ boson having no charge, it always decays to a fermion and its anti-particle, in the leptonic
channel this might be for example a electron - positron pair, in the hadronic channel an up and anti-up quark pair. This
thesis examines the hadronic decay channel, where both vector bosons essentially decay to to quarks.
channel this might be for example an electron - positron pair, in the hadronic channel an up and anti-up quark pair.
This thesis examines the hadronic decay channel, where both vector bosons essentially decay to two quarks.
The quantum chromodynamics (QCD) describes the strong interaction of particles. It applies to all
particles carrying colour (e.g. quarks). The force is mediated by gluons. These bosons carry colour as well,
@ -172,7 +176,7 @@ from cosmological sources, the Standard Model still has several shortcomings.
- **Gravity**: as already noted, the standard model doesn't include gravity as a force.
- **Dark Matter**: observations of the rotational velocity of galaxies can't be explained by the known matter. Dark
matter currently is our best theory to explain those.
matter currently the most popular theory to explain those.
- **Matter-antimatter asymmetry**: The amount of matter vastly outweights the amount of antimatter in the observable
universe. This can't be explained by the standard model, which predicts a similar amount of matter and antimatter.
- **Symmetries between particles**: Why do exactly three generations of fermions exist? Why is the charge of a quark
@ -184,12 +188,13 @@ from cosmological sources, the Standard Model still has several shortcomings.
## Excited quark states {#sec:qs}
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 to us so far. This could explain the symmetries
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\*\*\*...).
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 could decay under the emission of any
boson. Quarks are smaller than $10^{-18}$ m. This corresponds to an energy scale of approximately 1 TeV. Therefore the
excited quark states are expected to be in that region. That will cause the emitted boson to be highly boosted.
boson. Quarks are measured to be smaller than $10^{-18}$ m. This corresponds to an energy scale of approximately 1 TeV.
Therefore the excited quark states are expected to be in that region. That will cause the emitted boson to be highly
boosted.
\begin{figure}
\centering
@ -199,16 +204,16 @@ excited quark states are expected to be in that region. That will cause the emit
q1 [particle=\(q\)] -- v -- w [particle=\(W\)],
q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)],
};
\caption{Feynman diagram showing a possible decay of a q* particle to a W boson and a quark with the W boson also
decaying to two quarks.} \label{fig:qsfeynman}
\caption{Feynman diagram showing the decay of a q* particle to a W boson and a quark with the W boson decaying
hadronically.} \label{fig:qsfeynman}
\end{figure}
This thesis will search data collected by the CMS in the years 2016, 2017 and 2018 for the single excited quark state
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
This thesis will search data collected by the CMS in the years 2016, 2017 and 2018 for the decay of a single excited
quark state q\* to a quark and a vector boson . An example of a q\* decaying to a quark and a W boson can be seen in
[@fig:qsfeynman]. As explained in [@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 endstate. Because the boson is
channel. This research investigates only the hadronic channel with two quarks in the final state. Because the boson is
highly boosted, those will be very close together and therefore appear to the detector as only one jet. This means that
the decay of a q\* particle will have two jets in the endstate (assuming the W/Z boson decays to two quarks) and will
therefore be hard to distinguish from the QCD background described in [@sec:qcdbg].
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:qcdbg].
The choice of only examining the decay of the q\* particle to the vector bosons is motivated by the branching ratios
calculated for the decay [@QSTAR_THEORY]:
@ -228,9 +233,10 @@ decay, but virtually impossible to distinguish from the QCD background described
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 their four momenta, 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.
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 [@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
@ -239,13 +245,13 @@ the higher center of mass energy of the LHC as well as more data that is availab
### Quantum Chromodynamic background {#sec:qcdbg}
In this thesis, a decay with two jets in the endstate will be analysed. Therefore it will be hard to distinguish the
signal processes from QCD effects. Those can also produce two jets in the endstate, as can be seen in [@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:qs].
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: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:qs].
\begin{figure}
\centering
@ -270,46 +276,35 @@ Following on, the experimental setup used to gather the data analysed in this th
## Large Hadron Collider
The Large Hadron Collider is the world's largest and most powerful particle accelerator [@website]. It has a perimeter
of 27 km and can accelerate two beams of protons to an energy of 6.5 TeV resulting in a collision with a centre of mass
energy of 13 TeV. It is home to several experiments, 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 Large Hadron Collider [@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 $N_{event} = L\sigma_{event}$ with $\sigma_{event}$ being the cross
section of the event. The luminosity of the LHC for a Gaussian beam distribution can be described as follows:
\begin{equation}
L = \frac{N_b^2 n_b f_{rev} \gamma_r}{4 \pi \epsilon_n \beta^*}F
\end{equation}
Where $N_b$ is the number of particles per bunch, $n_b$ the number of bunches per beam, $f_{rev}$ the revolution
frequency, $\gamma_r$ the relativistic gamma factor, $\epsilon_n$ the normalised transverse beam emittance, $\beta^*$
the beta function at the collision point and F the geometric luminosity reduction factor due to the crossing angle at
the interaction point:
\begin{equation}
F = \left(1+\left( \frac{\theta_c\sigma_z}{2\sigma^*}\right)^2\right)^{-1/2}
\end{equation}
At the maximum luminosity of $10^{34}\si{\per\square\centi\metre\per\s}$, $N_b = 1.15 \cdot 10^{11}$, $n_b = 2808$,
$f_{rev} = \SI{11.2}{\kilo\Hz}$, $\beta^* = \SI{0.55}{\m}$, $\epsilon_n = \SI{3.75}{\micro\m}$ and $F = 0.85$.
