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@ -1623,3 +1623,21 @@ archivePrefix = {arXiv},
(CMS Public Pages)",
doi = "10.1088/1748-0221/12/10/P10003",
}
@ARTICLE{ASYMPTOTIC_LIMIT,
author = {{Cowan}, Glen and {Cranmer}, Kyle and {Gross}, Eilam and {Vitells}, Ofer},
title = "{Asymptotic formulae for likelihood-based tests of new physics}",
journal = {European Physical Journal C},
keywords = {Physics - Data Analysis, Statistics and Probability, High Energy Physics - Experiment},
year = "2011",
month = "Feb",
volume = {71},
eid = {1554},
pages = {1554},
doi = {10.1140/epjc/s10052-011-1554-0},
archivePrefix = {arXiv},
eprint = {1007.1727},
primaryClass = {physics.data-an},
adsurl = {https://ui.adsabs.harvard.edu/abs/2011EPJC...71.1554C},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

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@ -25,16 +25,19 @@
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@ -10301,6 +10301,58 @@
\endverb
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family={{Vitells}},
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@ -1999,24 +1999,29 @@
<bcf:citekey order="2">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="3">TAU21</bcf:citekey>
<bcf:citekey order="4">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="5">QSTAR_THEORY</bcf:citekey>
<bcf:citekey order="6">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="7">website</bcf:citekey>
<bcf:citekey order="8">CMS_PLOT</bcf:citekey>
<bcf:citekey order="9">CMS_PLOT</bcf:citekey>
<bcf:citekey order="10">ANTIKT</bcf:citekey>
<bcf:citekey order="11">ANTIKT</bcf:citekey>
<bcf:citekey order="12">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="13">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="14">QSTAR_THEORY</bcf:citekey>
<bcf:citekey order="15">TAU21</bcf:citekey>
<bcf:citekey order="16">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="17">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="18">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="19">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="20">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="21">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="22">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="5">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="6">TAU21</bcf:citekey>
<bcf:citekey order="7">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="8">QSTAR_THEORY</bcf:citekey>
<bcf:citekey order="9">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="10">website</bcf:citekey>
<bcf:citekey order="11">CMS_PLOT</bcf:citekey>
<bcf:citekey order="12">CMS_PLOT</bcf:citekey>
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<bcf:citekey order="16">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="17">QSTAR_THEORY</bcf:citekey>
<bcf:citekey order="18">TAU21</bcf:citekey>
<bcf:citekey order="19">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="20">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="21">DEEP_BOOSTED</bcf:citekey>
<bcf:citekey order="22">ASYMPTOTIC_LIMIT</bcf:citekey>
<bcf:citekey order="23">QSTAR_THEORY</bcf:citekey>
<bcf:citekey order="24">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="25">PREV_RESEARCH</bcf:citekey>
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<bcf:citekey order="27">PREV_RESEARCH</bcf:citekey>
<bcf:citekey order="0" nocite="1">*</bcf:citekey>
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@ -7,25 +7,40 @@ header-includes: |
\usepackage{siunitx}
\usepackage{tikz-feynman}
\usepackage{csquotes}
\usepackage{abstract}
\pagenumbering{gobble}
\setlength{\parskip}{0.5em}
\bibliographystyle{lucas_unsrt}
abstract: |
A search for an excited quark state, called q\*, is presented using data recorded by CMS during the years 2016, 2017
and 2018. By analysing its decay channels to qW and qZ, a minimum mass of 6.1 TeV resp. 5.5 TeV is established. This
limit is about 1 TeV higher than the limits found by a 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 is currently approximately at the same level as the N-subjettiness tagger, but has the potential to further
improve in performance.
