diff --git a/abstract.pdf b/abstract.pdf
new file mode 100644
index 0000000..631bf8d
Binary files /dev/null and b/abstract.pdf differ
diff --git a/appendix.md b/appendix.md
index c421d75..161c9ee 100644
--- a/appendix.md
+++ b/appendix.md
@@ -1,4 +1,6 @@
-# Appendix
+\appendix
+
+# Expected and observed cross section limits
 
 
 : Cross Section limits using 2016 data and the N-subjettiness tagger for the decay to qW
diff --git a/appendix.tex b/appendix.tex
index d375de2..e8d7aac 100644
--- a/appendix.tex
+++ b/appendix.tex
@@ -1,6 +1,8 @@
-\newpage
-\hypertarget{appendix}{%
-\section*{Appendix}\label{appendix}}
+\appendix
+
+\hypertarget{expected-and-observed-cross-section-limits}{%
+\section{Expected and observed cross section
+limits}\label{expected-and-observed-cross-section-limits}}
 
 \begin{longtable}[]{@{}lllll@{}}
 \caption{Cross Section limits using 2016 data and the N-subjettiness
diff --git a/bibliography.bib b/bibliography.bib
index e7715fb..a59bce3 100644
--- a/bibliography.bib
+++ b/bibliography.bib
@@ -1625,4 +1625,27 @@ archivePrefix = {arXiv},
        adsurl = {https://ui.adsabs.harvard.edu/abs/2011EPJC...71.1554C},
       adsnote = {Provided by the SAO/NASA Astrophysics Data System}
 }
-
+@misc{COORD_PLOT,
+    title={Development and Study of Different Muon Track Reconstruction Algorithms for the Level-1 Trigger for the CMS Muon Upgrade with GEM Detectors},
+    author={Thomas Lenzi and Gilles De Lentdecker},
+    year={2013},
+    eprint={1306.0858},
+    archivePrefix={arXiv},
+    primaryClass={physics.ins-det}
+}
+@online{SM,
+    title={Standard Model of Elementary Particles},
+    author={Wikipedia contributors},
+    year={2006},
+    url={https://en.wikipedia.org/wiki/Standard_Model#/media/File:Standard_Model_of_Elementary_Particles.svg},
+    note={Online; accessed Oct. 2019}
+}
+@article{ERECO,
+      author         = "Adam, Wolfgang and Frühwirth, R. and Strandlie, Are and
+                        Todor, T.",
+      title          = "{Reconstruction of Electrons with the Gaussian-Sum Filter
+                        in the CMS Tracker at the LHC}",
+      year           = "2005",
+      reportNumber   = "CMS-NOTE-2005-001, CERN-CMS-NOTE-2005-001",
+      SLACcitation   = "%%CITATION = CMS-NOTE-2005-001;%%"
+}
diff --git a/figures/2016/DATA/v1_invmass_N_jets-eps-converted-to.pdf b/figures/2016/DATA/v1_invmass_N_jets-eps-converted-to.pdf
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diff --git a/figures/get_eps.sh b/figures/get_eps.sh
new file mode 100755
index 0000000..0994f34
--- /dev/null
+++ b/figures/get_eps.sh
@@ -0,0 +1,29 @@
+#!/bin/sh
+for y in {2016,combined}
+do
+	cd $y
+	for f in *.eps
+	do
+		cp ../../nfs/plots/${y}/w2w5-pre/$f $f
+	done
+	for f in *invMass*.eps
+	do
+		cp ../../nfs/plots/${y}/w2w5-pre-log/$f $f
+	done
+	cd DATA
+	for f in *.eps
+	do
+		cp ../../../nfs/plots/${y}/data-bg/$f $f
+	done
+	for f in *invMass*.eps
+	do
+		cp ../../../nfs/plots/${y}/data-bg-log/$f $f
+	done
+	cd ../sideband
+	for f in *.eps
+	do
+		cp ../../../nfs/plots/${y}/data-bg-sideband-log/$f $f
+	done
+	cd ../../
+done
+
diff --git a/figures/limit_comp_z.pdf b/figures/limit_comp_z.pdf
index 2a7a9fe..bcfad96 100644
Binary files a/figures/limit_comp_z.pdf and b/figures/limit_comp_z.pdf differ
diff --git a/figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf b/figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf
index c163d97..c4d2d49 100644
Binary files a/figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf and b/figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf differ
diff --git a/figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf b/figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf
index 8258c46..307b049 100644
Binary files a/figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf and b/figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf differ
diff --git a/make.sh b/make.sh
index 24c299c..bdea6ea 100755
--- a/make.sh
+++ b/make.sh
@@ -1,5 +1,5 @@
 #!/bin/sh
-
+rm -f thesis.aux thesis.bcf thesis.blg thesis.log thesis.run.xml thesis.tex thesis.toc
 pandoc thesis.md -o thesis.tex --biblatex --bibliography=bibliography.bib -N --listings --pdf-engine=lualatex -s --filter pandoc-crossref --include-after-body=appendix.tex
 lualatex thesis
 biber thesis
diff --git a/thesis.aux b/thesis.aux
index 24e3db5..5bca6af 100644
--- a/thesis.aux
+++ b/thesis.aux
@@ -19,41 +19,39 @@
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+      \strng{authornamehash}{e2ceeea38f8620383cfbd3e99c5c0cd8}
+      \strng{authorfullhash}{e2ceeea38f8620383cfbd3e99c5c0cd8}
+      \field{sortinit}{c}
+      \field{sortinithash}{4c244ceae61406cdc0cc2ce1cb1ff703}
+      \field{labelnamesource}{author}
+      \field{labeltitlesource}{title}
+      \field{note}{Online; accessed Oct. 2019}
+      \field{title}{Standard Model of Elementary Particles}
+      \field{year}{2006}
+      \true{nocite}
+      \verb{urlraw}
+      \verb https://en.wikipedia.org/wiki/Standard_Model#/media/File:Standard_Model_of_Elementary_Particles.svg
+      \endverb
+      \verb{url}
+      \verb https://en.wikipedia.org/wiki/Standard_Model#/media/File:Standard_Model_of_Elementary_Particles.svg
+      \endverb
+    \endentry
     \entry{ASYMPTOTIC_LIMIT}{article}{}
       \name{author}{4}{}{%
         {{hash=66ffd2ca2c2d8aeb563033389eb813ff}{%
@@ -10445,6 +10511,38 @@
       \endverb
       \keyw{QCD Phenomenology,Jets,High Energy Physics - Phenomenology}
     \endentry
+    \entry{COORD_PLOT}{misc}{}
+      \name{author}{2}{}{%
+        {{hash=15b9a153219f506cf02e41def261c3d1}{%
+           family={Lenzi},
+           familyi={L\bibinitperiod},
+           given={Thomas},
+           giveni={T\bibinitperiod}}}%
+        {{hash=5dcf196111a4444664cd7cfd15d3d3d3}{%
+           family={Lentdecker},
+           familyi={L\bibinitperiod},
+           given={Gilles\bibnamedelima De},
+           giveni={G\bibinitperiod\bibinitdelim D\bibinitperiod}}}%
+      }
+      \strng{namehash}{8b71f4c0f74cc6925d823cbcc7f849aa}
+      \strng{fullhash}{8b71f4c0f74cc6925d823cbcc7f849aa}
+      \strng{bibnamehash}{8b71f4c0f74cc6925d823cbcc7f849aa}
+      \strng{authorbibnamehash}{8b71f4c0f74cc6925d823cbcc7f849aa}
+      \strng{authornamehash}{8b71f4c0f74cc6925d823cbcc7f849aa}
+      \strng{authorfullhash}{8b71f4c0f74cc6925d823cbcc7f849aa}
+      \field{sortinit}{L}
+      \field{sortinithash}{dad3efd0836470093a7b4a7bb756eb8c}
+      \field{labelnamesource}{author}
+      \field{labeltitlesource}{title}
+      \field{eprintclass}{physics.ins-det}
+      \field{eprinttype}{arXiv}
+      \field{title}{Development and Study of Different Muon Track Reconstruction Algorithms for the Level-1 Trigger for the CMS Muon Upgrade with GEM Detectors}
+      \field{year}{2013}
+      \true{nocite}
+      \verb{eprint}
+      \verb 1306.0858
+      \endverb
+    \endentry
     \entry{DEEP_BOOSTED}{report}{}
       \list{institution}{1}{%
         {CERN}%
diff --git a/thesis.bcf b/thesis.bcf
index e8a71b0..88b0cc8 100644
--- a/thesis.bcf
+++ b/thesis.bcf
@@ -1996,33 +1996,38 @@
   </bcf:bibdata>
   <bcf:section number="0">
     <bcf:citekey order="1">PREV_RESEARCH</bcf:citekey>
-    <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">DEEP_BOOSTED</bcf:citekey>
-    <bcf:citekey order="6">TAU21</bcf:citekey>
+    <bcf:citekey order="2">SM</bcf:citekey>
+    <bcf:citekey order="3">SM</bcf:citekey>
+    <bcf:citekey order="4">HADRONIZATION</bcf:citekey>
+    <bcf:citekey order="5">QSTAR_THEORY</bcf:citekey>
+    <bcf:citekey order="6">QSTAR_THEORY</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">LHC_MACHINE</bcf:citekey>
-    <bcf:citekey order="11">CMS_REPORT</bcf:citekey>
-    <bcf:citekey order="12">CMS_PLOT</bcf:citekey>
-    <bcf:citekey order="13">CMS_PLOT</bcf:citekey>
-    <bcf:citekey order="14">ANTIKT</bcf:citekey>
-    <bcf:citekey order="15">ANTIKT</bcf:citekey>
-    <bcf:citekey order="16">PREV_RESEARCH</bcf:citekey>
-    <bcf:citekey order="17">PREV_RESEARCH</bcf:citekey>
-    <bcf:citekey order="18">QSTAR_THEORY</bcf:citekey>
-    <bcf:citekey order="19">TAU21</bcf:citekey>
-    <bcf:citekey order="20">DEEP_BOOSTED</bcf:citekey>
-    <bcf:citekey order="21">DEEP_BOOSTED</bcf:citekey>
-    <bcf:citekey order="22">DEEP_BOOSTED</bcf:citekey>
-    <bcf:citekey order="23">ASYMPTOTIC_LIMIT</bcf:citekey>
-    <bcf:citekey order="24">QSTAR_THEORY</bcf:citekey>
-    <bcf:citekey order="25">PREV_RESEARCH</bcf:citekey>
-    <bcf:citekey order="26">PREV_RESEARCH</bcf:citekey>
-    <bcf:citekey order="27">PREV_RESEARCH</bcf:citekey>
-    <bcf:citekey order="28">PREV_RESEARCH</bcf:citekey>
+    <bcf:citekey order="8">LHC_MACHINE</bcf:citekey>
+    <bcf:citekey order="9">CMS_REPORT</bcf:citekey>
+    <bcf:citekey order="10">CMS_PLOT</bcf:citekey>
+    <bcf:citekey order="11">CMS_PLOT</bcf:citekey>
+    <bcf:citekey order="12">COORD_PLOT</bcf:citekey>
+    <bcf:citekey order="13">COORD_PLOT</bcf:citekey>
+    <bcf:citekey order="14">PARTICLE_FLOW</bcf:citekey>
+    <bcf:citekey order="15">ERECO</bcf:citekey>
+    <bcf:citekey order="16">ANTIKT</bcf:citekey>
+    <bcf:citekey order="17">ANTIKT</bcf:citekey>
+    <bcf:citekey order="18">ANTIKT</bcf:citekey>
+    <bcf:citekey order="19">SDM</bcf:citekey>
+    <bcf:citekey order="20">PREV_RESEARCH</bcf:citekey>
+    <bcf:citekey order="21">PREV_RESEARCH</bcf:citekey>
+    <bcf:citekey order="22">MONTECARLO</bcf:citekey>
+    <bcf:citekey order="23">QSTAR_THEORY</bcf:citekey>
+    <bcf:citekey order="24">TAU21</bcf:citekey>
+    <bcf:citekey order="25">DEEP_BOOSTED</bcf:citekey>
+    <bcf:citekey order="26">DEEP_BOOSTED</bcf:citekey>
+    <bcf:citekey order="27">DEEP_BOOSTED</bcf:citekey>
+    <bcf:citekey order="28">ASYMPTOTIC_LIMIT</bcf:citekey>
+    <bcf:citekey order="29">QSTAR_THEORY</bcf:citekey>
+    <bcf:citekey order="30">PREV_RESEARCH</bcf:citekey>
+    <bcf:citekey order="31">PREV_RESEARCH</bcf:citekey>
+    <bcf:citekey order="32">PREV_RESEARCH</bcf:citekey>
+    <bcf:citekey order="33">PREV_RESEARCH</bcf:citekey>
     <bcf:citekey order="0" nocite="1">*</bcf:citekey>
   </bcf:section>
   <!-- SORTING TEMPLATES -->
diff --git a/thesis.blg b/thesis.blg
index 66fdb64..bc9ec19 100644
--- a/thesis.blg
+++ b/thesis.blg
@@ -1,29 +1,29 @@
 [0] Config.pm:304> INFO - This is Biber 2.12
 [0] Config.pm:307> INFO - Logfile is 'thesis.blg'
-[25] biber:315> INFO - === Mo Okt 28, 2019, 15:09:45
-[41] Biber.pm:371> INFO - Reading 'thesis.bcf'
-[104] Biber.pm:886> INFO - Using all citekeys in bib section 0
-[118] Biber.pm:4093> INFO - Processing section 0
-[128] Biber.pm:4254> INFO - Looking for bibtex format file 'bibliography.bib' for section 0
-[139] bibtex.pm:1523> INFO - LaTeX decoding ...
-[272] bibtex.pm:1340> INFO - Found BibTeX data source 'bibliography.bib'
-[278] Utils.pm:193> WARN - month field 'Apr' in entry 'MONTECARLO' is not an integer - this will probably not sort properly.
-[281] Utils.pm:193> WARN - month field 'Aug' in entry 'PREV_RESEARCH' is not an integer - this will probably not sort properly.
-[2948] Utils.pm:193> WARN - month field 'Mar' in entry 'TAU21' is not an integer - this will probably not sort properly.
-[2949] Utils.pm:193> WARN - month field 'aug' in entry 'LHC_MACHINE' is not an integer - this will probably not sort properly.
-[2955] Utils.pm:193> WARN - month field 'Nov' in entry 'HADRONIZATION' is not an integer - this will probably not sort properly.
-[2964] Utils.pm:193> WARN - month field 'Feb' in entry 'ASYMPTOTIC_LIMIT' is not an integer - this will probably not sort properly.
-[2969] Utils.pm:193> WARN - month field 'Oct' in entry 'SUC_COMBINATION' is not an integer - this will probably not sort properly.
-[2972] Utils.pm:193> WARN - month field 'Jan' in entry 'PARTICLE_FLOW' is not an integer - this will probably not sort properly.
-[5781] Utils.pm:193> WARN - month field 'Jun' in entry 'CMS_PLOT' is not an integer - this will probably not sort properly.
-[5786] Utils.pm:193> WARN - month field 'Apr' in entry 'ANTIKT' is not an integer - this will probably not sort properly.
-[5790] Utils.pm:193> WARN - month field 'Oct' in entry 'CMS_TRIGGER' is not an integer - this will probably not sort properly.
-[5799] Utils.pm:193> WARN - month field 'May' in entry 'SDM' is not an integer - this will probably not sort properly.