To quantify the amount of data collected by one of the experiments at LHC, the integrated luminosity is introduced as
$L_{int} = \int L dt$.
explain pdf -> not all 13 TeV available for collision
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.
## Compact Muon Solenoid
The data used in this thesis was recorded by the Compact Muon Solenoid (CMS). 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:cms_setup]. The particles produced in a collision first go through a
tracking system. They then pass an electromegnetic 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 $\SI{63.67}{\per\femto\barn}$. Of that data, in 2016
$\SI{35.92}{\per\femto\barn}$, in 2017 $\SI{41.53}{\per\femto\barn}$ and in 2018 $\SI{59.74}{\per\femto\barn}$ were
usable for research. Therefore the combined integrated luminosity of data usable for research is
$\SI{137.19}{\per\femto\barn}$.
The data used in this thesis was recorded by the Compact Muon Solenoid (CMS) [@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: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.
![
The setup of the Compact Muon Solenoid showing its onion like structure, the different detector parts and where
@ -324,10 +319,9 @@ axis upwards and the x axis horizontal towards the LHC centre. The azimuthal ang
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: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 obviously 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.
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.
![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
@ -342,11 +336,11 @@ momentum. They are as close to the collision as possible to be able to identify
### 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 light in proportion to the particle's energy. This light
is measured by the photodetectors that convert this scintillation light to an electrical signal. To measure a particles
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 have are of higher energy and therefore only leave some energy in the ECAL
but are not stopped by it.
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.
### The hadronic calorimeter
@ -378,12 +372,12 @@ Level trigger uses a streamlined version of the CMS offline reconstruction softw
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
the track and its clusters 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
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.
## Jet clustering
@ -393,42 +387,40 @@ several algorithms exist to help with this problem. The algorithm used in this t
algorithm. It arises from a generalization of several other clustering algorithms, namely the $k_t$, Cambridge/Aachen
and SISCone clustering algorithms.
The anti-$k_t$ clustering algorithm associates hard particles with their soft particles surrounding them within a radius
$R = \sqrt{\eta^2 - \phi^2}$ 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:antiktcomparison]. For this analysis, a radius of 0.8 is used.
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.
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: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.
![
Comparison of the $k_t$, Cambridge/Aachen, SISCone and anti-$k_t$ algorithms clustering a sample parton-level event
with many random soft "ghosts". Taken from [@ANTIKT]
](./figures/antikt-comparision.png){#fig:antiktcomparison}
[@Fig:antiktcomparison] shows, that the jets reconstructed using the anti-$k_t$ algorithm have the clearest cone like
shape and is therefore chosen for this thesis.
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
# Method of analysis {#sec:moa}
This section gives an overview over how the data gathered 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 maybe confirm its existence.
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: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.
The decay q\* $\rightarrow$ qV + q $\rightarrow q\bar{q}$ + q 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 those two jets, which is identical to the mass of the q\* particle, is reconstructed. The
only background considered is the QCD background described in [@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.
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: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
@ -463,7 +455,7 @@ 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
- sigma: the functions width, in this case the resolution of the detector due to the very small resonance width expected
- n1, n2, alpha1, alpha2: parameters influencing the shape of the left and right tail
A gaussian and a poisson function have also been studied but found to be not able to reproduce the signal shape as they
@ -487,10 +479,10 @@ Combined fit of signal and background on a toy dataset with gaussian errors and
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
selection using kinematic variables and is also used to ensure a high trigger efficiency. 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 by comparing the data with the simulation in the signal as
well as a sideband region, where no signal events are expected.
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.
## Preselection
@ -507,67 +499,83 @@ case, the two jets with the highest $p_t$ are used for the reconstruction of the
The distributions of the number of jets before and after the selection can be seen in [@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. 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.}
\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 0. At the same time, particles
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: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 $\Delta\eta \le 1.3$. 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.}
\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: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 $m_{jj}$ distribution
should be a smoothly falling function for the QCD background and peak at the simulated resonance mass for the signal
events.
[@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}
@ -575,9 +583,9 @@ events.
\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.