A search for an excited quark state, called q\*, is presented using data recorded by the CMS experiment during the
years 2016, 2017 and 2018 with a centre-of-mass energy of $\sqrt{s} = \SI{13}{\tera\eV}$ and a total integrated
luminosity of $\SI{137.19}{\per\femto\barn}$. By analysing its decay channels to q + W and q + Z that further decay
to $q + q\bar{q}$, resulting in two jets in the final state, the q\* can be excluded up to a mass of 6.1 (qW) TeV
resp. 5.5 TeV (qZ) with a confidence level of 95 %. This limit is about 1 TeV higher than the limits found by a
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.
```{=tex}
\end{abstract}
\renewcommand{\abstractname}{Zusammenfassung}
\begin{abstract}
Abstract 2.
```
In dieser Arbeit wird eine Suche nach angeregten Quarkzuständen, genannt q\*, durchgeführt. Dafür werden Daten mit
einer gesamten integrierten Luminosität von $\SI{137.19}{\per\femto\barn}$ analysiert, welche über die Jahre 2016,
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.
documentclass: article
geometry:
- top=2.5cm
@ -280,6 +295,8 @@ $f_{rev} = \SI{11.2}{\kilo\Hz}$, $\beta^* = \SI{0.55}{\m}$, $\epsilon_n = \SI{3.
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
## Compact Muon Solenoid
@ -382,7 +399,7 @@ changed according to its hardness in regards to the transverse momentum. A softe
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 softdropmass can be used. It is
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.
@ -452,7 +469,9 @@ The signal is fitted using a double sided crystal ball function. It has six para
A gaussian and a poisson function have also been studied but found to be not able to reproduce the signal shape as they
couldn't model the tails on both sides of the peak.
An example of a fit of these functions to a toy dataset with gaussian errors can be seen in [@fig:cb_fit]. In this
A linear combination of the signal and background function is then fitted to a toy dataset with gaussian errors and a
simulated signal cross section of $\SI{1}{\per\pico\barn}$. The resulting coefficients of said combination then show the
expected signal rate for the simulated cross section. An example of such a fit can be seen in [@fig:cb_fit]. In this
figure, a binning of 200 GeV is used. For the actual analysis a 1 GeV binning will be used. It can be seen that the fit
works very well and therefore confirms the functions chosen to model signal and background. This is supported by a
$\chi^2 /$ ndof of 0.5 and a found mean for the signal at 2999 $\pm$ 23 $\si{\giga\eV}$ which is extremely close to the
@ -468,10 +487,10 @@ 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 make sure a good trigger efficiency is achieved. 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.
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.
## Preselection
@ -481,10 +500,10 @@ reconstruction. Furthermore, all events with one of the two highest $p_t$ jets h
than 0.8 from any electron or muon are discarded to allow future use of the results in studies of the semi or
all-leptonic decay channels.
From a decaying q\* particle, we expect two jets in the endstate. The dijet invariant mass of those two jets will be
used to reconstruct the mass of the q\* particle. Therefore a cut is added to have at least 2 jets.
More jets are also possible, for example caused by gluon radiation of a quark causing another jet. If this is the case,
the two jets with the highest $p_t$ are used for the reconstruction of the q\* mass.
From a decaying q\* particle, two jets are expected in the final state. The dijet invariant mass of those two jets will
be used to reconstruct the mass of the q\* particle. Therefore a cut is added to have at least 2 jets, accounting for
the possibility of more jets, for example caused by gluon radiation of a quark or other QCD effects. If this is the
case, the two jets with the highest $p_t$ are used for the reconstruction of the q\* mass.
The distributions of the number of jets before and after the selection can be seen in [@fig:njets].
\begin{figure}
@ -500,16 +519,17 @@ The distributions of the number of jets before and after the selection can be se
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/v1_Njet_N_jets_stack.eps}
\end{minipage}
\caption{Number of jet distribution showing the cut at number of jets $\ge$ 2. Left: distribution before the cut. Right:
\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.}
\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
first two jets in regards to their 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
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
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].