-[6091] Utils.pm:193> WARN - month field 'Aug' in entry 'PARTICLE_PHYSICS' is not an integer - this will probably not sort properly.
-[6233] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'variable = shifted' with 'variable = non-ignorable'
-[6233] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'normalization = NFD' with 'normalization = prenormalized'
-[6233] Biber.pm:3921> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'en-GB'
-[6233] Biber.pm:3927> INFO - No sort tailoring available for locale 'en-GB'
-[6394] bbl.pm:636> INFO - Writing 'thesis.bbl' with encoding 'UTF-8'
-[15771] bbl.pm:739> INFO - Output to thesis.bbl
-[15773] Biber.pm:110> INFO - WARNINGS: 13
+[20] biber:315> INFO - === Do Okt 31, 2019, 19:46:44
+[39] Biber.pm:371> INFO - Reading 'thesis.bcf'
+[97] Biber.pm:886> INFO - Using all citekeys in bib section 0
+[107] Biber.pm:4093> INFO - Processing section 0
+[117] Biber.pm:4254> INFO - Looking for bibtex format file 'bibliography.bib' for section 0
+[126] bibtex.pm:1523> INFO - LaTeX decoding ...
+[243] bibtex.pm:1340> INFO - Found BibTeX data source 'bibliography.bib'
+[254] Utils.pm:193> WARN - month field 'Aug' in entry 'PREV_RESEARCH' is not an integer - this will probably not sort properly.
+[263] Utils.pm:193> WARN - month field 'Nov' in entry 'HADRONIZATION' is not an integer - this will probably not sort properly.
+[270] Utils.pm:193> WARN - month field 'Jan' in entry 'PARTICLE_FLOW' is not an integer - this will probably not sort properly.
+[277] Utils.pm:193> WARN - month field 'Mar' in entry 'TAU21' is not an integer - this will probably not sort properly.
+[285] Utils.pm:193> WARN - month field 'May' in entry 'SDM' is not an integer - this will probably not sort properly.
+[292] Utils.pm:193> WARN - month field 'Feb' in entry 'ASYMPTOTIC_LIMIT' is not an integer - this will probably not sort properly.
+[298] Utils.pm:193> WARN - month field 'Apr' in entry 'ANTIKT' is not an integer - this will probably not sort properly.
+[572] Utils.pm:193> WARN - month field 'Aug' in entry 'PARTICLE_PHYSICS' is not an integer - this will probably not sort properly.
+[576] Utils.pm:193> WARN - month field 'Apr' in entry 'MONTECARLO' is not an integer - this will probably not sort properly.
+[579] Utils.pm:193> WARN - month field 'Oct' in entry 'CMS_TRIGGER' is not an integer - this will probably not sort properly.
+[3177] Utils.pm:193> WARN - month field 'Jun' in entry 'CMS_PLOT' is not an integer - this will probably not sort properly.
+[3181] Utils.pm:193> WARN - month field 'Oct' in entry 'SUC_COMBINATION' is not an integer - this will probably not sort properly.
+[5523] Utils.pm:193> WARN - month field 'aug' in entry 'LHC_MACHINE' is not an integer - this will probably not sort properly.
+[5662] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'variable = shifted' with 'variable = non-ignorable'
+[5662] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'normalization = NFD' with 'normalization = prenormalized'
+[5662] Biber.pm:3921> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'en-GB'
+[5662] Biber.pm:3927> INFO - No sort tailoring available for locale 'en-GB'
+[5817] bbl.pm:636> INFO - Writing 'thesis.bbl' with encoding 'UTF-8'
+[13628] bbl.pm:739> INFO - Output to thesis.bbl
+[13630] Biber.pm:110> INFO - WARNINGS: 13
diff --git a/thesis.log b/thesis.log
index 2589eb5..b636b75 100644
--- a/thesis.log
+++ b/thesis.log
@@ -1,4 +1,4 @@
-This is LuaTeX, Version 1.10.0 (TeX Live 2019/Arch Linux)  (format=lualatex 2019.8.29)  28 OCT 2019 15:10
+This is LuaTeX, Version 1.10.0 (TeX Live 2019/Arch Linux)  (format=lualatex 2019.8.29)  31 OCT 2019 19:46
  restricted system commands enabled.
 **thesis
 (./thesis.tex
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 '.
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 Document Class: article 2018/09/03 v1.4i Standard LaTeX document class
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diff --git a/thesis.md b/thesis.md
index c271dee..e30e0cb 100644
--- a/thesis.md
+++ b/thesis.md
@@ -1,6 +1,6 @@
 ---
 author: David Leppla-Weber
-title: Search for excited quark states decaying to qW/qZ
+#title: Search for excited quark states decaying to qW/qZ
 lang: en-GB
 header-includes: |
     \usepackage[onehalfspacing]{setspace}
@@ -11,38 +11,6 @@ header-includes: |
     \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 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, 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}
-    \end{abstract}
-    \renewcommand{\abstractname}{Zusammenfassung}
-    \begin{abstract}
-    ```
-
-    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 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:
 - top=2.5cm
@@ -52,7 +20,7 @@ geometry:
 papersize: a4
 mainfont: Times New Roman
 fontsize: 12pt
-toc: true
+toc: false
 nocite: |
     @*
 figPrefix: "Fig."
@@ -60,13 +28,92 @@ tblPrefix: "Table"
 secPrefix: "Sec."
 eqnPrefix: "Eq."
 ---
+\begin{titlepage}
+\begin{center}
+       \vspace*{1cm}
+       \Huge
+       \rule{\textwidth}{0.1cm}
+       \textbf{Search for excited quark states decaying to qW/qZ with the CMS experiment}
+       \rule{\textwidth}{0.1cm}
+
+       \vspace{2.5cm}
+       \Large
+       von\\
+       \LARGE
+       David Leppla-Weber\\
+       \Large
+       \vspace{0.5cm}
+       Geboren am\\
+       18.09.1996
+ 
+       \vfill
+ 
+       Bachelorarbeit im Studiengang Physik\\
+       Universität Hamburg\\
+       November 2019
+ 
+   \end{center}
+\end{titlepage}
+
+\newpage
+\mbox{}
+\vfill
+
+1. Gutachter: Dr. Andreas Hinzmann
+2. Gutachter: Jun.-Prof. Dr. Gregor Kasieczka
+
+\newpage
+
+\begin{abstract}
+A search for an excited quark state, called q*, is presented using data of proton-proton collisions at the LHC 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 an integrated luminosity of $\SI{137.19}{\per\femto\barn}$. Its decay channels to q 
++ W and q + Z with the vector bosons further decaying hadronically to $q + q\bar{q}'$ resp. $q + q\bar{q}$, resulting in 
+  two jets in the final state, are analysed. The dijet invariant mass spectrum of those two jets is then used to look 
+for a resonance and to reconstruct the q* mass. To identify jets originating from the decay of a vector boson, a 
+V-tagger is needed. For that, the new DeepAK8 tagger, based on a neural network, is compared to the older N-subjettiness 
+tagger. In the result, no significant deviation from the Standard Model can be observed, therefore the q* is excluded up 
+to a mass of 6.1\ TeV (qW) 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 with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$ collected 
+by the CMS experiment in 2016, excluding the q* particle up to a mass of 5.0\ TeV resp. 4.7\ TeV. The DeepAK8 tagger is 
+found to currently be at 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. By optimizing the neural network's training 
+for the datasets of 2016, 2017 and 2018, the sensitivity can likely be improved.
+
+\end{abstract}
+\newpage
+\renewcommand{\abstractname}{Zusammenfassung}
+\begin{abstract}
+
+In dieser Arbeit wird eine Suche nach angeregten Quarkzuständen, genannt q*, durchgeführt. Dafür werden Daten von 
+Proton-Proton Kollisionen am LHC mit einer 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. Es wird der Zerfall des q* Teilchens zu q + W und q + Z untersucht, bei anschließendem 
+hadronischen Zerfall des Vektorbosons zu $q\bar{q}'$ bzw. $q\bar{q}$. Der gesamte Zerfall resultiert damit in zwei Jets, 
+mithilfe deren invariantem Massenspektrum die q* Masse rekonstruiert und nach einer Resonanz gesucht wird. Zur 
+Identifizerung von Jets, welche durch den Zerfall eines Vektorbosons entstanden sind, wird ein V-Tagger benötigt. 
+Hierfür wird der neue DeepAK8 Tagger, welcher auf einem neuronalen Netzwerk basiert, mit dem älteren N-Subjettiness 
+Tagger verglichen. Im Ergebnis kann keine signifikante Abweichung vom Standardmodell beobachtet werden. Das q* Teilchen 
+wird mit einem Konfidenzniveau von 95 \% bis zu einer Masse von 6.1\ TeV (qW) bzw. 5.5\ TeV (qZ) ausgeschlossen. Das Limit 
+liegt etwa 1\ TeV höher, als das anhand des $\SI{35.92}{\per\femto\barn}$ großen Datensatzes von 2016 gefundene von 5.0 
+TeV bzw. 4.7\ TeV. Beim Zerfall zu qW erzielt der DeepAK8 Tagger ein um $\SI{0.1}{\tera\eV}$ besseres Ergebnis, als der 
+N-Subjettiness Tagger, beim Zerfall zu qZ jedoch ein um $\SI{0.6}{\tera\eV}$ schlechteres. Durch Verbesserung des 
+Trainings des neuronalen Netzwerkes für die drei Datensätze von 2016, 2017 und 2018, gibt es aber noch Potential die 
+Sensitivität zu verbessern.
+
+\end{abstract}
+
+\newpage
+\setcounter{tocdepth}{3}
+\tableofcontents
+
 \newpage
 \pagenumbering{arabic}
 
 # Introduction
 
 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 
+Still, it has a lot of limitations, 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.
 
@@ -79,20 +126,21 @@ under the emission of a boson. This thesis will look for their decay to a vector
 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 
-then, a lot more data has been collected, totalling to $\SI{137.19}{\per\femto\barn}$ of data usable for research. This 
-thesis uses this new data as well as a new technique to identify decays of highly boosted particles based on a deep 
-neural network. By using more data and new tagging techniques, it aims to either confirm the existence of the q\* 
-particle or improve the previously set lower limit of 5 TeV respectively 4.7 TeV for the decay to qW respectively qZ on 
-its mass to even higher values. It will also directly compare the performance of this new tagging technique to an older 
-tagger based on jet substructure studies used in the previous research.
+In a previous research [@PREV_RESEARCH], an exclusion 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 then, a lot more data has been collected by the CMS experiment, totalling to $\SI{137.19}{\per\femto\barn}$ of 
+data usable for research. This thesis takes advantage of this larger dataset as well as a new technique to identify 
+decays of highly boosted particles based on a deep neural network. By using more data and new tagging techniques, it 
+aims to either confirm the existence of the q\* particle or improve the previously set lower limit of 5 TeV respectively 
+4.7 TeV for the decay to qW respectively qZ on its mass to even higher values. It will also directly compare the 
+performance of this new tagging technique to an older tagger based on jet substructure studies used in the previous 
+research.
 
-In chapter 2, a theoretical background will be presented explaining in short the Standard Model, its shortcomings and 
-the theory of excited quarks. Then, in chapter 3, the Large Hadron Collider and the Compact Muon Solenoid, the detector 
-that collected the data for this analysis, will be described. After that, in chapters 4-7, the main analysis part 
-follows, describing how the data was used to extract limits on the mass of the excited quark particle. At the very end, 
-in chapter 8, the results are presented and compared to previous research.
+In chapter 2, a theoretical background will be presented briefly explaining the Standard Model, its shortcomings and the 
+theory of excited quarks. Then, in chapter 3, the Large Hadron Collider and the Compact Muon Solenoid, the detector that 
+collected the data for this analysis, will be described. After that, in chapters 4-7, the main analysis part follows, 
+describing how the data were used to extract limits on the mass of the excited quark particle. At the very end, in 
+chapter 8, the results are presented and compared to previous research.
 
 \newpage
 
@@ -100,7 +148,8 @@ in chapter 8, the results are presented and compared to previous research.
 
 This chapter presents a short summary of the theoretical background relevant to this thesis. It first gives an
 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.
+processes of quantum chromodynamics and the theory of q*, which are the relevant phenomena for the search described in 
+this thesis.
 
 ## Standard Model {#sec:sm}
 
@@ -112,14 +161,14 @@ The Standard Model divides all particles into spin-$\frac{n}{2}$ fermions and sp
 integer but so far is only known to be one for fermions and either one (gauge bosons) or zero (scalar bosons) for
 bosons. Fermions are further classified into quarks and leptons.
 Quarks and leptons can also be categorized into three generations, each of which contains two particles, also called 
-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 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.
+flavours. For leptons, the three generations each consist of a charged lepton and its corresponding neutrino, namely the 
+electron, the muon and 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. 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.
+Elementary particles of the Standard Model and their mass charge and spin. Taken from [@SM]
 ](./figures/sm_wikipedia.pdf){width=50% #fig:sm}
 
 The gauge bosons, namely the photon, $W^\pm$ bosons, $Z^0$ boson, and gluon, are mediators of the different
@@ -130,9 +179,9 @@ electrically charged particles. It itself carries no electromagnetic charge and
 either scattering or absorption. Photons of different energies can also be described as electromagnetic waves of 
 different wavelengths.
 
-The $W^\pm$ and $Z^0$ bosons mediate the weak force. All quarks and leptons carry a flavour, which is a conserved value.
-Only the weak interaction breaks this conservation, a quark or lepton can therefore, by interacting with a $W^\pm$
-boson, change its flavour. The probabilities of this happening are determined by the Cabibbo-Kobayashi-Maskawa matrix:
+The $W^\pm$ and $Z^0$ bosons mediate the weak force. All quarks and leptons carry a flavour, which is a conserved value 
+in all interactions but the weak one. There, a quark or lepton can, by interacting with a $W^\pm$ boson, change its 
+flavour. The probabilities of this happening are determined by the Cabibbo-Kobayashi-Maskawa matrix:
 
 \begin{equation}
   V_{CKM} =
@@ -148,6 +197,7 @@ boson, change its flavour. The probabilities of this happening are determined by
       0.008 & 0.041 & 0.999
     \end{pmatrix}
 \end{equation}
+
 The probability of a quark changing its flavour from $i$ to $j$ is given by the square of the absolute value of the
 matrix element $V_{ij}$. It is easy to see, that the change of flavour in the same generation is way more likely than
 any other flavour change.
@@ -157,17 +207,18 @@ Either in the leptonic or hadronic decay channel. In the leptonic channel, 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 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.
+This thesis examines the hadronic decay channel, where both vector bosons 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,
 although they don't carry only one colour but rather a combination of a colour and an anticolour, and can therefore
-interact with themselves and exist in eight different variants. As a result of this, processes, where a gluon decays 
-into two gluons are possible. Furthermore the strength of the strong force, binding to colour carrying particles, 
-increases with their distance making it at a certain point more energetically efficient to form a new quark - antiquark 
-pair than separating the two particles even further. This effect is known as colour confinement. Due to this effect, 
-colour carrying particles can't be observed directly, but rather form so called jets that cause hadronic showers in the 
-detector. Those jets are cone like structures made of hadrons and other particles. The effect is called Hadronisation.