Left: distribution before the
cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018.}
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}
@ -592,69 +600,77 @@ tenth.
## 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 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 of the variables that were used for the preselection can be seen for
year 2016 and the combined data of years 2016 to 2018.
year collected by the CMS detector. This is done for the year 2016 and for the combined dataset. In [@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. [source needed, but not sure where to find it]
by the CMS group. [cite todo]
\begin{figure}
\begin{minipage}{0.33\textwidth}
\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}{0.33\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}
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/DATA/v1_invmass_N_jets.eps}
\end{minipage}
\begin{minipage}{0.33\textwidth}
\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}{0.33\textwidth}
\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{Comparision of data with the Monte Carlo simulation.
1st row: data from 2016.
2nd row: combined data from 2016, 2017 and 2018.}
\caption{Comparison of data with the Monte Carlo simulation.}
\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 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
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 than the 105 GeV originates from the decay of a vector boson.
unlikely, that an event with a particle heavier than that originates from the decay of a vector boson.
In [@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:data-mc], the histograms are rescaled, so that
the dijet invariant mass distributions of data and simulation have the same integral.
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}{\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. 1st row: data from 2016. 2nd row:
combined data from 2016, 2017 and 2018.}
\caption{Comparison of data with the Monte Carlo simulation in the sideband region.}
\label{fig:sideband}
\end{figure}
@ -668,10 +684,10 @@ introduced, to further reduce the background to be able to look for the hypothet
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 cut
on the soft-drop mass of a jet. The soft-drop mass of at least one of the two leading jets is expected to be within
$\SI{35}{\giga\eV}$ and $\SI{105}{\giga\eV}$. This cut already provides a good separation of QCD and signal events, on
which the two taggers presented next can build.
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.
@ -695,7 +711,7 @@ Experiments showed, that rather than using $\tau_N$ directly, the ratio $\tau_{2
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
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.
@ -704,10 +720,11 @@ soft-drop mass window is used. If both of them pass, the one with higher $p_t$ i
The DeepAK8 tagger [@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 ~10 with the same signal efficiency compared to
non-machine-learning approaches like the N-Subjettiness method. This is supported by [@fig:ak8_eff], showing a
comparision of background and signal efficiency of the DeepAK8 tagger, with, between others, the $\tau_{21}$ tagger also
used in this analysis.
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.
![Comparison of tagger efficiencies, showing, between others, the DeepAK8 and $\tau_{21}$ tagger used in this analysis.
![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 [@DEEP_BOOSTED]](./figures/deep_ak8.pdf){#fig:ak8_eff width=60%}
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
@ -715,8 +732,8 @@ decreasing $p_t$. A total of 42 properties of the particles such es $p_t$, energ
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
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,
@ -725,10 +742,10 @@ particle. Its output is fed back to the network as a penalty so it avoids using
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 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.
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.
## Optimization {#sec:opt}
@ -778,7 +795,7 @@ for all masspoints of the decay to qW and qZ and for both datasets used, the one
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 [@ASYMPTOTIC_LIMIT]. Using the parameters and signal rate obtained
using the method described in [@sec:moa] as well as a shape analysis on the data recorded by the CMS, it determines an
by the method described in [@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 %.
@ -864,11 +881,11 @@ The limit established by using the N-subjettiness tagger on the 2016 data is alr
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. Comparing the expected limits, there is a difference between 3 % 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. 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:prev].
tagger (as can be seen in [@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:prev].
\begin{figure}
\begin{minipage}{0.5\textwidth}
@ -932,14 +949,14 @@ For further comparison, in [@fig:limit_comp] the expected limits of the differen
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: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 the best choice. To make sure,
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: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 much better in general.
explain, why it didn't perform better in general.
\begin{figure}
@ -963,33 +980,30 @@ decay to qZ}
# 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.
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 data analysis, the following selection was applied:
For the analysis, the following selection was applied to the data:
- #jets >= 2
- #jets $\ge$ 2
- $\Delta\eta < 1.4$
- $m_{jj} >= \SI{1050}{\giga\eV}$
- $m_{jj} \ge \SI{1050}{\giga\eV}$
- $\SI{35}{\giga\eV} < m_{SDM} < \SI{105}{\giga\eV}$
For the deep boosted tagger, a high purity category of $VvsQCD > 0.95$ and a low purity category of $VvsQCD <= 0.95$ 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 found by optimizing for the highest possible significance of the signal.
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.
After the selection, the cross section limits were extracted from the data and new exclusion limits for the mass of the
q\* particles 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.
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.
This research can also be used 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].
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

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@ -41,7 +41,7 @@
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@ -62,7 +62,7 @@
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@ -130,9 +130,10 @@ TeV resp. 4.7 TeV. Also a comparison of the new DeepAK8
\autocite{DEEP_BOOSTED} and the older N-subjettiness \autocite{TAU21}
tagger is conducted, showing that the newer DeepAK8 tagger, based on a
deep neural network, is currently approximately at the same level as the
N-subjettiness tagger, but has the potential to further improve in
performance, between others because of an improved training that was
just published.