@ -527,17 +547,19 @@ the $\Delta\eta$ distribution before and after the selection can be seen in [@fi
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/v1_Eta_deta_stack.eps}
\end{minipage}
\caption{$\Delta\eta$ distribution showing the cut at $\Delta\eta \le 1.3$. Left: distribution before the cut. Right:
distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves
are amplified by a factor of 10,000, to be visible.}
\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.}
\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 high trigger efficiency and can be seen in [@fig:invmass]. Also, it has a huge impact on the background because it
usually consists of way lighter particles. The q\* on the other hand is expected to have a very high invariant mass of
more than 1 TeV. The $m_{jj}$ distribution should be a smoothly falling function for the QCD background and peak at the
simulated resonance mass for the signal events.
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.
\begin{figure}
\begin{minipage}{0.5\textwidth}
@ -552,8 +574,8 @@ simulated resonance mass for the signal events.
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/v1_invmass_invMass_stack.eps}
\end{minipage}
\caption{Invariant mass distribution showing the cut at $m_{jj} \ge \SI{1050}{\giga\eV}$. It shows the expected smooth
falling functions of the background whereas the signal peaks at the simulated resonance mass.
\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.}
\label{fig:invmass}
@ -565,18 +587,18 @@ preselection is reduced to 5 % of the original events. For the combined data of
similar. Decaying to qW signal efficiencies between 49 % (1.6 TeV) and 56 % (7 TeV) are reached, wheres the efficiencies
when decaying to qZ are in the range of 46 % (1.6 TeV) to 50 % (7 TeV). Here, the background could be reduced to 8 % of
the original events. So while keeping around 50 % of the signal, the background was already reduced to less than a
tenth. Still, as can be seen in [@fig:njets] to [@fig:invmass], the amount of signal is very low.
tenth.
## Data - Monte Carlo Comparison
To ensure high data quality, the simulated QCD background sample is now being compared to the actual data of the
corresponding year collected by the CMS detector. This is done for the year 2016 and for the combined data of years
2016, 2017 and 2018. The distributions are rescaled so the integral over the invariant mass distribution of data and
simulation are the same. In [@fig:data-mc], the three distributions 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 real 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]
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.
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]
\begin{figure}
\begin{minipage}{0.33\textwidth}
@ -610,10 +632,10 @@ and simulation.
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 softdropmass 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:sideband], the comparison of data with simulation in the sideband region can be seen for the softdropmass
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.
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.
It can be seen, that in the sideband region data and simulation match very well.
@ -640,14 +662,14 @@ combined data from 2016, 2017 and 2018.}
# Jet substructure selection
So far it was made sure, that the actual data and the simulation are in good agreement after the preselection and no
unwanted side effects are introduced in the data by the used cuts. Now another selection has to be introduced, to
further reduce the background to be able to extract the hypothetical signal events from the actual data.
So far it was made sure, that the data collected by the CMS and the simulation are in good agreement after the
preselection and no unwanted side effects are introduced in the data by the used cuts. Now another selection has to be
introduced, to further reduce the background to be able to look for the hypothetical signal events in the data.
This is done by distinguishing between QCD and signal events using a tagger to identify jets coming
from a vector boson. Two different taggers will be used to later compare their performance. The decay analysed includes
either a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a cut
on the softdropmass of a jet. The softdropmass of at least one of the two leading jets is expected to be within
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.
@ -675,7 +697,7 @@ discriminator between QCD events and events originating from the decay of a boos
The lower the $\tau_{21}$ is, the more likely a jet is caused by the decay of a vector boson. Therefore a selection will
be introduced, so that $\tau_{21}$ of one candidate jet is smaller then some value that will be determined by an
optimization process described in the next chapter. As candidate jet the one of the two highest $p_t$ jets passing the
softdropmass window is used. If both of them pass, the one with higher $p_t$ is chosen.
soft-drop mass window is used. If both of them pass, the one with higher $p_t$ is chosen.