+interact with themselves and exist in eight different variants. As a result of this, processes where a gluon decays into 
+two gluons are possible. Furthermore the strength of the strong force, binding colour carrying particles, increases with 
+their distance making it at a certain point more energetically efficient to form a new quark - antiquark pair than 
+separating the two particles even further. This effect is known as colour confinement. Due to this effect, colour 
+carrying particles can't be observed directly, but rather form so called jets that cause hadronic showers in the 
+detector. Those jets are cone like structures made of hadrons and other particles. The effect is called hadronisation 
+[@HADRONIZATION].
 
 ### Shortcomings of the Standard Model
 
@@ -189,12 +240,12 @@ from cosmological 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 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 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.
+between the different fermions. A common prediction of those models are excited quark states (q\*, q\*\*, q\*\*\*...) 
+[@QSTAR_THEORY]. 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 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 energy region. That will cause the 
+emitted boson to be highly boosted.
 
 \begin{figure}
 \centering
@@ -207,6 +258,7 @@ boosted.
 \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 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 
@@ -230,7 +282,7 @@ calculated for the decay [@QSTAR_THEORY]:
 
 The decay to the vector bosons have the second highest branching ratio. The decay to a gluon and a quark is the dominant 
 decay, but virtually impossible to distinguish from the QCD background described in the next section. This makes the 
-decay to the vector bosons the obvious choice.
+decay to the vector bosons the most promising choice.
 
 To reconstruct the mass of the q\* particle from an event successfully recognized to be the decay of such a particle, 
 the dijet invariant mass has to be calculated. This can be achieved by adding the four momenta of the two jets in the 
@@ -238,10 +290,11 @@ final state, vectors consisting of the energy and momentum of a particle, togeth
 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\* 
+A search for the excited quark predicted by this theory has already been investigated in [@PREV_RESEARCH] analysing data 
+with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$ recorded by the CMS experiment in 2016, excluding the q\* 
 particle up to a mass of 5 TeV resp. 4.7 TeV for the decay to qW resp. qZ analysing the hadronic decay of the vector 
 boson. This thesis aims to either exclude the particle to higher masses or find a resonance showing its existence using 
-the higher center of mass energy of the LHC as well as more data that is available now.
+more data that is available now.
 
 ### Quantum Chromodynamic background {#sec:qcdbg}
 
@@ -277,10 +330,11 @@ Following on, the experimental setup used to gather the data analysed in this th
 ## Large Hadron Collider
 
 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.
+circumference 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, between others the Compact Muon Solenoid (CMS), 
+which is the one used for the search presented in this thesis. It is a general-purpose detector 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 
@@ -319,19 +373,19 @@ 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 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 is 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 
+$\phi$. The Z axis is in beam direction. Taken from [@COORD_PLOT]
 ](./figures/cms_coordinates.png){#fig:cmscoords width=60%}
 
 ### The tracking system
 
 The tracking system is built of two parts, closest to the collision is a pixel detector and around that silicon strip 
-sensors. They are used to reconstruct the tracks of charged particles, measuring their charge sign, direction and 
-momentum. They are as close to the collision as possible to be able to identify secondary vertices.
+sensors. They are used to measure their charge sign, direction and momentum to be later able to reconstruct the tracks 
+of charged particles. They are as close to the collision as possible to be able to identify secondary vertices.
 
 ### The electromagnetic calorimeter
 
@@ -339,8 +393,8 @@ The electromagnetic calorimeter measures the energy of photons and electrons. It
 photodetectors. When passed by particles, the crystal produces scintillation light in proportion to the particle's 
 energy. This light is measured by the photodetectors that convert it to an electrical signal. To measure a particles 
 energy, it has to leave its whole energy in the ECAL, which is true for photons and electrons, but not for other 
-particles such as hadrons and muons. Those are of higher energy and therefore only leave some energy in the ECAL but are 
-not stopped by it.
+particles such as hadrons and muons. Those interact with matter differently and therefore only leave some energy in the 
+ECAL but are not stopped by it.
 
 ### The hadronic calorimeter
 
@@ -355,9 +409,9 @@ and therefore makes it possible to measure momentum of charged particles by bend
 
 ### The muon system
 
-Outside of the solenoid there is only the muon system. It consists of three types of gas detectors, the drift tubes,
-cathode strip chambers and resistive plate chambers. It covers a total of $0 < |\eta| < 2.4$. The muons are the only 
-detected particles, that can pass all the other systems without a significant energy loss.
+Outside of the solenoid, but still in its return yoke, there is only the muon system. It consists of three types of gas 
+detectors, the drift tubes, cathode strip chambers and resistive plate chambers. It covers a total of $0 < |\eta| < 
+2.4$. The muons are the only detected particles, that can pass all the other systems without a significant energy loss.
 
 ### The Trigger system
 
@@ -369,23 +423,23 @@ Level trigger uses a streamlined version of the CMS offline reconstruction softw
 
 ### The Particle Flow algorithm
 
-The particle flow algorithm is used to identify and reconstruct all the particles arising from the proton - proton
-collision by using all the information available from the different sub-detectors of the CMS. It does so by
+The particle flow algorithm [@PARTICLE_FLOW] 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. It does so by 
 extrapolating the tracks through the different calorimeters and associating clusters they cross with them. The set of
-clusters already associated to a track is then no more used for the detection of other particles. This is first done for 
-muons and then for charged hadrons, so a muon can't give rise to a wrongly identified charged hadron. Due to 
+clusters already associated to a track is then no more used for the reconstruction 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.
+is used [@ERECO]. After identifying charged hadrons, muons and electrons, all remaining clusters within the HCAL 
+correspond to neutral hadrons and within ECAL to photons. When 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
 
 Because of the hadronisation it is not possible to uniquely identify the originating particle of a jet. Nonetheless,
-several algorithms exist to help with this problem. The algorithm used in this thesis is the anti-$k_t$ clustering
-algorithm. It arises from a generalization of several other clustering algorithms, namely the $k_t$, Cambridge/Aachen
-and SISCone clustering algorithms.
+several algorithms exist to help with this problem. The algorithm used in this thesis is the anti-$k_t$ [@ANTIKT] 
+clustering algorithm. It arises from a generalization of several other clustering algorithms, namely the $k_t$, 
+Cambridge/Aachen and SISCone clustering algorithms.
 
 The anti-$k_t$ clustering algorithm associates high $p_t$ particles with the lower $p_t$ particles surrounding them 
 within a radius R in the $\eta$ - $\phi$ plane forming cone like jets. If two jets overlap, the jets shape is changed 
@@ -399,50 +453,53 @@ Comparison of the $k_t$, Cambridge/Aachen, SISCone and anti-$k_t$ algorithms clu
 with many random soft "ghosts". Taken from [@ANTIKT]
 ](./figures/antikt-comparision.png){#fig:antiktcomparison}
 
-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.
+Furthermore, to approximate the mass of a heavy particle that caused a jet, the soft-drop mass [@SDM] can be used. In 
+its calculation, to reduce the contamination from initial state radiation, underlying event and multiple hadron 
+scattering, wide angle soft particles are removed from the jet. 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 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.
+This section gives an overview over how the data collected by 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.
 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.
+close together and therefore be reconstructed as one jet. The dijet invariant mass of the two jets in the final state is 
+then used to reconstruct the mass of the q\* particle. The only background considered is the QCD multijet 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 
 clustered using the anti-$k_t$ algorithm with the distance parameter R being 0.8.
 
-The analysis will be conducted with two different sets of data. First, only the data collected by CMS in 2016 will be
-used to compare the results to the previous analysis [@PREV_RESEARCH]. Then the combined data from 2016, 2017 and 2018 
-will be used to improve the previously set limits for the mass of the q\* particle. Also, two different V-tagging 
-mechanisms will be used to compare their performance. One based on the N-subjettiness variable used in the previous 
-research [@PREV_RESEARCH], the other being a novel approach using a deep neural network, that will be explained in the 
-following.
+The analysis will be conducted in two steps. First, only the data collected by the CMS experiment in 2016 with an 
+integrated luminosity of $\SI{35.92}{\per\femto\barn}$ will be used to compare the results to the previous analysis 
+[@PREV_RESEARCH]. Then the combined data from 2016, 2017 and 2018 with an integrated luminosity of 
+$\SI{137.19}{\per\femto\barn}$ will be used to improve the previously set limits for the mass of the q\* particle. Also, 
+two different V-tagging methods will be used to compare their performance. One based on the N-subjettiness variable used 
+in the previous research [@PREV_RESEARCH], the other being a novel approach using a deep neural network, that will be 
+explained in the following.
 
 ## Signal and Background modelling
 
-To make sure the setup is working as intended, at first simulated samples of background and signal are used. In those 
-Monte Carlo simulations, the different particle interactions that take place in a proton - proton
-collision are simulated using the probabilities provided by the Standard Model by calculating the cross sections of the 
-different feynman diagrams. Later on, also detector effects (like its limited resolution) are
-applied to make sure, they look like real data coming from the CMS detector. The q\* signal samples are simulated by the
-probabilities given by the q\* theory [@QSTAR_THEORY] and assuming a cross section of $\SI{1}{\per\pico\barn}$. The 
-simulation was done using MadGraph. Because of the expected high mass, the signal width will be dominated by the 
-resolution of the detector, not by the natural resonance width.
+Before looking at the data collected by the CMS experiment, Monte Carlo simulations [@MONTECARLO] of background and 
+signal are used to understand how the data is expected to look like. To replicate the QCD background processes, the 
+different particle interactions that take place in a proton - proton collision are simulated using the probabilities 
+provided by the Standard Model by calculating the cross sections of the different Feynman diagrams. This was done using 
+MadGraph and Pythia 8. Later on, also detector effects (like its limited resolution) are applied to make sure, they look 
+like real data coming from the CMS detector.
+
+The q\* signal samples are simulated by the probabilities given by the q\* theory [@QSTAR_THEORY] and assuming a cross 
+section of $\SI{1}{\per\pico\barn}$. The simulation was done using MadGraph for eleven masspoints between 1.6 TeV and 7 
+TeV. Because of the expected high mass, the signal width will be dominated by the resolution of the detector, not by the 
+natural resonance width.
 
 The dijet invariant mass distribution of the QCD background is expected to smoothly fall with higher masses.
 It is therefore fitted using the following smooth falling function with three parameters p0, p1, p2:
@@ -450,7 +507,8 @@ It is therefore fitted using the following smooth falling function with three pa
 \frac{dN}{dm_{jj}} = \frac{p_0 \cdot ( 1 - m_{jj} / \sqrt{s} )^{p_2}}{ (m_{jj} / \sqrt{s})^{p_1}}
 \end{equation}
 Whereas $m_{jj}$ is the invariant mass of the dijet and $p_0$ is a normalisation parameter. It is the same function as 
-used in the previous research studying 2016 data only.
+used in the previous research studying 2016 data only but was also found to reliably reproduce the background shape of 
+the other years.
 
 The signal is fitted using a double sided crystal ball function. It has six parameters:
 
@@ -464,10 +522,11 @@ couldn't model the tails on both sides of the peak.
 A linear combination of the signal and background function is then fitted to a toy dataset with gaussian errors and a 
 simulated signal cross section of $\SI{1}{\per\pico\barn}$. The resulting coefficients of said combination then show the 
 expected signal rate for the simulated cross section. An example of such a fit can be seen in [@fig: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.
+figure, a binning of 200 GeV is used for presentational purposes. The analysis itself is conducted using a 1 GeV 
+binning. 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 in very good agreement with the expected 3000 GeV mean. Those numbers clearly show that the 
+method in use is able to successfully describe the simulated toy data.
 
 ![
 Combined fit of signal and background on a toy dataset with gaussian errors and a simulated resonance mass of 3 TeV.
@@ -477,26 +536,31 @@ Combined fit of signal and background on a toy dataset with gaussian errors and
 
 # Preselection and data quality
 
-To reduce the background and increase the signal sensitivity, a selection of events by different variables is 
-introduced. It is divided into two stages. The first one (the preselection) adds some general physics motivated 
-selections using kinematic variables and is also used to ensure a high trigger efficiency. In the second part, the 
-discriminators introduced by different taggers will be used to identify jets originating from the decay of a vector 
-boson. After the preselection, it is made sure, that the simulated samples represent the real data well by comparing the 
-data with the simulation in the signal as well as a sideband region, where no signal events are expected.
+To reduce the background and increase the signal sensitivity, a selection of events that satisfy certain requirements is 
+introduced. This is done taking into account different variables. The selection is divided into two stages. The first 
+one (the preselection) introduces some general physics motivated selections using kinematic variables and is also used 
+to ensure a high trigger efficiency. In the second part, the discriminants 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
 
 First, all events are cleaned of jets with a $p_t < \SI{200}{\giga\eV}$ and a pseudorapidity $|\eta| > 2.4$. This is to
 discard soft background and to make sure the particles are in the barrel region of the detector for an optimal track 
 reconstruction. Furthermore, all events with one of the two highest $p_t$ jets having an angular separation smaller
-than 0.8 from any electron or muon are discarded to allow future use of the results in studies of the semi or
-all-leptonic decay channels.
+than 0.8 from any electron or muon are discarded to allow future use of the data in studies investigating the leptonic 
+decay channel of the vector boson.
 
 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].
+The distributions of the number of jets before and after the selection can be seen in [@fig:njets]. The light blue 
+filled histogram shows the QCD background, the green and red line show the expected signal for a decay of the q\* 
+particle to qW with a mass of 2 TeV (green) and 5 TeV (red). By comparing the left to the right distributions, it is 
+clear that the requirement of at least 2 jets reduces the background significantly while keeping mostly all signal 
+events.
 
 \begin{figure}
 \begin{minipage}{\textwidth}
@@ -527,41 +591,53 @@ The next selection is done using $\Delta\eta = |\eta_1 - \eta_2|$, with $\eta_1$
 two jets with the highest transverse momentum. The q\* particle is expected to be very heavy in regards to the center of 
 mass energy of the collision and will therefore be almost stationary. Its decay products should therefore be close to 
 back to back, which means the $\Delta\eta$ distribution is expected to peak at zero. At the same time, particles 
-originating from QCD effects are expected to have a higher $\Delta\eta$ as they mainly form from less heavy resonances. 
-To maintain comparability, the same selection as in previous research of $\Delta\eta \le 1.3$ is used. A comparison of 
-the $\Delta\eta$ distribution before and after the selection can be seen in [@fig:deta].
+originating from QCD effects are expected to have a higher $\Delta\eta$. To maintain comparability, the same selection 
+as in previous research of $\Delta\eta \le 1.3$ is used. The comparison of the $m_{jj}$ distribution seen in [@fig:deta] 
+before and after the cut clearly shows, that the signal sensitivity was greatly improved by this cut.
 
 \begin{figure}
 \begin{minipage}{\textwidth}
-\centering\textbf{Comparison for 2016}
+\centering\textbf{$\Delta\eta$ cut with signal amplified by 10'000}
 \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}
+\begin{minipage}{\textwidth}
+\vspace{0.1cm}
+\centering\textbf{$m_{jj}$ distribution before the cut}
 \end{minipage}
-\caption{Comparison of the $\Delta\eta$ distribution before and after the cut at $\Delta\eta \le 1.3$. \newline
-Left: distribution before the cut. Right: distribution after the cut. \newline
-The signal curves are amplified by a factor of 10'000 to be visible.}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/2016/v1_Njet_invMass_stack.eps}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/combined/v1_Njet_invMass_stack.eps}
+\end{minipage}
+\begin{minipage}{\textwidth}
+\vspace{0.1cm}
+\centering\textbf{$m_{jj}$ distribution after the cut}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/2016/v1_Eta_invMass_stack.eps}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/combined/v1_Eta_invMass_stack.eps}
+\end{minipage}
+\caption{Demonstration of the effect of the $\Delta\eta$ cut at $\Delta\eta \le 1.3$. \newline
+Left: Partial dataset of $\SI{35.92}{\per\femto\barn}$ Right: Full dataset of $\SI{137.19}{\per\femto\barn}$.