N-subjettiness tagger, giving a \(\SI{0.1}{\tera\eV}\) better result for
the decay to qW but a by \(\SI{0.6}{\tera\eV}\) worse one for the decay
to qZ. It still has the potential to further improve in performance,
between others because of an improved training.
\end{abstract}
\renewcommand{\abstractname}{Zusammenfassung}
@ -146,14 +147,15 @@ die Jahre 2016, 2017 und 2018 bei einer Schwerpunktsenergie von
Indem der Zerfall des q* Teilchens zu q + W und q + Z untersucht wird,
kann dieses mit einem Konfidenzniveau von 95 \% bis zu einer Masse von
6.1 TeV (qW) bzw. 5.5 TeV (qZ) ausgeschlossen werden. Dieses Limit liegt
etwa 1 TeV höher, als das von vorhergegangener Forschung
\autocite{PREV_RESEARCH} gesetzte von 5.0 TeV bzw. 4.7 TeV. Dabei wird
der neue DeepAK8 Tagger \autocite{DEEP_BOOSTED}, welcher auf einem
neuronalen Netzwerk basiert, mit dem älteren N-Subjetiness Tagger
\autocite{TAU21} verglichen. Das Endergebnis der beiden Tagger
unterscheidet sich kaum, jedoch gibt es beim DeepAK8 Tagger noch
potential zur Verbesserung, unter anderem durch ein verbessertes
Traininig, welches vor kurzem veröffentlicht wurde.
etwa 1 TeV höher, als das anhand der Daten von 2016 gefundene von 5.0
TeV bzw. 4.7 TeV \autocite{PREV_RESEARCH}. Dabei wird der neue DeepAK8
Tagger \autocite{DEEP_BOOSTED}, welcher auf einem neuronalen Netzwerk
basiert, mit dem älteren N-Subjetiness Tagger \autocite{TAU21}
verglichen. Beim Zerfall zu qW erzielt er ein um \(\SI{0.1}{\tera\eV}\)
besseres Ergebnis, beim Zerfall zu qZ jedoch ein um
\(\SI{0.6}{\tera\eV}\) schlechteres. Mit einem verbesserten Training,
welches vor kurzem veröffentlicht wurde, gibt es aber noch Potential,
die Leistung zu steigern. \newpage
\end{abstract}
{
@ -167,10 +169,11 @@ Traininig, welches vor kurzem veröffentlicht wurde.
\section{Introduction}\label{introduction}}
The Standard Model is a very successful theory in describing most of the
effects on a particle level. But it still has a lot of shortcomings that
show that it isn't yet a full \enquote{theory of everything}. To solve
these shortcomings, lots of theories beyond the standard model exist
that try to explain some of them.
interactions happening between particles. Still, it has a lot of
shortcomings that show that it isn't yet a full \enquote{theory of
everything}. To solve these shortcomings, lots of theories beyond the
standard model exist that try to expand the Standard Model in different
ways to solve these issues.
One category of such theories is based on a composite quark model.
Quarks are currently considered elementary particles by the Standard
@ -181,10 +184,10 @@ particles and reduce the number of constants needed to explain the
properties of the known particles. One common prediction of those
theories are excited quark states. Those are quark states of higher
energy that can decay to an unexcited quark under the emission of a
boson. This thesis will search for their decay to a quark and a W/Z
boson. The W/Z boson then decays in the hadronic channel, to two more
quarks. The endstate of this decay has only quarks, making Quantum
Chromodynamics effects the main background.
boson. This thesis will look for their decay to a vector boson that then
further decays hadronically. The final state of this decay consists only
of quarks forming two jets, making Quantum Chromodynamics the main
background.
In a previous research \autocite{PREV_RESEARCH}, a lower limit for the
mass of an excited quark has already been set using data from the 2016
@ -222,7 +225,7 @@ explain the background processes of quantum chromodynamics and the
theory of q*, which will be the main topic of this thesis.
\hypertarget{sec:sm}{%
\subsection{Standard model}\label{sec:sm}}
\subsection{Standard Model}\label{sec:sm}}
The Standard Model of physics proved to be very successful in describing
three of the four fundamental interactions currently known: the
@ -240,14 +243,10 @@ corresponding neutrino, namely first the electron, then the muon and
third, the tau. The three quark generations consist of first, the up and
down, second, the charm and strange, and third, the top and bottom
quark. So overall, their exists a total of six quark and six lepton
flavours. A full list of particles known to the standard model can be
found in fig.~\ref{fig:sm}. Furthermore, all fermions have an associated
anti particle with reversed charge.