## DeepAK8
@ -686,7 +708,7 @@ comparision of background and signal efficiency of the DeepAK8 tagger, with, bet
used in this analysis.
![Comparison of tagger efficiencies, showing, between others, the DeepAK8 and $\tau_{21}$ tagger used in this analysis.
Taken from [@DEEP_BOOSTED]](./figures/deep_ak8.pdf){#fig:ak8_eff width=80%}
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
decreasing $p_t$. A total of 42 properties of the particles such es $p_t$, energy deposit, charge and the
@ -701,7 +723,7 @@ In this thesis, the mass decorrelated version of the DeepAK8 tagger is used. It
that is trained to quantify how strongly the output of the non-decorrelated tagger is correlated to the mass of a
particle. Its output is fed back to the network as a penalty so it avoids using features of the particles correlated to
their mass. The result is a largely mass decorrelated tagger of heavy resonances.
As the mass variable is already in use for the softdropmass selection, this version of the tagger is to be preferred.
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
@ -751,14 +773,19 @@ the deep boosted tagger the opposite cut from the high purity category is used:
After the optimization, now the optimal selection for the N-subjettiness as well as the deep boosted tagger is found and
applied to the simulated samples as well as the data collected by the CMS. The fit described in [@sec:moa] is performed
for all masspoints of the decay to qW and qZ and for both datasets used, the one from 2016 und the combined one of 2016,
2017 and 2018.
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 extract the signal from the background, its cross section limit is calculated using a frequentist asymptotic limit
calculator. It performs a shape analysis of the dijet invariant mass spectrum to determine an expected and an observed
limit. If there's no resonance of the q\* particle in the data, the observed limit should lie within the $2\sigma$
environment of the expected limit. After that, the crossing of the theory line, representing the cross section limits
expected, if the q\* particle would exist, and the observed data is calculated, to have a limit of mass up to which the
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
expected and an observed cross section limit by doing a signal + background versus background-only hypothesis test. It
also calculates upper and lower limits of the expected cross section corresponding to a confidence level of 95 %.
If there's no resonance of the q\* particle in the data, the observed limit should lie within the $2\sigma$ environment,
meaning a 95 % confidence level, of the expected limit. This observed limit is plotted together with a theory line,
representing the cross section limits expected, if the q\* predicted by [@QSTAR_THEORY] would exist.
The crossing of the theory line with the observed limit is then calculated, to have a limit of mass up to which the
existence of the q\* particle can be excluded. To find the uncertainty of this result, the crossing of the theory line
plus, respectively minus, its uncertainty with the observed limit is also calculated.

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@ -77,6 +77,7 @@
\usepackage{siunitx}
\usepackage{tikz-feynman}
\usepackage{csquotes}
\usepackage{abstract}
\pagenumbering{gobble}
\setlength{\parskip}{0.5em}
\bibliographystyle{lucas_unsrt}
@ -116,20 +117,43 @@
\maketitle
\begin{abstract}
A search for an excited quark state, called q*, is presented using data
recorded by CMS during the years 2016, 2017 and 2018. By analysing its
decay channels to qW and qZ, a minimum mass of 6.1 TeV resp. 5.5 TeV is
established. This limit is about 1 TeV higher than the limits found by a
previous research of data collected by CMS in 2016
recorded by the CMS experiment during the years 2016, 2017 and 2018 with
a centre-of-mass energy of \(\sqrt{s} = \SI{13}{\tera\eV}\) and a total
integrated luminosity of \(\SI{137.19}{\per\femto\barn}\). By analysing
its decay channels to q + W and q + Z that further decay to
\(q + q\bar{q}\), resulting in two jets in the final state, the q* can
be excluded up to a mass of 6.1 (qW) TeV resp. 5.5 TeV (qZ) with a
confidence level of 95 \%. This limit is about 1 TeV higher than the
limits found by a previous research of data collected by CMS in 2016
\autocite{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
\autocite{DEEP_BOOSTED} and the older N-subjettiness \autocite{TAU21}
tagger is conducted, showing that the newer DeepAK8 tagger is currently
approximately at the same level as the N-subjettiness tagger, but has
the potential to further improve in performance.