+}
 \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 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.
+with the highest transverse momentum. A comparison of the $m_{jj}$ 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 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}
@@ -592,22 +668,25 @@ Left: distribution before the cut. Right: distribution after the cut.}
 After the preselection, the signal efficiency for q* decaying to qW of 2016 ranges from 48 % for 1.6 TeV to 49 % for 7 
 TeV. Decaying to qZ, the efficiencies are between 45 % (1.6 TeV) and 50 % (7 TeV). The amount of background after the 
 preselection is reduced to 5 % of the original events. For the combined data of the three years those values look 
-similar. Decaying to qW signal efficiencies between 49 % (1.6 TeV) and 56 % (7 TeV) are reached, wheres the efficiencies 
-when decaying to qZ are in the range of 46 % (1.6 TeV) to 50 % (7 TeV). Here, the background could be reduced to 8 % of 
-the original events. So while keeping around 50 % of the signal, the background was already reduced to less than a 
-tenth.
+similar. Decaying to qW signal efficiencies between 49 % (1.6 TeV) and 56 % (7 TeV) are reached, whereas 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.
 
 ## Data - Monte Carlo Comparison
 
-To ensure high data quality, the simulated QCD background sample is now being compared to the data of the corresponding 
-year collected by the CMS detector. This is done for the year 2016 and for the combined dataset. In [@fig: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.
+To ensure that the simulation reproduces the data well, 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 partial dataset of year 2016 and for 
+the full dataset separately. In [@fig:data-mc], this comparison can be seen for the distributions of the variables used 
+during the preselection.
+To compensate for the simulation overpredicting the scale of the QCD background, histograms are rescaled, so that the 
+dijet invariant mass distributions of data and simulation have the same integral.
+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]
+For analysing the data from the CMS experiment, jet energy corrections have to be applied. Those are to calibrate the 
+ECAL and HCAL parts of the CMS, so the energy of the detected particles can be measured correctly. The corrections used 
+were published by the CMS group. [cite todo]
 
 \begin{figure}
 \begin{minipage}{0.5\textwidth}
@@ -641,15 +720,14 @@ by the CMS group. [cite todo]
 
 ### Sideband
 
-The sideband region is introduced to make sure no bias in the data and Monte Carlo simulation is introduced. It is a 
-region in which no signal event is expected. Again, data and the Monte Carlo simulation are compared. For this analysis, 
-the region where the soft-drop mass of both of the two jets with the highest transverse momentum is more than 105 GeV is
-chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the heavier vector boson. Therefore it is very 
-unlikely, that an event with a particle heavier than that originates from the decay of a vector boson.
-In [@fig: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.
+The sideband region is introduced to make sure no bias in the data and Monte Carlo simulation is introduced and also to 
+verify the agreement of data and simulation. 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: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. It can be seen, that in the 
+sideband region data and simulation match very well.
 
 \begin{figure}
 \begin{minipage}{\textwidth}
@@ -686,19 +764,20 @@ This is done by distinguishing between QCD and signal events using a tagger to i
 from a vector boson. Two different taggers will be used to later compare their performance. The decay analysed includes 
 either a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a 
 selection using the soft-drop mass of a jet. The soft-drop mass of at least one of the two leading jets is expected to 
-be within $\SI{34}{\giga\eV}$ and $\SI{105}{\giga\eV}$. This cut already provides a good separation of QCD and signal 
+be within $\SI{35}{\giga\eV}$ and $\SI{105}{\giga\eV}$. This cut already provides a good separation of QCD and signal 
 events, on which the two taggers presented next can build.
 
-Both taggers provide a discriminator value to choose whether an event originates in the decay of a vector boson or from 
-QCD effects. This value will be optimized afterwards to make sure the maximum efficiency possible is achieved.
+Both taggers provide a discriminant to choose whether an event can be classified as the decay of a vector boson or 
+originates from QCD effects. This value will be optimized afterwards to make sure the maximum signal significance 
+possible is achieved.
 
 ## N-Subjettiness
 
 The N-subjettiness [@TAU21] $\tau_N$ is a jet shape parameter designed to identify boosted hadronically-decaying 
-objects. When a vector boson decays hadronically, it produces two quarks each causing a jet. But because of the high 
-mass of the vector bosons, the particles are highly boosted and appear, after applying a clustering algorithm, as just 
-one. This algorithm now tries to figure out, whether one jet might consist of two subjets by using the kinematics and 
-positions of the constituent particles of this jet.
+objects. When a vector boson decays hadronically, it produces two quarks each causing a jet. But in the case of the 
+decay of a q\* particle, the vector boson is highly boosted and so are its decay products. They therefore appear, after 
+applying a clustering algorithm, as just one jet. This algorithm now tries to figure out, whether one jet might consist 
+of two subjets by using the kinematics and positions of the constituent particles of this jet.
 The N-subjettiness is defined as
 
 \begin{equation} \tau_N = \frac{1}{d_0} \sum_k p_{T,k} \cdot \text{min}\{ \Delta R_{1,k}, \Delta R_{2,k}, …, \Delta
@@ -706,9 +785,11 @@ R_{N,k} \} \end{equation}
 
 with k going over the constituent particles in a given jet, $p_{T,k}$ being their transverse momenta and $\Delta R_{J,k}
 = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}$ being the distance of a candidate subjet J and a constituent particle k in the
-$\eta$ - $\phi$ plane. It quantifies to what degree a jet can be regarded as a jet composed of $N$ subjets.
-Experiments showed, that rather than using $\tau_N$ directly, the ratio $\tau_{21} = \tau_2/\tau_1$ is a better
-discriminator between QCD events and events originating from the decay of a boosted vector boson.
+$\eta$ - $\phi$ plane. It quantifies to what degree a jet can be regarded as a jet composed of $N$ subjets. In the 
+hadronic decay of a highly boosted vector boson, two subjets are expected. Therefore it seems that $\tau_2$ would be a 
+good choice for a discriminant. However, experiments showed, that rather than using $\tau_2$ directly, the ratio 
+$\tau_{21} = \tau_2/\tau_1$ is a better discriminant between QCD effects and events originating from the decay of a 
+boosted vector boson.
 
 The lower the $\tau_{21}$ is, the more likely a jet is caused by the decay of a vector boson. Therefore a selection will 
 be introduced, so that $\tau_{21}$ of one candidate jet is smaller then some value that will be determined by the 
@@ -718,10 +799,9 @@ soft-drop mass window is used. If both of them pass, the one with higher $p_t$ i
 ## DeepAK8
 
 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 
-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.
+reduces 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 shown by [@fig:ak8_eff], showing a comparison of background and 
+signal efficiency of the DeepAK8 tagger with, between others, the $\tau_{20}$ tagger that is also 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.
@@ -739,17 +819,18 @@ million jets were used for development and validation.
 In this thesis, the mass decorrelated version of the DeepAK8 tagger is used. It adds an additional mass predictor layer,
 that is trained to quantify how strongly the output of the non-decorrelated tagger is correlated to the mass of a
 particle. Its output is fed back to the network as a penalty so it avoids using features of the particles correlated to
-their mass. The result is a largely mass decorrelated tagger of heavy resonances.
-As the mass variable is already in use for the soft-drop mass selection, this version of the tagger is to be preferred.
+their mass. The result is a largely mass decorrelated tagger of heavy resonances, that doesn't introduce a bias in the 
+jet mass shape. As can be seen in [@fig:ak8_eff], it performs not as good as the non-mass-decorrelated version, but 
+still better than the other taggers it was compared to.
 
-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 
+The higher the discriminant 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}
 
-To figure out the best value to cut on the discriminators introduced by the two taggers, a value to quantify how good a
+To figure out the best value to cut on the discriminants introduced by the two taggers, a value to quantify how good a
 cut is has to be introduced. For that, the significance calculated by $\frac{S}{\sqrt{B}}$ will be used. S stands for
 the amount of signal events and B for the amount of background events in a given interval. This value assumes a gaussian
 error on the background so it will be calculated for the 2 TeV masspoint where enough background events exist to justify
@@ -779,36 +860,42 @@ boosted cut is placed at $\ge 0.95$. For the deep boosted tagger, 0.97 would giv
 it is very close to the edge where the significance drops very low and the higher the cut the less background will be 
 left to calculate the cross section limits, especially at higher resonance masses, the slightly less strict cut is 
 chosen.
-The significance for the $\tau_{21}$ cut is 14, and for the deep boosted tagger 26.
 
 For both taggers also a low purity category is introduced for high TeV regions. Using the cuts optimized for 2 TeV, 
 there are very few background events left for higher resonance masses, but to reliably calculate cross section limits, 
-those are needed. As low purity category for the N-subjettiness tagger, a cut at $0.35 < \tau_{21} < 0.75$ is used. For 
-the deep boosted tagger the opposite cut from the high purity category is used: $VvsQCD < 0.95$.
+those are needed. Therefore in the final cross section calculation, the two categories are combined to have a high 
+signal sensitivity for all masspoints between 1.6 TeV and 7 TeV that were simulated. As low purity category for the 
+N-subjettiness tagger, a cut at $0.35 < \tau_{21} < 0.75$ is used. For the deep boosted tagger the opposite cut from the 
+high purity category is used: $VvsQCD < 0.95$.
+
+\newpage
 
 # Signal extraction {#sec:extr}
 
 After the optimization, now the optimal selection for the N-subjettiness as well as the deep boosted tagger is found and 
-applied to the simulated samples as well as the data collected by the CMS. The fit described in [@sec: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.
+applied to the simulated samples as well as the data collected by the CMS experiment. The fit described in [@sec:moa] is 
+performed for all masspoints of the decay to qW and qZ and for the partial dataset of $\SI{35.92}{\per\femto\barn}$ as 
+well as the complete dataset of $\SI{137.19}{\per\femto\barn}$ separately.
 
 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 
-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 %.
+frequentist asymptotic limit criterion described in [@ASYMPTOTIC_LIMIT]. Using the parameters and signal rate obtained 
+by the method described in [@sec:moa] as well as a shape analysis of the data recorded by the CMS experiment, 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.
+In the absence of the q\* particle in the data, the observed limits 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.
+Since no significant deviation from the Standard Model is found while looking for the resonance, the crossing of the 
+theory line with the observed limit is calculated, to have a limit of mass up to which the existence of the q\* particle 
+can be excluded. To find the uncertainty of this result, the crossing of the theory line plus, respectively minus, its 
+uncertainty with the observed limit is also calculated.
 
-## Uncertainties
+## Systematic Uncertainties
 
-For calculating the cross section of the signal, four sources of uncertainties are considered.
+The variables used in this analysis are affected by systematic uncertainties.
+For calculating the cross section of the signal, four sources of such uncertainties are considered.
 
 First, the uncertainty of the Jet Energy Corrections. When measuring a particle's energy with the ECAL or HCAL part of 
 the CMS, the electronic signals send by the photodetectors in the calorimeters have to be converted to actual energy 
@@ -816,76 +903,82 @@ values. Therefore an error in this calibration causes the energy measured to be
 causing also the position of the signal peak in the $m_{jj}$ distribution to vary. The uncertainty is approximated to be 
 2 %.
 
-Second, the tagger is not perfect and therefore some events, that don't originate from a V boson are wrongly chosen and 
-on the other hand sometimes events that do originate from one are not. It influences the events chose for analysis and 
-is therefore also considered as an uncertainty, which is approximated to be 6 %.
+Second, the tagger does not work perfectly and therefore some events, that don't originate from a V boson are wrongly 
+chosen and on the other hand sometimes events that do originate from one are not. It influences the events chose for 
+analysis and is therefore also considered as an uncertainty, which is approximated to be 6 %.
 
 Third, the uncertainty of the parameters of the background fit is also considered, as it might change the background 
 shape a little and therefore influence how many signal and background events are reconstructed from the data.
 
-Fourth, the uncertainty on the Luminosity of the LHC of 2.5 % is also taken into account for the final results.
+Fourth, the uncertainty on the luminosity influence the normalization of the processes. Its value is 2.5 % [cite todo].
+\newpage
 
 # Results
 
-This chapter will start by presenting the results for the data of year 2016 using both taggers and comparing it to the 
-previous research [@PREV_RESEARCH]. It will then go on showing the results for the combined dataset, again using both 
-taggers comparing their performances.
+This chapter will start by presenting the results for the partial dataset of year 2016 with an integrated luminosity of 
+$\SI{35.92}{\per\femto\barn}$ using both taggers and comparing it to the previous research [@PREV_RESEARCH]. It will 
+then go on showing the results for the combined dataset with an integrated luminosity of $\SI{137.19}{\per\femto\barn}$, 
+again using both taggers comparing their performances.
 
-## 2016
+## Partial dataset
 
-Using the data collected by the CMS experiment on 2016, the cross section limits seen in [@fig:res2016] were obtained.
+Using the $\SI{35.92}{\per\femto\barn}$ of data collected by the CMS experiment during 2016, the cross section limits 
+seen in [@fig:res2016] were obtained.
 
 As described in [@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: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:res2016]. The table also shows the 
-upper and lower limits on the mass found by calculating the crossing of the theory plus resp. minus its uncertainty. Due 
-to the theory and the observed limits line being very flat in the high TeV region, even a small uncertainty of the 
-theory can cause a high difference of the mass limit.
+limit. In [@fig:res2016dw,@fig:res2016dz] it can be seen, that the observed limit using the deep boosted tagger 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 at lower resonance masses, 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: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 slowly 
+falling in the high TeV region, even a small uncertainty of the theory can cause a high difference of the mass limit.
 
 
-: Mass limits found using the data collected in 2016 {#tbl:res2016}
+: Mass limits found using the partial dataset of $\SI{35.92}{\per\femto\barn}$ {#tbl:res2016}
 
 | Decay | Tagger       | Limit [TeV] | Upper Limit [TeV] | Lower Limit [TeV] |
 |-------|--------------|-------------|-------------------|-------------------|
 | qW    | $\tau_{21}$  | 5.39        | 6.01              | 4.99              |
 | qW    | deep boosted | 4.96        | 5.19              | 4.84              |
 | qZ    | $\tau_{21}$  | 4.86        | 4.96              | 4.70              |
-| qZ    | deep boosted | 4.49        | 4.61              | 4.40              |
+| qZ    | deep boosted | 4.62        | 4.71              | 4.49              |
 
 
-
-\begin{figure}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_2016tau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_2016db_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_2016tau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf}
-  \end{minipage}
-\caption{Results of the cross section limits for 2016 using the $\tau_{21}$ tagger (left) and the deep boosted tagger 
-(right).}
+\begin{figure}%
+  \centering
+  \subfloat[Decay to qW, using N-subjettiness tagger]{%
+  \label{fig:res2016tw}%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_2016tau_13TeV.pdf}}
+  \subfloat[Decay to qW, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_2016db_13TeV.pdf}%
+  \label{fig:res2016dw}}\\
+  \subfloat[Decay to qZ, using N-subjettiness tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_2016tau_13TeV.pdf}%
+  \label{fig:res2016tz}}%
+  \subfloat[Decay to qZ, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf}%
+  \label{fig:res2016dz}}%
+\caption{Results of the cross section limits for the partial dataset of 2016 using the $\tau_{21}$ tagger and the deep 
+boosted tagger.}
 \label{fig:res2016}
 \end{figure}
 
-### Previous research
+### Comparison with existing results
 
-The limit established by using the N-subjettiness tagger on the 2016 data is already slightly higher than the one from 
-previous research, which was found to be 5 TeV for the decay to qW and 4.7 TeV for the decay to qZ. This is mainly due 
-to the fact, that in our data, the observed limit at the intersection point happens to be in the lower region of the 
-expected limit interval and therefore causing a very late crossing with the theory line when using the N-subjettiness 
-tagger (as can be seen in [@fig: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].