The matter around us, is built from so called hadrons, that are bound
states of quarks, for example protons and neutrons. Long lived hadrons
consist of up and down quarks, as the heavier ones over time decay to
those.
flavours. A full list of particles of the standard model can be found in
Fig.~\ref{fig:sm}. Furthermore, all fermions have an associated anti
particle with reversed charge. Bound states of multiple quarks also
exist and are called hadrons.
\begin{figure}
\hypertarget{fig:sm}{%
@ -299,9 +298,9 @@ a lepton and the corresponding anti-lepton neutrino, in the hadronic
channel it decays to a quark and an anti-quark of a different flavour.
Due to the \(Z^0\) boson having no charge, it always decays to a fermion
and its anti-particle, in the leptonic channel this might be for example
a electron - positron pair, in the hadronic channel an up and anti-up
an electron - positron pair, in the hadronic channel an up and anti-up
quark pair. This thesis examines the hadronic decay channel, where both
vector bosons essentially decay to to quarks.
vector bosons essentially decay to two quarks.
The quantum chromodynamics (QCD) describes the strong interaction of
particles. It applies to all particles carrying colour (e.g.~quarks).
@ -335,7 +334,7 @@ sources, the Standard Model still has several shortcomings.
\item
\textbf{Dark Matter}: observations of the rotational velocity of
galaxies can't be explained by the known matter. Dark matter currently
is our best theory to explain those.
the most popular theory to explain those.
\item
\textbf{Matter-antimatter asymmetry}: The amount of matter vastly
outweights the amount of antimatter in the observable universe. This
@ -358,16 +357,17 @@ sources, the Standard Model still has several shortcomings.
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 to us so far. This
could explain the symmetries between the different fermions. A common
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
could decay under the emission of any boson. Quarks are smaller than
\(10^{-18}\) m. This corresponds to an energy scale of approximately 1
TeV. Therefore the excited quark states are expected to be in that
region. That will cause the emitted boson to be highly boosted.
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
approximately 1 TeV. Therefore the excited quark states are expected to
be in that region. That will cause the emitted boson to be highly
boosted.
\begin{figure}
\centering
@ -377,22 +377,22 @@ region. That will cause the emitted boson to be highly boosted.
q1 [particle=\(q\)] -- v -- w [particle=\(W\)],
q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)],
};
\caption{Feynman diagram showing a possible decay of a q* particle to a W boson and a quark with the W boson also
decaying to two quarks.} \label{fig:qsfeynman}
\caption{Feynman diagram showing the decay of a q* particle to a W boson and a quark with the W boson decaying
hadronically.} \label{fig:qsfeynman}
\end{figure}
This thesis will search data collected by the CMS in the years 2016,
2017 and 2018 for the single excited quark state 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 fig.~\ref{fig:qsfeynman}. As explained in
sec.~\ref{sec:sm}, the vector boson can then decay either in the
2017 and 2018 for the decay of a single excited quark state q* to a
quark and a vector boson . An example of a q* decaying to a quark and a
W boson can be seen in Fig.~\ref{fig:qsfeynman}. As explained in
Sec.~\ref{sec:sm}, the vector boson can then decay either in the
hadronic or leptonic decay channel. This research investigates only the
hadronic channel with two quarks in the endstate. Because the boson is
highly boosted, those will be very close together and therefore appear
to the detector as only one jet. This means that the decay of a q*
particle will have two jets in the endstate (assuming the W/Z boson
decays to two quarks) and will therefore be hard to distinguish from the
QCD background described in sec.~\ref{sec:qcdbg}.
hadronic channel with two quarks in the final state. Because the boson
is highly boosted, those will be very close together and therefore
appear to the detector as only one jet. This means that the investigated
decay of a q* particle will have two jets in the final state and will
therefore be hard to distinguish from the QCD background described in
Sec.~\ref{sec:qcdbg}.
The choice of only examining the decay of the q* particle to the vector
bosons is motivated by the branching ratios calculated for the decay
@ -428,10 +428,10 @@ 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 their four momenta,
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.
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
@ -444,17 +444,17 @@ that is available now.
\hypertarget{sec:qcdbg}{%
\subsubsection{Quantum Chromodynamic background}\label{sec:qcdbg}}
In this thesis, a decay with two jets in the endstate will be analysed.
Therefore it will be hard to distinguish the signal processes from QCD
effects. Those can also produce two jets in the endstate, 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
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}.
background of the signal described in Sec.~\ref{sec:qs}.
\begin{figure}
\centering
@ -482,59 +482,52 @@ this thesis will be described.