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.
\end{abstract}
\renewcommand{\abstractname}{Zusammenfassung}
\begin{abstract}
Abstract 2.
In dieser Arbeit wird eine Suche nach angeregten Quarkzuständen, genannt
q*, durchgeführt. Dafür werden Daten mit einer gesamten integrierten
Luminosität von \(\SI{137.19}{\per\femto\barn}\) analysiert, welche über
die Jahre 2016, 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
\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.
\end{abstract}
{
@ -490,6 +514,8 @@ due to the crossing angle at the interaction point: \begin{equation}
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
\hypertarget{compact-muon-solenoid}{%
\subsection{Compact Muon Solenoid}\label{compact-muon-solenoid}}
@ -654,7 +680,7 @@ 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 softdropmass can be used. It is calculated by removing wide
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
@ -765,15 +791,19 @@ A gaussian and a poisson function have also been studied but found to be
not able to reproduce the signal shape as they couldn't model the tails
on both sides of the peak.
An example of a fit of these functions to a toy dataset with gaussian
errors can be seen in fig.~\ref{fig:cb_fit}. In this figure, a binning
of 200 GeV is used. For the actual analysis a 1 GeV binning will be
used. It can be seen that the fit works very well and therefore confirms
the functions chosen to model signal and background. This is supported
by a \(\chi^2 /\) ndof of 0.5 and a found mean for the signal at 2999
\(\pm\) 23 \(\si{\giga\eV}\) which is extremely close to the expected
3000 GeV mean. Those numbers clearly show that the method in use is able
to successfully describe the data.
A linear combination of the signal and background function is then
fitted to a toy dataset with gaussian errors and a simulated signal
cross section of \(\SI{1}{\per\pico\barn}\). The resulting coefficients
of said combination then show the expected signal rate for the simulated
cross section. An example of such a fit can be seen in
fig.~\ref{fig:cb_fit}. In this figure, a binning of 200 GeV is used. For
the actual analysis a 1 GeV binning will be used. It can be seen that
the fit works very well and therefore confirms the functions chosen to
model signal and background. This is supported by a \(\chi^2 /\) ndof of
0.5 and a found mean for the signal at 2999 \(\pm\) 23 \(\si{\giga\eV}\)
which is extremely close to the expected 3000 GeV mean. Those numbers
clearly show that the method in use is able to successfully describe the
data.
\begin{figure}
\hypertarget{fig:cb_fit}{%
@ -795,9 +825,9 @@ 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 make sure a good trigger efficiency is achieved. 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
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.
@ -814,14 +844,14 @@ an angular separation smaller than 0.8 from any electron or muon are
discarded to allow future use of the results in studies of the semi or
all-leptonic decay channels.
From a decaying q* particle, we expect two jets in the endstate. The
dijet invariant mass of those two jets will be used to reconstruct the
mass of the q* particle. Therefore a cut is added to have at least 2
jets. More jets are also possible, for example caused by gluon radiation
of a quark causing another jet. 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}.
From a decaying q* particle, two jets are expected in the final state.
The dijet invariant mass of those two jets will be used to reconstruct
the mass of the q* particle. Therefore a cut is added to have at least 2
jets, accounting for the possibility of more jets, for example caused by
gluon radiation of a quark or other QCD effects. If this is the case,
the two jets with the highest \(p_t\) are used for the reconstruction of
the q* mass. The distributions of the number of jets before and after
the selection can be seen in fig.~\ref{fig:njets}.
\begin{figure}
\begin{minipage}{0.5\textwidth}
@ -836,25 +866,25 @@ be seen in fig.~\ref{fig:njets}.