+The result will now be compared to an existing result using the same dataset. This research, however, uses a newer 
+detector calibration as well as an improved reconstruction so slight variations in the results are to be expected.
+
+The limit established by using the N-subjettiness tagger with the partial dataset is $\SI{0.39}{\tera\eV}$ (decay to qW) 
+resp. $\SI{0.16}{\tera\eV}$ (decay to qZ) higher than the one from previous research, which was found to be 5 TeV for 
+the decay to qW and 4.7 TeV for the decay to qZ. This is mainly due to the fact, that in our data, the observed limit at 
+the intersection point happens to be in the lower region of the expected limit interval and therefore causing a very 
+late crossing with the theory line when using the N-subjettiness tagger (as can be seen in [@fig:res2016]). 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. As already noted, a slight variations in the results was expected, 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}
@@ -901,62 +994,70 @@ Taken from \cite{PREV_RESEARCH}.}
 
 ## Combined dataset
 
-Using the combined data, the cross section limits seen in [@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.
+Using the full available dataset of $\SI{137.19}{\per\femto\barn}$, the cross section limits seen in [@fig:resCombined] 
+were obtained. The cross section limits are, compared to only using the 2016 dataset, reduced to about 50 %. This shows 
+the big improvement achieved by using more than three times the amount of data.
 
-The results for the mass limits of the combined years are as follows:
+The results for the mass limits of the combined years are presented in the following table.
 
 
-: Mass limits found using the data collected in 2016 - 2018
+: Mass limits found using $\SI{137.19}{\per\femto\barn}$ of data {#tbl:resCombined}
 
 | Decay | Tagger       | Limit [TeV] | Upper Limit [TeV] | Lower Limit [TeV] |
 |-------|--------------|-------------|-------------------|-------------------|
 | qW    | $\tau_{21}$  | 6.00        | 6.26              | 5.74              |
 | qW    | deep boosted | 6.11        | 6.31              | 5.39              |
 | qZ    | $\tau_{21}$  | 5.49        | 5.76              | 5.29              |
-| qZ    | deep boosted | 4.92        | 5.02              | 4.80              |
+| qZ    | deep boosted | 4.95        | 5.13              | 4.85              |
 
 
 The combination of the three years not just improved the cross section limits, but also the limit for the mass of the 
 q\* particle. The final result is 1 TeV higher for the decay to qW and almost 0.8 TeV higher for the decay to qZ than 
 what was concluded by the previous research [@PREV_RESEARCH].
 
-\begin{figure}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_Combinedtau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_Combineddb_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_Combinedtau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf}
-  \end{minipage}
-\caption{Results of the cross section limits for the three combined years using the $\tau_{21}$ tagger (left) and the 
-deep boosted tagger (right).}
+
+\begin{figure}%
+  \centering
+  \subfloat[Decay to qW, using N-subjettiness tagger]{%
+  \label{fig:resCombinedtw}%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_Combinedtau_13TeV.pdf}}
+  \subfloat[Decay to qW, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_Combineddb_13TeV.pdf}%
+  \label{fig:resCombineddw}}\\
+  \subfloat[Decay to qZ, using N-subjettiness tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_Combinedtau_13TeV.pdf}%
+  \label{fig:resCombinedtz}}%
+  \subfloat[Decay to qZ, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf}%
+  \label{fig:resCombineddz}}%
+\caption{Results of the cross section limits for the combined dataset using the $\tau_{21}$ tagger and the deep boosted 
+tagger.}
 \label{fig:resCombined}
 \end{figure}
 
 
 ## Comparison of taggers
 
-The previously shown results already show, that the deep boosted tagger was not able to significantly improve the 
-results compared to the N-subjettiness tagger.
+The results presented in [@tbl:res2016, @tbl:resCombined] show, that the deep boosted tagger was not able to 
+significantly improve the results compared to the N-subjettiness tagger.
 For further comparison, in [@fig:limit_comp] the expected limits of the different taggers for the q\* $\rightarrow$ qW 
 and the q\* $\rightarrow$ qZ decay are shown. It can be seen, that the deep boosted is at best as good as the 
 N-subjettiness tagger. This was not the expected result, as the deep neural network was 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 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.
+section limits. 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 is working but the assumption of it also applying to the combined dataset did not hold.
+
+This can be explained by some training issues identified lately.
+The training of the DeepAK8 tagger was done for the data of year 2016. It therefore performs differently for the data of 
+the other years. This caused the DeepAK8 tagger to perform significantly worse than it could have for several reasons. 
+First, the optimization done for the data of year 2018 could therefore not be applied to the other datasets. Second, 
+even for the data of 2016, a newer version of the background simulation was used, that, in combination with the samples 
+used for the signal, turned out to be the worst case scenario for the used training.
+Recently, the training was improved to better perform across all datasets, but those changes could not be incorporated 
+into this thesis due to it not being possible to do this in a reasonable timeframe.
 
-Recently, some issues with the training of the deep boosted tagger used in this analysis were also found, which might 
-explain, why it didn't perform better in general.
 
 
 \begin{figure}
@@ -973,44 +1074,40 @@ decay to qZ}
 
 
 ![Comparision of deep boosted and N-subjettiness tagger in the high purity category using the data from year 2018.
-](./figures/limit_comp_2018.pdf){#fig:comp_2018 width=60%}
+](./figures/limit_comp_2018.pdf){#fig:comp_2018 width=70%}
 
 \clearpage
 \newpage
 
 # Summary
 
-In this thesis, a limit on the mass of the q\* particle has been successfully established. This was done searching for 
-its decay to qW and qW with the vector boson then decaying hadronically. By combining the data from the years 2016, 2017 
-and 2018, collected by the CMS experiment, the previously set limit could be significantly improved.
+In this thesis, a search for the q\* particle decaying to q + W and q + Z was presented. Data of proton - proton 
+collisions at the LHC of an integrated luminosity of $\SI{137.19}{\per\femto\barn}$ collected by the CMS experiment at a 
+centre-of-mass energy of $\sqrt{s} = \SI{13}{\tera\eV}$ has been searched. Also a partial dataset of 
+$\SI{35.92}{\per\femto\barn}$ was analysed, to be able to compare the results to previous research. Monte Carlo 
+simulations were used to estimate the QCD background and signal.
 
-For the analysis, the following selection was applied to the data:
+A selection was introduced to reduce background events and enhance signal sensitivity. This selection required at least 
+two jets, a $\Delta\eta \ge 1.3$ between the two highest $p_t$ jets, an invariant mass of the two highest $p_t$ jets 
+greater than $\SI{1050}{\giga\eV}$ and a soft-drop mass of at least one jet between $\SI{35}{\giga\eV}$ and 
+$\SI{105}{\giga\eV}$.
 
-- #jets $\ge$ 2
-- $\Delta\eta < 1.4$
-- $m_{jj} \ge \SI{1050}{\giga\eV}$
-- $\SI{35}{\giga\eV} < m_{SDM} < \SI{105}{\giga\eV}$
+Two taggers, the DeepAK8 and the N-subjettiness tagger, have been used to identify jets originating from the decay of a 
+vector boson. For both of them, two categories were introduced. A high purity category, aiming for maximal signal 
+sensitivity in the low TeV region of the invariant mass spectrum and a low purity category, aiming for better statistics 
+in the high TeV region. For the DeepAK8 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.
 
-For the deep boosted tagger, a high purity category of $VvsQCD > 0.95$ and a low purity category of $VvsQCD \le 0.95$ 
-was used. For the N-subjettiness tagger the high purity category was $\tau_{21} < 0.35$ and the low purity category 
-$0.35 < \tau_{21} < 0.75$. These values were obtained by optimizing for the highest possible significance of the signal.
+A combined fit to the dijet invariant mass distribution of background plus 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. 
+Because no significant deviation from the Standard Model was observed, new exclusion limits for the mass of the q\* 
+particle were 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.
-
-The optimization process used to find the optimal values for the discriminant provided by the taggers, was found to not 
-be optimal. It was only done using 2018 data, with which the deep boosted tagger showed a higher significance than the 
-N-subjettiness tagger. Apparently, the assumption, that the same optimization would apply to the data of the other years 
-as well, did not hold. Using the combined dataset, the deep boosted tagger showed no better cross section limits than 
-the N-subjettiness tagger, which are directly related to the significance used for the optimization. Therefore, with a 
-better optimization and the fixed training issues of the deep boosted tagger, it is very likely, that the result 
-presented could be further improved.
+The DeepAK8 tagger performed worse than was expected. This can be explained with some training issues identified lately. 
+Therefore, with an updated training, it is expected that the presented results can be further improved.
 
 \newpage
 
diff --git a/thesis.pdf b/thesis.pdf
index fbcbaee..a65051d 100644
Binary files a/thesis.pdf and b/thesis.pdf differ
diff --git a/thesis.tex b/thesis.tex
index 010addc..098ea2b 100644
--- a/thesis.tex
+++ b/thesis.tex
@@ -40,7 +40,6 @@
 \IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
 \IfFileExists{bookmark.sty}{\usepackage{bookmark}}{\usepackage{hyperref}}
 \hypersetup{
-  pdftitle={Search for excited quark states decaying to qW/qZ},
   pdfauthor={David Leppla-Weber},
   pdflang={en-GB},
   hidelinks,
@@ -109,59 +108,96 @@
 \usepackage[]{biblatex}
 \addbibresource{bibliography.bib}
 
-\title{Search for excited quark states decaying to qW/qZ}
 \author{David Leppla-Weber}
 \date{}
 
 \begin{document}
-\maketitle
+
+\begin{titlepage}
+\begin{center}
+       \vspace*{1cm}
+       \Huge
+       \rule{\textwidth}{0.1cm}
+       \textbf{Search for excited quark states decaying to qW/qZ with the CMS experiment}
+       \rule{\textwidth}{0.1cm}
+
+       \vspace{2.5cm}
+       \Large
+       von\\
+       \LARGE
+       David Leppla-Weber\\
+       \Large
+       \vspace{0.5cm}
+       Geboren am\\
+       18.09.1996
+ 
+       \vfill
+ 
+       Bachelorarbeit im Studiengang Physik\\
+       Universität Hamburg\\
+       November 2019
+ 
+   \end{center}
+\end{titlepage}
+
+\newpage
+\mbox{}
+\vfill
+
+\begin{enumerate}
+\def\labelenumi{\arabic{enumi}.}
+\tightlist
+\item
+  Gutachter: Dr.~Andreas Hinzmann
+\item
+  Gutachter: Jun.-Prof.~Dr.~Gregor Kasieczka
+\end{enumerate}
+
+\newpage
+
 \begin{abstract}
-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
-\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, based on a
-deep neural network, is currently approximately at 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.
+A search for an excited quark state, called q*, is presented using data of proton-proton collisions at the LHC 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 an integrated luminosity of $\SI{137.19}{\per\femto\barn}$. Its decay channels to q 
++ W and q + Z with the vector bosons further decaying hadronically to $q + q\bar{q}'$ resp. $q + q\bar{q}$, resulting in 
+  two jets in the final state, are analysed. The dijet invariant mass spectrum of those two jets is then used to look 
+for a resonance and to reconstruct the q* mass. To identify jets originating from the decay of a vector boson, a 
+V-tagger is needed. For that, the new DeepAK8 tagger, based on a neural network, is compared to the older N-subjettiness 
+tagger. In the result, no significant deviation from the Standard Model can be observed, therefore the q* is excluded up 
+to a mass of 6.1\ TeV (qW) 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 with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$ collected 
+by the CMS experiment in 2016, excluding the q* particle up to a mass of 5.0\ TeV resp. 4.7\ TeV. The DeepAK8 tagger is 
+found to currently be at 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. By optimizing the neural network's training 
+for the datasets of 2016, 2017 and 2018, the sensitivity can likely be improved.
 
 \end{abstract}
+\newpage
 \renewcommand{\abstractname}{Zusammenfassung}
 \begin{abstract}
 
-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 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
+In dieser Arbeit wird eine Suche nach angeregten Quarkzuständen, genannt q*, durchgeführt. Dafür werden Daten von 
+Proton-Proton Kollisionen am LHC mit einer 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. Es wird der Zerfall des q* Teilchens zu q + W und q + Z untersucht, bei anschließendem 
+hadronischen Zerfall des Vektorbosons zu $q\bar{q}'$ bzw. $q\bar{q}$. Der gesamte Zerfall resultiert damit in zwei Jets, 
+mithilfe deren invariantem Massenspektrum die q* Masse rekonstruiert und nach einer Resonanz gesucht wird. Zur 
+Identifizerung von Jets, welche durch den Zerfall eines Vektorbosons entstanden sind, wird ein V-Tagger benötigt. 
+Hierfür wird der neue DeepAK8 Tagger, welcher auf einem neuronalen Netzwerk basiert, mit dem älteren N-Subjettiness 
+Tagger verglichen. Im Ergebnis kann keine signifikante Abweichung vom Standardmodell beobachtet werden. Das q* Teilchen 
+wird mit einem Konfidenzniveau von 95 \% bis zu einer Masse von 6.1\ TeV (qW) bzw. 5.5\ TeV (qZ) ausgeschlossen. Das Limit 
+liegt etwa 1\ TeV höher, als das anhand des $\SI{35.92}{\per\femto\barn}$ großen Datensatzes von 2016 gefundene von 5.0 
+TeV bzw. 4.7\ TeV. Beim Zerfall zu qW erzielt der DeepAK8 Tagger ein um $\SI{0.1}{\tera\eV}$ besseres Ergebnis, als der 
+N-Subjettiness Tagger, beim Zerfall zu qZ jedoch ein um $\SI{0.6}{\tera\eV}$ schlechteres. Durch Verbesserung des 
+Trainings des neuronalen Netzwerkes für die drei Datensätze von 2016, 2017 und 2018, gibt es aber noch Potential die 
+Sensitivität zu verbessern.
+
 \end{abstract}
 
-{
+\newpage
 \setcounter{tocdepth}{3}
 \tableofcontents
-}
+
 \newpage
 \pagenumbering{arabic}
 
@@ -170,7 +206,7 @@ die Leistung zu steigern. \newpage
 
 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 \enquote{theory of
+limitations, 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.
@@ -189,12 +225,13 @@ 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
-run of the Large Hadron Collider with an integrated luminosity of
+In a previous research \autocite{PREV_RESEARCH}, an exclusion 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 then, a lot more data has been
-collected, totalling to \(\SI{137.19}{\per\femto\barn}\) of data usable
-for research. This thesis uses this new data as well as a new technique
+collected by the CMS experiment, totalling to
+\(\SI{137.19}{\per\femto\barn}\) of data usable for research. This
+thesis takes advantage of this larger dataset as well as a new technique
 to identify decays of highly boosted particles based on a deep neural
 network. By using more data and new tagging techniques, it aims to
 either confirm the existence of the q* particle or improve the
@@ -204,14 +241,14 @@ directly compare the performance of this new tagging technique to an
 older tagger based on jet substructure studies used in the previous
 research.