\hypertarget{large-hadron-collider}{%
\subsection{Large Hadron Collider}\label{large-hadron-collider}}
The Large Hadron Collider is the world's largest and most powerful
particle accelerator \autocite{website}. It has a perimeter of 27 km and
can 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 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 \(N_{event} = L\sigma_{event}\) with
\(\sigma_{event}\) being the cross section of the event. The luminosity
of the LHC for a Gaussian beam distribution can be described as follows:
\begin{equation}
L = \frac{N_b^2 n_b f_{rev} \gamma_r}{4 \pi \epsilon_n \beta^*}F
\end{equation} Where \(N_b\) is the number of particles per bunch,
\(n_b\) the number of bunches per beam, \(f_{rev}\) the revolution
frequency, \(\gamma_r\) the relativistic gamma factor, \(\epsilon_n\)
the normalised transverse beam emittance, \(\beta^*\) the beta function
at the collision point and F the geometric luminosity reduction factor
due to the crossing angle at the interaction point: \begin{equation}
F = \left(1+\left( \frac{\theta_c\sigma_z}{2\sigma^*}\right)^2\right)^{-1/2}
\end{equation} At the maximum luminosity of
\(10^{34}\si{\per\square\centi\metre\per\s}\),
\(N_b = 1.15 \cdot 10^{11}\), \(n_b = 2808\),
\(f_{rev} = \SI{11.2}{\kilo\Hz}\), \(\beta^* = \SI{0.55}{\m}\),
\(\epsilon_n = \SI{3.75}{\micro\m}\) and \(F = 0.85\).
To quantify the amount of data collected by one of the experiments at
LHC, the integrated luminosity is introduced as \(L_{int} = \int L dt\).
explain pdf -\textgreater{} not all 13 TeV available for collision
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). 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 electromegnetic 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
\(\SI{63.67}{\per\femto\barn}\). Of that data, in 2016
\(\SI{35.92}{\per\femto\barn}\), in 2017 \(\SI{41.53}{\per\femto\barn}\)
and in 2018 \(\SI{59.74}{\per\femto\barn}\) were usable for research.
Therefore the combined integrated luminosity of data usable for research
is \(\SI{137.19}{\per\femto\barn}\).
(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}{%
@ -556,14 +549,14 @@ 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
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 obviously 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.
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}{%
@ -590,13 +583,13 @@ 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 light in proportion to the
particle's energy. This light is measured by the photodetectors that
convert this scintillation light to an electrical signal. To measure a
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 have are of higher energy and therefore only
leave some energy in the ECAL but are not stopped by it.
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
@ -646,15 +639,15 @@ 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 the track and
its clusters 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
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.
@ -669,23 +662,16 @@ anti-\(k_t\) clustering algorithm. It arises from a generalization of
several other clustering algorithms, namely the \(k_t\),
Cambridge/Aachen and SISCone clustering algorithms.
The anti-\(k_t\) clustering algorithm associates hard particles with
their soft particles surrounding them within a radius
\(R = \sqrt{\eta^2 - \phi^2}\) 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}. For this analysis, a radius of 0.8 is
used.
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.
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}{%
@ -698,35 +684,40 @@ random soft \enquote{ghosts}. Taken from
}
\end{figure}
Fig.~\ref{fig:antiktcomparison} shows, that the jets reconstructed using
the anti-\(k_t\) algorithm have the clearest cone like shape and is
therefore chosen for this thesis.
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 gathered 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 maybe confirm its existence.
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
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.
The decay q* \(\rightarrow\) qV + q \(\rightarrow q\bar{q}\) + q 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 those two jets,
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.
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
@ -781,7 +772,7 @@ six parameters:
mean: the functions mean, in this case the resonance mass
\item
sigma: the functions width, in this case the resolution of the
detector
detector due to the very small resonance width expected
\item
n1, n2, alpha1, alpha2: parameters influencing the shape of the left
and right tail
@ -796,7 +787,7 @@ 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
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
@ -824,13 +815,13 @@ 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 selection using kinematic variables and is also used
to ensure a high trigger efficiency. 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 by comparing the data
with the simulation in the signal as well as a sideband region, where no
signal events are expected.
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}}
@ -851,25 +842,30 @@ jets, accounting for the possibility of more jets, for example caused by
gluon radiation of a quark or other QCD effects. If this is the case,
the two jets with the highest \(p_t\) are used for the reconstruction of
the q* mass. The distributions of the number of jets before and after
the selection can be seen in fig.~\ref{fig:njets}.
the 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. 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.}
\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}
@ -879,29 +875,35 @@ 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 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
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}.
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 $\Delta\eta \le 1.3$. 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.}
\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}
@ -910,20 +912,26 @@ The last selection in the preselection is on the dijet invariant mass:
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 way lighter
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}
@ -931,9 +939,9 @@ simulated resonance mass for the signal events.
\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.
Left: distribution before the
cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018.}
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}
@ -955,80 +963,86 @@ 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 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.~\ref{fig:data-mc}, the three distributions of the
variables that were used for the preselection can be seen for year 2016
and the combined data of years 2016 to 2018. 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. {[}source needed, but not sure where to find
it{]}
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}{0.33\textwidth}
\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}{0.33\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}
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/DATA/v1_invmass_N_jets.eps}
\end{minipage}
\begin{minipage}{0.33\textwidth}
\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}{0.33\textwidth}
\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{Comparision of data with the Monte Carlo simulation.