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/v1_Njet_N_jets_stack.eps}
\end{minipage}
\caption{Number of jet distribution showing the cut at number of jets $\ge$ 2. Left: distribution before the cut. Right:
\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.}
\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 first two jets
in regards to their 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 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}.
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 originating from QCD
effects are expected to have a higher \(\Delta\eta\) as they mainly form
from less heavy resonances. To maintain comparability, the same
selection as in previous research of \(\Delta\eta \le 1.3\) is used. A
comparison of the \(\Delta\eta\) distribution before and after the
selection can be seen in fig.~\ref{fig:deta}.
\begin{figure}
\begin{minipage}{0.5\textwidth}
@ -869,16 +899,19 @@ fig.~\ref{fig:deta}.
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/v1_Eta_deta_stack.eps}
\end{minipage}
\caption{$\Delta\eta$ distribution showing the cut at $\Delta\eta \le 1.3$. Left: distribution before the cut. Right:
distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves
are amplified by a factor of 10,000, to be visible.}
\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.}
\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 high trigger
efficiency and can be seen in fig.~\ref{fig:invmass}. Also, it has a
huge impact on the background because it usually consists of way lighter
\(m_{jj} \ge \SI{1050}{\giga\eV}\). It is important for a trigger
efficiency higher than 99 \% with a soft-drop mass cut of
\(m_{SDM} > \SI{65}{\giga\eV}\) applied to the jet with the highest
transverse momentum. A comparison of its distribution before and after
the selection can be seen in fig.~\ref{fig:invmass}. Also, it has a huge
impact on the background because it usually consists of 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
@ -897,8 +930,8 @@ simulated resonance mass for the signal events.
\begin{minipage}{0.5\textwidth}
\includegraphics{./figures/combined/v1_invmass_invMass_stack.eps}
\end{minipage}
\caption{Invariant mass distribution showing the cut at $m_{jj} \ge \SI{1050}{\giga\eV}$. It shows the expected smooth
falling functions of the background whereas the signal peaks at the simulated resonance mass.
\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.}
\label{fig:invmass}
@ -914,22 +947,21 @@ and 56 \% (7 TeV) are reached, wheres the efficiencies when decaying to
qZ are in the range of 46 \% (1.6 TeV) to 50 \% (7 TeV). Here, the
background could be reduced to 8 \% of the original events. So while
keeping around 50 \% of the signal, the background was already reduced
to less than a tenth. Still, as can be seen in fig.~\ref{fig:njets} to
fig.~\ref{fig:invmass}, the amount of signal is very low.
to less than a tenth.
\hypertarget{data---monte-carlo-comparison}{%
\subsection{Data - Monte Carlo
Comparison}\label{data---monte-carlo-comparison}}
To ensure high data quality, the simulated QCD background sample is now
being compared to the actual data of the corresponding year collected by
the CMS detector. This is done for the year 2016 and for the combined
data of years 2016, 2017 and 2018. The distributions are rescaled so the
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 real data
from the CMS, jet energy corrections have to be applied. Those are to
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
@ -970,12 +1002,12 @@ simulation.
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 softdropmass 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
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
simulation in the sideband region can be seen for the softdropmass
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
@ -1005,19 +1037,19 @@ combined data from 2016, 2017 and 2018.}
\hypertarget{jet-substructure-selection}{%
\section{Jet substructure selection}\label{jet-substructure-selection}}
So far it was made sure, that the actual data and the simulation are in
good agreement after the preselection and no unwanted side effects are
introduced in the data by the used cuts. Now another selection has to be
introduced, to further reduce the background to be able to extract the
hypothetical signal events from the actual data.
So far it was made sure, that the data collected by the CMS and the
simulation are in good agreement after the preselection and no unwanted
side effects are introduced in the data by the used cuts. Now another
selection has to be introduced, to further reduce the background to be
able to look for the hypothetical signal events in the data.