 
-In chapter 2, a theoretical background will be presented explaining in
-short the Standard Model, its shortcomings and the theory of excited
-quarks. Then, in chapter 3, the Large Hadron Collider and the Compact
-Muon Solenoid, the detector that collected the data for this analysis,
-will be described. After that, in chapters 4-7, the main analysis part
-follows, describing how the data was used to extract limits on the mass
-of the excited quark particle. At the very end, in chapter 8, the
-results are presented and compared to previous research.
+In chapter 2, a theoretical background will be presented briefly
+explaining the Standard Model, its shortcomings and the theory of
+excited quarks. Then, in chapter 3, the Large Hadron Collider and the
+Compact Muon Solenoid, the detector that collected the data for this
+analysis, will be described. After that, in chapters 4-7, the main
+analysis part follows, describing how the data were used to extract
+limits on the mass of the excited quark particle. At the very end, in
+chapter 8, the results are presented and compared to previous research.
 
 \newpage
 
@@ -222,7 +259,8 @@ This chapter presents a short summary of the theoretical background
 relevant to this thesis. It first gives an 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.
+theory of q*, which are the relevant phenomena for the search described
+in this thesis.
 
 \hypertarget{sec:sm}{%
 \subsection{Standard Model}\label{sec:sm}}
@@ -238,22 +276,21 @@ only known to be one for fermions and either one (gauge bosons) or zero
 (scalar bosons) for bosons. Fermions are further classified into quarks
 and leptons. Quarks and leptons can also be categorized into three
 generations, each of which contains two particles, also called 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 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.
+For leptons, the three generations each consist of a charged lepton and
+its corresponding neutrino, namely the electron, the muon and 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. 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}{%
 \centering
 \includegraphics[width=0.5\textwidth,height=\textheight]{./figures/sm_wikipedia.pdf}
 \caption{Elementary particles of the Standard Model and their mass
-charge and spin.}\label{fig:sm}
+charge and spin. Taken from \autocite{SM}}\label{fig:sm}
 }
 \end{figure}
 
@@ -267,11 +304,10 @@ scattering or absorption. Photons of different energies can also be
 described as electromagnetic waves of different wavelengths.
 
 The \(W^\pm\) and \(Z^0\) bosons mediate the weak force. All quarks and
-leptons carry a flavour, which is a conserved value. Only the weak
-interaction breaks this conservation, a quark or lepton can therefore,
-by interacting with a \(W^\pm\) boson, change its flavour. The
-probabilities of this happening are determined by the
-Cabibbo-Kobayashi-Maskawa matrix:
+leptons carry a flavour, which is a conserved value in all interactions
+but the weak one. There, a quark or lepton can, by interacting with a
+\(W^\pm\) boson, change its flavour. The probabilities of this happening
+are determined by the Cabibbo-Kobayashi-Maskawa matrix:
 
 \begin{equation}
   V_{CKM} =
@@ -286,10 +322,12 @@ Cabibbo-Kobayashi-Maskawa matrix:
       0.224 & 0.974 & 0.042 \\
       0.008 & 0.041 & 0.999
     \end{pmatrix}
-\end{equation} The probability of a quark changing its flavour from
-\(i\) to \(j\) is given by the square of the absolute value of the
-matrix element \(V_{ij}\). It is easy to see, that the change of flavour
-in the same generation is way more likely than any other flavour change.
+\end{equation}
+
+The probability of a quark changing its flavour from \(i\) to \(j\) is
+given by the square of the absolute value of the matrix element
+\(V_{ij}\). It is easy to see, that the change of flavour in the same
+generation is way more likely than any other flavour change.
 
 Due to their high masses of 80.39 GeV resp. 91.19 GeV, the \(W^\pm\) and
 \(Z^0\) bosons themselves decay very quickly. Either in the leptonic or
@@ -300,23 +338,23 @@ 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
 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.
+vector bosons 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,
 although they don't carry only one colour but rather a combination of a
 colour and an anticolour, and can therefore interact with themselves and
-exist in eight different variants. As a result of this, processes, where
+exist in eight different variants. As a result of this, processes where
 a gluon decays into two gluons are possible. Furthermore the strength of
-the strong force, binding to colour carrying particles, increases with
+the strong force, binding colour carrying particles, increases with
 their distance making it at a certain point more energetically efficient
 to form a new quark - antiquark pair than separating the two particles
 even further. This effect is known as colour confinement. Due to this
 effect, colour carrying particles can't be observed directly, but rather
 form so called jets that cause hadronic showers in the detector. Those
 jets are cone like structures made of hadrons and other particles. The
-effect is called Hadronisation.
+effect is called hadronisation \autocite{HADRONIZATION}.
 
 \hypertarget{shortcomings-of-the-standard-model}{%
 \subsubsection{Shortcomings of the Standard
@@ -360,14 +398,14 @@ particles of the standard model are the composite quark models. Those
 state, that quarks consist of some particles unknown so far. This could
 explain the symmetries between the different fermions. A common
 prediction of those models are excited quark states (q*, q**,
-q***\ldots). Similar to atoms, that can be excited by the absorption of
-a photon and can then decay again under emission of a photon with an
-energy corresponding to the excited state, those excited quark states
-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.
+q***\ldots) \autocite{QSTAR_THEORY}. 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 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 energy region. That will cause the
+emitted boson to be highly boosted.
 
 \begin{figure}
 \centering
@@ -424,7 +462,8 @@ decay mode & br. ratio {[}\%{]} & decay mode & br. ratio
 The decay to the vector bosons have the second highest branching ratio.
 The decay to a gluon and a quark is the dominant decay, but virtually
 impossible to distinguish from the QCD background described in the next
-section. This makes the decay to the vector bosons the obvious choice.
+section. This makes the decay to the vector bosons the most promising
+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
@@ -433,12 +472,13 @@ the two jets in the final state, vectors consisting of the energy and
 momentum of a particle, together. From the four momentum it's easy to
 derive the mass by solving \(E=\sqrt{p^2 + m^2}\) for m.
 
-This theory has already been investigated in \autocite{PREV_RESEARCH}
-analysing data recorded by CMS in 2016, excluding the q* particle up to
-a mass of 5 TeV resp. 4.7 TeV for the decay to qW resp. qZ analysing the
-hadronic decay of the vector boson. This thesis aims to either exclude
-the particle to higher masses or find a resonance showing its existence
-using the higher center of mass energy of the LHC as well as more data
+A search for the excited quark predicted by this theory has already been
+investigated in \autocite{PREV_RESEARCH} analysing data with an
+integrated luminosity of \(\SI{35.92}{\per\femto\barn}\) recorded by the
+CMS experiment in 2016, excluding the q* particle up to a mass of 5 TeV
+resp. 4.7 TeV for the decay to qW resp. qZ analysing the hadronic decay
+of the vector boson. This thesis aims to either exclude the particle to
+higher masses or find a resonance showing its existence using more data
 that is available now.
 
 \hypertarget{sec:qcdbg}{%
@@ -483,14 +523,14 @@ this thesis will be described.
 \subsection{Large Hadron Collider}\label{large-hadron-collider}}
 
 The Large Hadron Collider \autocite{LHC_MACHINE} is the world's largest
-and most powerful particle accelerator. It has a circumference of 25 km
+and most powerful particle accelerator. It has a circumference 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 LHC
-may also be used for colliding ions but this ability is to no interest
-for this research.
+home to several experiments, between others the Compact Muon Solenoid
+(CMS), which is the one used for the search presented in this thesis. It
+is a general-purpose detector 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.
@@ -552,11 +592,11 @@ pseudorapidity \(\eta\), which is defined as
 coordinates are visualised in Fig.~\ref{fig:cmscoords}. Furthermore, to
 describe a particle's momentum, often the transverse momentum, \(p_t\)
 is used. It is the component of the momentum transversal to the beam
-axis. Before the collision, the transverse momentum has to be zero,
-therefore, due to conservation of energy, the sum of all transverse
-momenta after the collision has to be zero, too. If this is not the case
-for the detected events, it implies particles that weren't detected such
-as neutrinos.
+axis. Before the collision, the transverse momentum is 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}{%
@@ -564,7 +604,7 @@ as neutrinos.
 \includegraphics[width=0.6\textwidth,height=\textheight]{./figures/cms_coordinates.png}
 \caption{Coordinate conventions of the CMS illustrating the use of
 \(\eta\) and \(\phi\). The Z axis is in beam direction. Taken from
-https://inspirehep.net/record/1236817/plots}\label{fig:cmscoords}
+\autocite{COORD_PLOT}}\label{fig:cmscoords}
 }
 \end{figure}
 
@@ -573,9 +613,9 @@ https://inspirehep.net/record/1236817/plots}\label{fig:cmscoords}
 
 The tracking system is built of two parts, closest to the collision is a
 pixel detector and around that silicon strip sensors. They are used to
-reconstruct the tracks of charged particles, measuring their charge
-sign, direction and momentum. They are as close to the collision as
-possible to be able to identify secondary vertices.
+measure their charge sign, direction and momentum to be later able to
+reconstruct the tracks of charged particles. They are as close to the
+collision as possible to be able to identify secondary vertices.
 
 \hypertarget{the-electromagnetic-calorimeter}{%
 \subsubsection{The electromagnetic
@@ -588,8 +628,8 @@ proportion to the particle's energy. This light is measured by the
 photodetectors that convert it to an electrical signal. To measure a
 particles energy, it has to leave its whole energy in the ECAL, which is
 true for photons and electrons, but not for other particles such as
-hadrons and muons. Those are of higher energy and therefore only leave
-some energy in the ECAL but are not stopped by it.
+hadrons and muons. Those interact with matter differently and therefore
+only leave some energy in the ECAL but are not stopped by it.
 
 \hypertarget{the-hadronic-calorimeter}{%
 \subsubsection{The hadronic
@@ -612,11 +652,12 @@ tracks.
 \hypertarget{the-muon-system}{%
 \subsubsection{The muon system}\label{the-muon-system}}
 
-Outside of the solenoid there is only the muon system. It consists of
-three types of gas detectors, the drift tubes, cathode strip chambers
-and resistive plate chambers. It covers a total of \(0 < |\eta| < 2.4\).
-The muons are the only detected particles, that can pass all the other
-systems without a significant energy loss.
+Outside of the solenoid, but still in its return yoke, there is only the
+muon system. It consists of three types of gas detectors, the drift
+tubes, cathode strip chambers and resistive plate chambers. It covers a
+total of \(0 < |\eta| < 2.4\). The muons are the only detected
+particles, that can pass all the other systems without a significant
+energy loss.
 
 \hypertarget{the-trigger-system}{%
 \subsubsection{The Trigger system}\label{the-trigger-system}}
@@ -635,22 +676,23 @@ decision making.
 \subsubsection{The Particle Flow
 algorithm}\label{the-particle-flow-algorithm}}
 
-The particle flow algorithm is used to identify and reconstruct all the
-particles arising from the proton - proton collision by using all the
-information available from the different sub-detectors of the CMS. It
-does so by extrapolating the tracks through the different calorimeters
-and associating clusters they cross with them. The set of clusters
-already associated to a track is then no more used for the detection of
-other particles. This is first done for muons and then for charged
-hadrons, so a muon can't give rise to a wrongly identified charged
-hadron. Due to Bremsstrahlung photon emission, electrons are harder to
-reconstruct. For them a specific track reconstruction algorithm is used.
-After identifying charged hadrons, muons and electrons, all remaining
-clusters within the HCAL correspond to neutral hadrons and within ECAL
-to photons. If the list of particles and their corresponding deposits is
-established, it can be used to determine the particles four momenta.
-From that, the missing transverse energy can be calculated and tau
-particles can be reconstructed by their decay products.
+The particle flow algorithm \autocite{PARTICLE_FLOW} 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. It does so by extrapolating the tracks through the
+different calorimeters and associating clusters they cross with them.
+The set of clusters already associated to a track is then no more used
+for the reconstruction 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 \autocite{ERECO}. After identifying
+charged hadrons, muons and electrons, all remaining clusters within the
+HCAL correspond to neutral hadrons and within ECAL to photons. When the
+list of particles and their corresponding deposits is established, it
+can be used to determine the particles four momenta. From that, the
+missing transverse energy can be calculated and tau particles can be
+reconstructed by their decay products.
 
 \hypertarget{jet-clustering}{%
 \subsection{Jet clustering}\label{jet-clustering}}
@@ -658,9 +700,9 @@ particles can be reconstructed by their decay products.
 Because of the hadronisation it is not possible to uniquely identify the
 originating particle of a jet. Nonetheless, several algorithms exist to
 help with this problem. The algorithm used in this thesis is the
-anti-\(k_t\) clustering algorithm. It arises from a generalization of
-several other clustering algorithms, namely the \(k_t\),
-Cambridge/Aachen and SISCone clustering algorithms.
+anti-\(k_t\) \autocite{ANTIKT} clustering algorithm. It arises from a
+generalization of several other clustering algorithms, namely the
+\(k_t\), Cambridge/Aachen and SISCone clustering algorithms.
 
 The anti-\(k_t\) clustering algorithm associates high \(p_t\) particles
 with the lower \(p_t\) particles surrounding them within a radius R in
@@ -685,22 +727,21 @@ random soft \enquote{ghosts}. Taken from
 \end{figure}
 
 Furthermore, to approximate the mass of a heavy particle that caused a
-jet, the soft-drop mass can be used. It is calculated by removing wide
-angle soft particles from the jet to counter the effects of
-contamination from initial state radiation, underlying event and
-multiple hadron scattering. It therefore is more accurate in determining
-the mass of a particle causing a jet than taking the mass of all
-constituent particles of the jet combined.
+jet, the soft-drop mass \autocite{SDM} can be used. In its calculation,
+to reduce the contamination from initial state radiation, underlying
+event and multiple hadron scattering, wide angle soft particles are
+removed from the jet. It therefore is more accurate in determining the
+mass of a particle causing a jet than taking the mass of all constituent
+particles of the jet combined.
 
 \newpage
 
 \hypertarget{sec:moa}{%
 \section{Method of analysis}\label{sec:moa}}
 
-This section gives an overview over how the data collected by the LHC
-and CMS is going to be analysed to be able to either exclude the q*
-particle to even higher masses than already done or confirm its
-existence.
+This section gives an overview over how the data collected by CMS is
+going to be analysed to be able to either exclude the q* particle to
+even higher masses than already done or confirm its existence.
 
 As described in Sec.~\ref{sec:qs}, the decay of the q* particle to a
 quark and a vector boson with the vector boson then decaying
@@ -710,8 +751,8 @@ to a quark and a gluon. Therefore it is a good choice for this research.
 It results in two jets, because the decay products of the heavy vector
 boson are highly boosted, causing them to be very close together and
 therefore be reconstructed as one jet. The dijet invariant mass of the
-two jets in the final state, which is identical to the mass of the q*
-particle, is reconstructed. The only background considered is the QCD
+two jets in the final state is then used to reconstruct the mass of the
+q* particle. The only background considered is the QCD multijet
 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
@@ -725,34 +766,39 @@ reconstruct jets and all the other particles forming during the
 collision. The jets are then clustered using the anti-\(k_t\) algorithm
 with the distance parameter R being 0.8.