1st row: data from 2016.
2nd row: combined data from 2016, 2017 and 2018.}
\caption{Comparison of data with the Monte Carlo simulation.}
\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.
\hypertarget{sideband}{%
\subsubsection{Sideband}\label{sideband}}
The sideband 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 (\(p_t\)) is more than 105
GeV was 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 a particle
heavier than t In fig.~\ref{fig:sideband}, the comparison of data with
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:data-mc{]}, the histograms are rescaled, so that the dijet
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. 1st row: data from 2016. 2nd row:
combined data from 2016, 2017 and 2018.}
\caption{Comparison of data with the Monte Carlo simulation in the sideband region.}
\label{fig:sideband}
\end{figure}
@ -1047,12 +1061,12 @@ 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 cut
on the soft-drop mass of a jet. The soft-drop mass of at least one of
the two leading jets is expected to be within \(\SI{35}{\giga\eV}\) and
\(\SI{105}{\giga\eV}\). This cut already provides a good separation of
QCD and signal events, on which the two taggers presented next can
build.
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
@ -1087,7 +1101,7 @@ 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
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.
@ -1100,17 +1114,19 @@ The DeepAK8 tagger \autocite{DEEP_BOOSTED} uses a deep neural network
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 comparision of background and signal
efficiency of the DeepAK8 tagger, with, between others, the
\(\tau_{21}\) tagger also used in this analysis.
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 and \(\tau_{21}\) tagger used in this analysis. Taken from
\autocite{DEEP_BOOSTED}}\label{fig:ak8_eff}
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}
@ -1122,11 +1138,11 @@ 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.
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
@ -1138,12 +1154,12 @@ 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 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.
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}}
@ -1205,15 +1221,15 @@ category is used: \(VvsQCD < 0.95\).
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
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 using the method described in
sec.~\ref{sec:moa} as well as a shape analysis on the data recorded by
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
@ -1270,18 +1286,18 @@ combined dataset, again using both taggers comparing their performances.
\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.
section limits seen in Fig.~\ref{fig:res2016} were obtained.
As described in sec.~\ref{sec:extr}, the calculated cross section limits
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
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 tbl.~\ref{tbl:res2016}. The
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
@ -1337,14 +1353,15 @@ 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}). This could be caused by small
differences of the setup used or slightly differently processed data.
Comparing the expected limits, there is a difference between 3 \% 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. 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}.
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}
@ -1362,7 +1379,7 @@ Taken from \cite{PREV_RESEARCH}.}
\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,
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.
@ -1419,17 +1436,17 @@ deep boosted tagger (right).}
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
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
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 the best choice. To
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
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
@ -1437,7 +1454,7 @@ 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 much better in general.
perform better in general.
\begin{figure}
\begin{minipage}{0.5\textwidth}
@ -1468,47 +1485,45 @@ high purity category using the data from year
\section{Summary}\label{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.
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 data analysis, the following selection was applied:
For the analysis, the following selection was applied to the data:
\begin{itemize}
\tightlist
\item
\#jets \textgreater= 2
\#jets \(\ge\) 2
\item
\(\Delta\eta < 1.4\)
\item
\(m_{jj} >= \SI{1050}{\giga\eV}\)
\(m_{jj} \ge \SI{1050}{\giga\eV}\)
\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 \(VvsQCD <= 0.95\) was used. For the
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 found by optimizing for the highest possible significance of the
were obtained by optimizing for the highest possible significance of the
signal.
After the selection, the cross section limits were extracted from the
data and new exclusion limits for the mass of the q* particles 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.
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.
This research can also be used 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.~\ref{fig:res2016} and fig.~\ref{fig:resCombined}.