This is done by distinguishing between QCD and signal events using a
tagger to identify jets coming from a vector boson. Two different
taggers will be used to later compare their performance. The decay
analysed includes either a W or Z boson, which are, compared to the
particles in QCD effects, very heavy. This can be used by adding a cut
on the softdropmass of a jet. The softdropmass of at least one of the
two leading jets is expected to be within \(\SI{35}{\giga\eV}\) and
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.
@ -1057,7 +1089,7 @@ decay of a vector boson. Therefore a selection will be introduced, so
that \(\tau_{21}\) of one candidate jet is smaller then some value that
will be determined by an optimization process described in the next
chapter. As candidate jet the one of the two highest \(p_t\) jets
passing the softdropmass window is used. If both of them pass, the one
passing the soft-drop mass window is used. If both of them pass, the one
with higher \(p_t\) is chosen.
\hypertarget{deepak8}{%
@ -1075,7 +1107,7 @@ efficiency of the DeepAK8 tagger, with, between others, the
\begin{figure}
\hypertarget{fig:ak8_eff}{%
\centering
\includegraphics[width=0.8\textwidth,height=\textheight]{./figures/deep_ak8.pdf}
\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}
@ -1103,7 +1135,7 @@ correlated to the mass of a particle. Its output is fed back to the
network as a penalty so it avoids using features of the particles
correlated to their mass. The result is a largely mass decorrelated
tagger of heavy resonances. As the mass variable is already in use for
the softdropmass selection, this version of the tagger is to be
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
@ -1175,20 +1207,28 @@ as well as the deep boosted tagger is found and applied to the simulated
samples as well as the data collected by the CMS. The fit described in
sec.~\ref{sec:moa} is performed for all masspoints of the decay to qW
and qZ and for both datasets used, the one from 2016 und the combined
one of 2016, 2017 and 2018.
one of years 2016, 2017 and 2018.
To extract the signal from the background, its cross section limit is
calculated using a frequentist asymptotic limit calculator. It performs
a shape analysis of the dijet invariant mass spectrum to determine an
expected and an observed limit. If there's no resonance of the q*
particle in the data, the observed limit should lie within the
\(2\sigma\) environment of the expected limit. After that, the crossing
of the theory line, representing the cross section limits expected, if
the q* particle would exist, and the observed data is calculated, to
have a limit of mass up to which the existence of the q* particle can be
excluded. To find the uncertainty of this result, the crossing of the
theory line plus, respectively minus, its uncertainty with the observed
limit is also calculated.
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
the CMS, it determines an expected and an observed cross section limit
by doing a signal + background versus background-only hypothesis test.
It also calculates upper and lower limits of the expected cross section
corresponding to a confidence level of 95 \%.
If there's no resonance of the q* particle in the data, the observed
limit should lie within the \(2\sigma\) environment, meaning a 95 \%
confidence level, of the expected limit. This observed limit is plotted
together with a theory line, representing the cross section limits
expected, if the q* predicted by \autocite{QSTAR_THEORY} would exist.
The crossing of the theory line with the observed limit is then
calculated, to have a limit of mass up to which the existence of the q*
particle can be excluded. To find the uncertainty of this result, the
crossing of the theory line plus, respectively minus, its uncertainty
with the observed limit is also calculated.
\hypertarget{uncertainties}{%
\subsection{Uncertainties}\label{uncertainties}}

4
thesis.toc
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@ -34,5 +34,5 @@
\contentsline {subsection}{\numberline {8.1}2016}{24}{subsection.8.1}%
\contentsline {subsubsection}{\numberline {8.1.1}Previous research}{24}{subsubsection.8.1.1}%
\contentsline {subsection}{\numberline {8.2}Combined dataset}{26}{subsection.8.2}%
\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{28}{subsection.8.3}%
\contentsline {section}{\numberline {9}Summary}{30}{section.9}%
\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{27}{subsection.8.3}%
\contentsline {section}{\numberline {9}Summary}{29}{section.9}%