 
-The analysis will be conducted with two different sets of data. First,
-only the data collected by CMS in 2016 will be used to compare the
-results to the previous analysis \autocite{PREV_RESEARCH}. Then the
-combined data from 2016, 2017 and 2018 will be used to improve the
-previously set limits for the mass of the q* particle. Also, two
-different V-tagging mechanisms will be used to compare their
-performance. One based on the N-subjettiness variable used in the
-previous research \autocite{PREV_RESEARCH}, the other being a novel
-approach using a deep neural network, that will be explained in the
-following.
+The analysis will be conducted in two steps. First, only the data
+collected by the CMS experiment in 2016 with an integrated luminosity of
+\(\SI{35.92}{\per\femto\barn}\) will be used to compare the results to
+the previous analysis \autocite{PREV_RESEARCH}. Then the combined data
+from 2016, 2017 and 2018 with an integrated luminosity of
+\(\SI{137.19}{\per\femto\barn}\) will be used to improve the previously
+set limits for the mass of the q* particle. Also, two different
+V-tagging methods will be used to compare their performance. One based
+on the N-subjettiness variable used in the previous research
+\autocite{PREV_RESEARCH}, the other being a novel approach using a deep
+neural network, that will be explained in the following.
 
 \hypertarget{signal-and-background-modelling}{%
 \subsection{Signal and Background
 modelling}\label{signal-and-background-modelling}}
 
-To make sure the setup is working as intended, at first simulated
-samples of background and signal are used. In those Monte Carlo
-simulations, the different particle interactions that take place in a
-proton - proton collision are simulated using the probabilities provided
-by the Standard Model by calculating the cross sections of the different
-feynman diagrams. Later on, also detector effects (like its limited
+Before looking at the data collected by the CMS experiment, Monte Carlo
+simulations \autocite{MONTECARLO} of background and signal are used to
+understand how the data is expected to look like. To replicate the QCD
+background processes, the different particle interactions that take
+place in a proton - proton collision are simulated using the
+probabilities provided by the Standard Model by calculating the cross
+sections of the different Feynman diagrams. This was done using MadGraph
+and Pythia 8. Later on, also detector effects (like its limited
 resolution) are applied to make sure, they look like real data coming
-from the CMS detector. The q* signal samples are simulated by the
-probabilities given by the q* theory \autocite{QSTAR_THEORY} and
-assuming a cross section of \(\SI{1}{\per\pico\barn}\). The simulation
-was done using MadGraph. Because of the expected high mass, the signal
-width will be dominated by the resolution of the detector, not by the
-natural resonance width.
+from the CMS detector.
+
+The q* signal samples are simulated by the probabilities given by the q*
+theory \autocite{QSTAR_THEORY} and assuming a cross section of
+\(\SI{1}{\per\pico\barn}\). The simulation was done using MadGraph for
+eleven masspoints between 1.6 TeV and 7 TeV. Because of the expected
+high mass, the signal width will be dominated by the resolution of the
+detector, not by the natural resonance width.
 
 The dijet invariant mass distribution of the QCD background is expected
 to smoothly fall with higher masses. It is therefore fitted using the
@@ -761,7 +807,8 @@ following smooth falling function with three parameters p0, p1, p2:
 \frac{dN}{dm_{jj}} = \frac{p_0 \cdot ( 1 - m_{jj} / \sqrt{s} )^{p_2}}{ (m_{jj} / \sqrt{s})^{p_1}}
 \end{equation} Whereas \(m_{jj}\) is the invariant mass of the dijet and
 \(p_0\) is a normalisation parameter. It is the same function as used in
-the previous research studying 2016 data only.
+the previous research studying 2016 data only but was also found to
+reliably reproduce the background shape of the other years.
 
 The signal is fitted using a double sided crystal ball function. It has
 six parameters:
@@ -787,14 +834,14 @@ 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.
+Fig.~\ref{fig:cb_fit}. In this figure, a binning of 200 GeV is used for
+presentational purposes. The analysis itself is conducted using a 1 GeV
+binning. 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 in very good agreement
+with the expected 3000 GeV mean. Those numbers clearly show that the
+method in use is able to successfully describe the simulated toy data.
 
 \begin{figure}
 \hypertarget{fig:cb_fit}{%
@@ -813,12 +860,13 @@ TeV.}\label{fig:cb_fit}
 quality}\label{preselection-and-data-quality}}
 
 To reduce the background and increase the signal sensitivity, a
-selection of events by different variables is introduced. It is divided
-into two stages. The first one (the preselection) adds some general
-physics motivated selections using kinematic variables and is also used
-to ensure a high trigger efficiency. In the second part, the
-discriminators introduced by different taggers will be used to identify
-jets originating from the decay of a vector boson. After the
+selection of events that satisfy certain requirements is introduced.
+This is done taking into account different variables. The selection is
+divided into two stages. The first one (the preselection) introduces
+some general physics motivated selections using kinematic variables and
+is also used to ensure a high trigger efficiency. In the second part,
+the discriminants 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.
@@ -832,8 +880,8 @@ is to discard soft background and to make sure the particles are in the
 barrel region of the detector for an optimal track reconstruction.
 Furthermore, all events with one of the two highest \(p_t\) jets having
 an angular separation smaller than 0.8 from any electron or muon are
-discarded to allow future use of the results in studies of the semi or
-all-leptonic decay channels.
+discarded to allow future use of the data in studies investigating the
+leptonic decay channel of the vector boson.
 
 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
@@ -842,7 +890,13 @@ 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}. The light blue filled
+histogram shows the QCD background, the green and red line show the
+expected signal for a decay of the q* particle to qW with a mass of 2
+TeV (green) and 5 TeV (red). By comparing the left to the right
+distributions, it is clear that the requirement of at least 2 jets
+reduces the background significantly while keeping mostly all signal
+events.
 
 \begin{figure}
 \begin{minipage}{\textwidth}
@@ -876,34 +930,46 @@ heavy in regards to the center of mass energy of the collision and will
 therefore be almost stationary. Its decay products should therefore be
 close to back to back, which means the \(\Delta\eta\) distribution is
 expected to peak at zero. At the same time, particles originating from
-QCD effects are expected to have a higher \(\Delta\eta\) as they mainly
-form from less heavy resonances. To maintain comparability, the same
-selection as in previous research of \(\Delta\eta \le 1.3\) is used. A
-comparison of the \(\Delta\eta\) distribution before and after the
-selection can be seen in Fig.~\ref{fig:deta}.
+QCD effects are expected to have a higher \(\Delta\eta\). To maintain
+comparability, the same selection as in previous research of
+\(\Delta\eta \le 1.3\) is used. The comparison of the \(m_{jj}\)
+distribution seen in Fig.~\ref{fig:deta} before and after the cut
+clearly shows, that the signal sensitivity was greatly improved by this
+cut.
 
 \begin{figure}
 \begin{minipage}{\textwidth}
-\centering\textbf{Comparison for 2016}
+\centering\textbf{$\Delta\eta$ cut with signal amplified by 10'000}
 \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}
+\begin{minipage}{\textwidth}
+\vspace{0.1cm}
+\centering\textbf{$m_{jj}$ distribution before the cut}
 \end{minipage}
-\caption{Comparison of the $\Delta\eta$ distribution before and after the cut at $\Delta\eta \le 1.3$. \newline
-Left: distribution before the cut. Right: distribution after the cut. \newline
-The signal curves are amplified by a factor of 10'000 to be visible.}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/2016/v1_Njet_invMass_stack.eps}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/combined/v1_Njet_invMass_stack.eps}
+\end{minipage}
+\begin{minipage}{\textwidth}
+\vspace{0.1cm}
+\centering\textbf{$m_{jj}$ distribution after the cut}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/2016/v1_Eta_invMass_stack.eps}
+\end{minipage}
+\begin{minipage}{0.5\textwidth}
+\includegraphics{./figures/combined/v1_Eta_invMass_stack.eps}
+\end{minipage}
+\caption{Demonstration of the effect of the $\Delta\eta$ cut at $\Delta\eta \le 1.3$. \newline
+Left: Partial dataset of $\SI{35.92}{\per\femto\barn}$ Right: Full dataset of $\SI{137.19}{\per\femto\barn}$.
+}
 \label{fig:deta}
 \end{figure}
 
@@ -911,13 +977,13 @@ The last selection in the preselection is on the dijet invariant mass:
 \(m_{jj} \ge \SI{1050}{\giga\eV}\). It is important for a trigger
 efficiency higher than 99 \% with a soft-drop mass cut of
 \(m_{SDM} > \SI{65}{\giga\eV}\) applied to the jet with the highest
-transverse momentum. A comparison of its distribution before and after
-the selection can be seen in Fig.~\ref{fig:invmass}. Also, it has a huge
-impact on the background because it usually consists of lighter
-particles. The q* on the other hand is expected to have a very high
-invariant mass of more than 1 TeV. The \(m_{jj}\) distribution should be
-a smoothly falling function for the QCD background and peak at the
-simulated resonance mass for the signal events.
+transverse momentum. A comparison of the \(m_{jj}\) distribution before
+and after the selection can be seen in Fig.~\ref{fig:invmass}. Also, it
+has a huge impact on the background because it usually consists of
+lighter particles. The q* on the other hand is expected to have a very
+high invariant mass of more than 1 TeV. The \(m_{jj}\) distribution
+should be a smoothly falling function for the QCD background and peak at
+the simulated resonance mass for the signal events.
 
 \begin{figure}
 \begin{minipage}{\textwidth}
@@ -951,7 +1017,7 @@ the efficiencies are between 45 \% (1.6 TeV) and 50 \% (7 TeV). The
 amount of background after the preselection is reduced to 5 \% of the
 original events. For the combined data of the three years those values
 look similar. Decaying to qW signal efficiencies between 49 \% (1.6 TeV)
-and 56 \% (7 TeV) are reached, wheres the efficiencies when decaying to
+and 56 \% (7 TeV) are reached, whereas 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
@@ -961,19 +1027,24 @@ to less than a tenth.
 \subsection{Data - Monte Carlo
 Comparison}\label{data---monte-carlo-comparison}}
 
-To ensure high data quality, the simulated QCD background sample is now
-being compared to the data of the corresponding year collected by the
-CMS detector. This is done for the year 2016 and for the combined
-dataset. In Fig.~\ref{fig:data-mc}, this comparison can be seen for the
-distributions of the variables used during the preselection. The
+To ensure that the simulation reproduces the data well, 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
+partial dataset of year 2016 and for the full dataset separately. In
+Fig.~\ref{fig:data-mc}, this comparison can be seen for the
+distributions of the variables used during the preselection. To
+compensate for the simulation overpredicting the scale of the QCD
+background, histograms are rescaled, so that the dijet invariant mass
+distributions of data and simulation have the same integral. 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{]}
+For analysing the data from the CMS experiment, jet energy corrections
+have to be applied. Those are to calibrate the ECAL and HCAL parts of
+the CMS, so the energy of the detected particles can be measured
+correctly. The corrections used were published by the CMS group. {[}cite
+todo{]}
 
 \begin{figure}
 \begin{minipage}{0.5\textwidth}
@@ -1008,20 +1079,18 @@ corrections used were published by the CMS group. {[}cite todo{]}
 \subsubsection{Sideband}\label{sideband}}
 
 The sideband region is introduced to make sure no bias in the data and
-Monte Carlo simulation is introduced. It is a region in which no signal
-event is expected. Again, data and the Monte Carlo simulation are
-compared. For this analysis, the region where the soft-drop mass of both
-of the two jets with the highest transverse momentum is more than 105
-GeV is chosen. 105 GeV is well above the mass of 91 GeV of the Z boson,
-the heavier vector boson. Therefore it is very unlikely, that an event
-with a particle heavier than that originates from the decay of a vector
+Monte Carlo simulation is introduced and also to verify the agreement of
+data and simulation. It is a region in which no signal event is
+expected. Again, data and the Monte Carlo simulation are compared. For
+this analysis, the region where the soft-drop mass of both of the two
+jets with the highest transverse momentum is more than 105 GeV is
+chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the
+heavier vector boson. Therefore it is very unlikely, that an event with
+a particle heavier than that originates from the decay of a vector
 boson. In Fig.~\ref{fig:sideband}, the comparison of data with
 simulation in the sideband region can be seen for the soft-drop mass
-distribution as well as the dijet invariant mass distribution. As in
-Fig.~\ref{fig:data-mc}, the histograms are rescaled, so that the dijet
-invariant mass distributions of data and simulation have the same
-integral. It can be seen, that in the sideband region data and
-simulation match very well.
+distribution as well as the dijet invariant mass distribution. It can be
+seen, that in the sideband region data and simulation match very well.
 
 \begin{figure}
 \begin{minipage}{\textwidth}
@@ -1064,14 +1133,14 @@ analysed includes either a W or Z boson, which are, compared to the
 particles in QCD effects, very heavy. This can be used by adding a
 selection using the soft-drop mass of a jet. The soft-drop mass of at
 least one of the two leading jets is expected to be within
-\(\SI{34}{\giga\eV}\) and \(\SI{105}{\giga\eV}\). This cut already
+\(\SI{35}{\giga\eV}\) and \(\SI{105}{\giga\eV}\). This cut already
 provides a good separation of QCD and signal events, on which the two
 taggers presented next can build.
 
-Both taggers provide a discriminator value to choose whether an event
-originates in the decay of a vector boson or from QCD effects. This
-value will be optimized afterwards to make sure the maximum efficiency
-possible is achieved.
+Both taggers provide a discriminant to choose whether an event can be
+classified as the decay of a vector boson or originates from QCD
+effects. This value will be optimized afterwards to make sure the
+maximum signal significance possible is achieved.
 
 \hypertarget{n-subjettiness}{%
 \subsection{N-Subjettiness}\label{n-subjettiness}}
@@ -1079,11 +1148,12 @@ possible is achieved.
 The N-subjettiness \autocite{TAU21} \(\tau_N\) is a jet shape parameter
 designed to identify boosted hadronically-decaying objects. When a
 vector boson decays hadronically, it produces two quarks each causing a
-jet. But because of the high mass of the vector bosons, the particles
-are highly boosted and appear, after applying a clustering algorithm, as
-just one. This algorithm now tries to figure out, whether one jet might
-consist of two subjets by using the kinematics and positions of the
-constituent particles of this jet. The N-subjettiness is defined as
+jet. But in the case of the decay of a q* particle, the vector boson is
+highly boosted and so are its decay products. They therefore appear,
+after applying a clustering algorithm, as just one jet. This algorithm
+now tries to figure out, whether one jet might consist of two subjets by
+using the kinematics and positions of the constituent particles of this
+jet. The N-subjettiness is defined as
 
 \begin{equation} \tau_N = \frac{1}{d_0} \sum_k p_{T,k} \cdot \text{min}\{ \Delta R_{1,k}, \Delta R_{2,k}, …, \Delta
 R_{N,k} \} \end{equation}
@@ -1093,10 +1163,13 @@ being their transverse momenta and
 \(\Delta R_{J,k} = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}\) being the
 distance of a candidate subjet J and a constituent particle k in the
 \(\eta\) - \(\phi\) plane. It quantifies to what degree a jet can be
-regarded as a jet composed of \(N\) subjets. Experiments showed, that
-rather than using \(\tau_N\) directly, the ratio
-\(\tau_{21} = \tau_2/\tau_1\) is a better discriminator between QCD
-events and events originating from the decay of a boosted vector boson.
+regarded as a jet composed of \(N\) subjets. In the hadronic decay of a
+highly boosted vector boson, two subjets are expected. Therefore it
+seems that \(\tau_2\) would be a good choice for a discriminant.