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

View File

@ -2,28 +2,28 @@
\babel@toc {british}{}
\contentsline {section}{\numberline {1}Introduction}{1}{section.1}%
\contentsline {section}{\numberline {2}Theoretical motivation}{2}{section.2}%
\contentsline {subsection}{\numberline {2.1}Standard model}{2}{subsection.2.1}%
\contentsline {subsubsection}{\numberline {2.1.1}Shortcomings of the Standard Model}{4}{subsubsection.2.1.1}%
\contentsline {subsection}{\numberline {2.1}Standard Model}{2}{subsection.2.1}%
\contentsline {subsubsection}{\numberline {2.1.1}Shortcomings of the Standard Model}{3}{subsubsection.2.1.1}%
\contentsline {subsection}{\numberline {2.2}Excited quark states}{4}{subsection.2.2}%
\contentsline {subsubsection}{\numberline {2.2.1}Quantum Chromodynamic background}{5}{subsubsection.2.2.1}%
\contentsline {section}{\numberline {3}Experimental Setup}{7}{section.3}%
\contentsline {subsection}{\numberline {3.1}Large Hadron Collider}{7}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Compact Muon Solenoid}{7}{subsection.3.2}%
\contentsline {subsubsection}{\numberline {3.2.1}Coordinate conventions}{8}{subsubsection.3.2.1}%
\contentsline {subsubsection}{\numberline {3.2.2}The tracking system}{9}{subsubsection.3.2.2}%
\contentsline {subsubsection}{\numberline {3.2.3}The electromagnetic calorimeter}{9}{subsubsection.3.2.3}%
\contentsline {subsubsection}{\numberline {3.2.4}The hadronic calorimeter}{9}{subsubsection.3.2.4}%
\contentsline {subsubsection}{\numberline {3.2.5}The solenoid}{10}{subsubsection.3.2.5}%
\contentsline {subsubsection}{\numberline {3.2.6}The muon system}{10}{subsubsection.3.2.6}%
\contentsline {subsubsection}{\numberline {3.2.7}The Trigger system}{10}{subsubsection.3.2.7}%
\contentsline {subsubsection}{\numberline {3.2.8}The Particle Flow algorithm}{10}{subsubsection.3.2.8}%
\contentsline {subsection}{\numberline {3.3}Jet clustering}{10}{subsection.3.3}%
\contentsline {section}{\numberline {4}Method of analysis}{12}{section.4}%
\contentsline {subsection}{\numberline {4.1}Signal and Background modelling}{12}{subsection.4.1}%
\contentsline {section}{\numberline {5}Preselection and data quality}{14}{section.5}%
\contentsline {subsection}{\numberline {5.1}Preselection}{14}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Data - Monte Carlo Comparison}{18}{subsection.5.2}%
\contentsline {subsubsection}{\numberline {5.2.1}Sideband}{19}{subsubsection.5.2.1}%
\contentsline {section}{\numberline {3}Experimental Setup}{6}{section.3}%
\contentsline {subsection}{\numberline {3.1}Large Hadron Collider}{6}{subsection.3.1}%
\contentsline {subsection}{\numberline {3.2}Compact Muon Solenoid}{6}{subsection.3.2}%
\contentsline {subsubsection}{\numberline {3.2.1}Coordinate conventions}{7}{subsubsection.3.2.1}%
\contentsline {subsubsection}{\numberline {3.2.2}The tracking system}{7}{subsubsection.3.2.2}%
\contentsline {subsubsection}{\numberline {3.2.3}The electromagnetic calorimeter}{8}{subsubsection.3.2.3}%
\contentsline {subsubsection}{\numberline {3.2.4}The hadronic calorimeter}{8}{subsubsection.3.2.4}%
\contentsline {subsubsection}{\numberline {3.2.5}The solenoid}{8}{subsubsection.3.2.5}%
\contentsline {subsubsection}{\numberline {3.2.6}The muon system}{9}{subsubsection.3.2.6}%
\contentsline {subsubsection}{\numberline {3.2.7}The Trigger system}{9}{subsubsection.3.2.7}%
\contentsline {subsubsection}{\numberline {3.2.8}The Particle Flow algorithm}{9}{subsubsection.3.2.8}%
\contentsline {subsection}{\numberline {3.3}Jet clustering}{9}{subsection.3.3}%
\contentsline {section}{\numberline {4}Method of analysis}{11}{section.4}%
\contentsline {subsection}{\numberline {4.1}Signal and Background modelling}{11}{subsection.4.1}%
\contentsline {section}{\numberline {5}Preselection and data quality}{13}{section.5}%
\contentsline {subsection}{\numberline {5.1}Preselection}{13}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Data - Monte Carlo Comparison}{17}{subsection.5.2}%
\contentsline {subsubsection}{\numberline {5.2.1}Sideband}{17}{subsubsection.5.2.1}%
\contentsline {section}{\numberline {6}Jet substructure selection}{20}{section.6}%
\contentsline {subsection}{\numberline {6.1}N-Subjettiness}{20}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}DeepAK8}{21}{subsection.6.2}%
@ -32,7 +32,7 @@
\contentsline {subsection}{\numberline {7.1}Uncertainties}{23}{subsection.7.1}%
\contentsline {section}{\numberline {8}Results}{24}{section.8}%
\contentsline {subsection}{\numberline {8.1}2016}{24}{subsection.8.1}%
\contentsline {subsubsection}{\numberline {8.1.1}Previous research}{24}{subsubsection.8.1.1}%
\contentsline {subsubsection}{\numberline {8.1.1}Previous research}{26}{subsubsection.8.1.1}%
\contentsline {subsection}{\numberline {8.2}Combined dataset}{26}{subsection.8.2}%
\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{27}{subsection.8.3}%
\contentsline {section}{\numberline {9}Summary}{29}{section.9}%