+However, experiments showed, that rather than using \(\tau_2\) directly,
+the ratio \(\tau_{21} = \tau_2/\tau_1\) is a better discriminant between
+QCD effects 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
@@ -1110,14 +1183,13 @@ with higher \(p_t\) is chosen.
 \subsection{DeepAK8}\label{deepak8}}
 
 The DeepAK8 tagger \autocite{DEEP_BOOSTED} uses a deep neural network
-(DNN) to identify decays originating in a vector boson. It claims to
-reduce the background rate by up to a factor of \textasciitilde10 with
-the same signal efficiency compared to non-machine-learning approaches
-like the N-Subjettiness method. This is supported by
-Fig.~\ref{fig:ak8_eff}, showing a comparison of background and signal
-efficiency of the DeepAK8-MD (MD being short for mass decorrelated)
-tagger, with, between others, the \(\tau_{20}\) tagger that are used in
-this analysis.
+(DNN) to identify decays originating in a vector boson. It reduces 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 shown by Fig.~\ref{fig:ak8_eff}, showing
+a comparison of background and signal efficiency of the DeepAK8 tagger
+with, between others, the \(\tau_{20}\) tagger that is also used in this
+analysis.
 
 \begin{figure}
 \hypertarget{fig:ak8_eff}{%
@@ -1150,11 +1222,12 @@ quantify how strongly the output of the non-decorrelated tagger is
 correlated to the mass of a particle. Its output is fed back to the
 network as a penalty so it avoids using features of the particles
 correlated to their mass. The result is a largely mass decorrelated
-tagger of heavy resonances. As the mass variable is already in use for
-the soft-drop mass selection, this version of the tagger is to be
-preferred.
+tagger of heavy resonances, that doesn't introduce a bias in the jet
+mass shape. As can be seen in Fig.~\ref{fig:ak8_eff}, it performs not as
+good as the non-mass-decorrelated version, but still better than the
+other taggers it was compared to.
 
-The higher the discriminator value, called WvsQCD resp. ZvsQCD, of the
+The higher the discriminant 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
@@ -1164,7 +1237,7 @@ value determined by the optimization presented next.
 \hypertarget{sec:opt}{%
 \subsection{Optimization}\label{sec:opt}}
 
-To figure out the best value to cut on the discriminators introduced by
+To figure out the best value to cut on the discriminants introduced by
 the two taggers, a value to quantify how good a cut is has to be
 introduced. For that, the significance calculated by
 \(\frac{S}{\sqrt{B}}\) will be used. S stands for the amount of signal
@@ -1203,54 +1276,60 @@ the value previous research chose and the deep boosted cut is placed at
 higher significance but as it is very close to the edge where the
 significance drops very low and the higher the cut the less background
 will be left to calculate the cross section limits, especially at higher
-resonance masses, the slightly less strict cut is chosen. The
-significance for the \(\tau_{21}\) cut is 14, and for the deep boosted
-tagger 26.
+resonance masses, the slightly less strict cut is chosen.
 
 For both taggers also a low purity category is introduced for high TeV
 regions. Using the cuts optimized for 2 TeV, there are very few
 background events left for higher resonance masses, but to reliably
-calculate cross section limits, those are needed. As low purity category
-for the N-subjettiness tagger, a cut at \(0.35 < \tau_{21} < 0.75\) is
-used. For the deep boosted tagger the opposite cut from the high purity
-category is used: \(VvsQCD < 0.95\).
+calculate cross section limits, those are needed. Therefore in the final
+cross section calculation, the two categories are combined to have a
+high signal sensitivity for all masspoints between 1.6 TeV and 7 TeV
+that were simulated. As low purity category for the N-subjettiness
+tagger, a cut at \(0.35 < \tau_{21} < 0.75\) is used. For the deep
+boosted tagger the opposite cut from the high purity category is used:
+\(VvsQCD < 0.95\).
+
+\newpage
 
 \hypertarget{sec:extr}{%
 \section{Signal extraction}\label{sec:extr}}
 
 After the optimization, now the optimal selection for the N-subjettiness
 as well as the deep boosted tagger is found and applied to the simulated
-samples as well as the data collected by the CMS. The fit described in
-Sec.~\ref{sec:moa} is performed for all masspoints of the decay to qW
-and qZ and for both datasets used, the one from 2016 und the combined
-one of years 2016, 2017 and 2018.
+samples as well as the data collected by the CMS experiment. The fit
+described in Sec.~\ref{sec:moa} is performed for all masspoints of the
+decay to qW and qZ and for the partial dataset of
+\(\SI{35.92}{\per\femto\barn}\) as well as the complete dataset of
+\(\SI{137.19}{\per\femto\barn}\) separately.
 
 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
+limit criterion described in \autocite{ASYMPTOTIC_LIMIT}. Using the
 parameters and signal rate obtained by the method described in
-Sec.~\ref{sec:moa} as well as a shape analysis on the data recorded by
-the CMS, it determines an expected and an observed cross section limit
-by doing a signal + background versus background-only hypothesis test.
-It also calculates upper and lower limits of the expected cross section
-corresponding to a confidence level of 95 \%.
+Sec.~\ref{sec:moa} as well as a shape analysis of the data recorded by
+the CMS experiment, 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
+In the absence of the q* particle in the data, the observed limits 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. Since no significant
+deviation from the Standard Model is found while looking for the
+resonance, the crossing of the theory line with the observed limit 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.
 
-\hypertarget{uncertainties}{%
-\subsection{Uncertainties}\label{uncertainties}}
+\hypertarget{systematic-uncertainties}{%
+\subsection{Systematic Uncertainties}\label{systematic-uncertainties}}
 
-For calculating the cross section of the signal, four sources of
-uncertainties are considered.
+The variables used in this analysis are affected by systematic
+uncertainties. For calculating the cross section of the signal, four
+sources of such uncertainties are considered.
 
 First, the uncertainty of the Jet Energy Corrections. When measuring a
 particle's energy with the ECAL or HCAL part of the CMS, the electronic
@@ -1260,10 +1339,10 @@ calibration causes the energy measured to be shifted to higher or lower
 values causing also the position of the signal peak in the \(m_{jj}\)
 distribution to vary. The uncertainty is approximated to be 2 \%.
 
-Second, the tagger is not perfect and therefore some events, that don't
-originate from a V boson are wrongly chosen and on the other hand
-sometimes events that do originate from one are not. It influences the
-events chose for analysis and is therefore also considered as an
+Second, the tagger does not work perfectly and therefore some events,
+that don't originate from a V boson are wrongly chosen and on the other
+hand sometimes events that do originate from one are not. It influences
+the events chose for analysis and is therefore also considered as an
 uncertainty, which is approximated to be 6 \%.
 
 Third, the uncertainty of the parameters of the background fit is also
@@ -1271,43 +1350,48 @@ considered, as it might change the background shape a little and
 therefore influence how many signal and background events are
 reconstructed from the data.
 
-Fourth, the uncertainty on the Luminosity of the LHC of 2.5 \% is also
-taken into account for the final results.
+Fourth, the uncertainty on the luminosity influence the normalization of
+the processes. Its value is 2.5 \% {[}cite todo{]}. \newpage
 
 \hypertarget{results}{%
 \section{Results}\label{results}}
 
-This chapter will start by presenting the results for the data of year
-2016 using both taggers and comparing it to the previous research
-\autocite{PREV_RESEARCH}. It will then go on showing the results for the
-combined dataset, again using both taggers comparing their performances.
+This chapter will start by presenting the results for the partial
+dataset of year 2016 with an integrated luminosity of
+\(\SI{35.92}{\per\femto\barn}\) using both taggers and comparing it to
+the previous research \autocite{PREV_RESEARCH}. It will then go on
+showing the results for the combined dataset with an integrated
+luminosity of \(\SI{137.19}{\per\femto\barn}\), again using both taggers
+comparing their performances.
 
-\hypertarget{section}{%
-\subsection{2016}\label{section}}
+\hypertarget{partial-dataset}{%
+\subsection{Partial dataset}\label{partial-dataset}}
 
-Using the data collected by the CMS experiment on 2016, the cross
-section limits seen in Fig.~\ref{fig:res2016} were obtained.
+Using the \(\SI{35.92}{\per\femto\barn}\) of data collected by the CMS
+experiment during 2016, the cross section limits seen in
+Fig.~\ref{fig:res2016} were obtained.
 
 As described in Sec.~\ref{sec:extr}, the calculated cross section limits
 are used to then calculate a mass limit, meaning the lowest possible
 mass of the q* particle, by finding the crossing of the theory line with
-the observed cross section limit. In Fig.~\ref{fig:res2016} it can be
-seen, that the observed limit in the region where theory and observed
-limit cross is very high compared to when using the N-subjettiness
-tagger. Therefore the two lines cross earlier, which results in lower
-exclusion limits on the mass of the q* particle causing the deep boosted
-tagger to perform worse than the N-subjettiness tagger in regards of
-establishing those limits as can be seen in Table~\ref{tbl:res2016}. The
-table also shows the upper and lower limits on the mass found by
-calculating the crossing of the theory plus resp. minus its uncertainty.
-Due to the theory and the observed limits line being very flat in the
-high TeV region, even a small uncertainty of the theory can cause a high
-difference of the mass limit.
+the observed cross section limit. In Fig.~\ref{fig:res2016dw} it can be
+seen, that the observed limit using the deep boosted tagger 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 at
+lower resonance masses, which results in lower exclusion limits on the
+mass of the q* particle causing the deep boosted tagger to perform worse
+than the N-subjettiness tagger in regards of establishing those limits
+as can be seen in Table~\ref{tbl:res2016}. The table also shows the
+upper and lower limits on the mass found by calculating the crossing of
+the theory plus resp. minus its uncertainty. Due to the theory and the
+observed limits line being slowly falling in the high TeV region, even a
+small uncertainty of the theory can cause a high difference of the mass
+limit.
 
 \hypertarget{tbl:res2016}{}
 \begin{longtable}[]{@{}lllll@{}}
-\caption{\label{tbl:res2016}Mass limits found using the data collected
-in 2016}\tabularnewline
+\caption{\label{tbl:res2016}Mass limits found using the partial dataset
+of \(\SI{35.92}{\per\femto\barn}\)}\tabularnewline
 \toprule
 Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
 {[}TeV{]}\tabularnewline
@@ -1321,45 +1405,52 @@ Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
 qW & \(\tau_{21}\) & 5.39 & 6.01 & 4.99\tabularnewline
 qW & deep boosted & 4.96 & 5.19 & 4.84\tabularnewline
 qZ & \(\tau_{21}\) & 4.86 & 4.96 & 4.70\tabularnewline
-qZ & deep boosted & 4.49 & 4.61 & 4.40\tabularnewline
+qZ & deep boosted & 4.62 & 4.71 & 4.49\tabularnewline
 \bottomrule
 \end{longtable}
 
-\begin{figure}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_2016tau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_2016db_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_2016tau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf}
-  \end{minipage}
-\caption{Results of the cross section limits for 2016 using the $\tau_{21}$ tagger (left) and the deep boosted tagger 
-(right).}
+\begin{figure}%
+  \centering
+  \subfloat[Decay to qW, using N-subjettiness tagger]{%
+  \label{fig:res2016tw}%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_2016tau_13TeV.pdf}}
+  \subfloat[Decay to qW, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_2016db_13TeV.pdf}%
+  \label{fig:res2016dw}}\\
+  \subfloat[Decay to qZ, using N-subjettiness tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_2016tau_13TeV.pdf}%
+  \label{fig:res2016tz}}%
+  \subfloat[Decay to qZ, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_2016db_13TeV.pdf}%
+  \label{fig:res2016dz}}%
+\caption{Results of the cross section limits for the partial dataset of 2016 using the $\tau_{21}$ tagger and the deep 
+boosted tagger.}
 \label{fig:res2016}
 \end{figure}
 
-\hypertarget{previous-research}{%
-\subsubsection{Previous research}\label{previous-research}}
+\hypertarget{comparison-with-existing-results}{%
+\subsubsection{Comparison with existing
+results}\label{comparison-with-existing-results}}
 
-The limit established by using the N-subjettiness tagger on the 2016
-data is already slightly higher than the one from previous research,
-which was found to be 5 TeV for the decay to qW and 4.7 TeV for the
-decay to qZ. This is mainly due to the fact, that in our data, the
-observed limit at the intersection point happens to be in the lower
+The result will now be compared to an existing result using the same
+dataset. This research, however, uses a newer detector calibration as
+well as an improved reconstruction so slight variations in the results
+are to be expected.
+
+The limit established by using the N-subjettiness tagger with the
+partial dataset is \(\SI{0.39}{\tera\eV}\) (decay to qW) resp.
+\(\SI{0.16}{\tera\eV}\) (decay to qZ) higher than the one from previous
+research, which was found to be 5 TeV for the decay to qW and 4.7 TeV
+for the decay to qZ. This is mainly due to the fact, that in our data,
+the observed limit at the intersection point happens to be in the lower
 region of the expected limit interval and therefore causing a very late
 crossing with the theory line when using the N-subjettiness tagger (as
 can be seen in Fig.~\ref{fig:res2016}). Comparing the expected limits,
 there is a difference between 2 \% and 30 \%, between the values
 calculated by this thesis compared to the previous research. It is not,
 however, that one of the two results was constantly lower or higher but
-rather fluctuating. This is likely caused by a newer detector
-calibration as well as updated reconstruction algorithms used for this
-analysis. Therefore it can be said, that the results are in good
+rather fluctuating. As already noted, a slight variations in the results
+was expected, 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}.
 
@@ -1378,17 +1469,19 @@ Taken from \cite{PREV_RESEARCH}.}
 \hypertarget{combined-dataset}{%
 \subsection{Combined dataset}\label{combined-dataset}}
 
-Using the combined data, the cross section limits seen in
-Fig.~\ref{fig:resCombined} were obtained. The cross section limits are,
-compared to only using the 2016 dataset, almost cut in half. This shows
-the big improvement achieved by using more than three times the amount
-of data.
+Using the full available dataset of \(\SI{137.19}{\per\femto\barn}\),
+the cross section limits seen in Fig.~\ref{fig:resCombined} were
+obtained. The cross section limits are, compared to only using the 2016
+dataset, reduced to about 50 \%. This shows the big improvement achieved
+by using more than three times the amount of data.
 
-The results for the mass limits of the combined years are as follows:
+The results for the mass limits of the combined years are presented in
+the following table.
 
+\hypertarget{tbl:resCombined}{}
 \begin{longtable}[]{@{}lllll@{}}
-\caption{Mass limits found using the data collected in 2016 -
-2018}\tabularnewline
+\caption{\label{tbl:resCombined}Mass limits found using
+\(\SI{137.19}{\per\femto\barn}\) of data}\tabularnewline
 \toprule
 Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
 {[}TeV{]}\tabularnewline
@@ -1402,7 +1495,7 @@ Decay & Tagger & Limit {[}TeV{]} & Upper Limit {[}TeV{]} & Lower Limit
 qW & \(\tau_{21}\) & 6.00 & 6.26 & 5.74\tabularnewline
 qW & deep boosted & 6.11 & 6.31 & 5.39\tabularnewline
 qZ & \(\tau_{21}\) & 5.49 & 5.76 & 5.29\tabularnewline
-qZ & deep boosted & 4.92 & 5.02 & 4.80\tabularnewline
+qZ & deep boosted & 4.95 & 5.13 & 4.85\tabularnewline
 \bottomrule
 \end{longtable}
 
@@ -1412,49 +1505,58 @@ result is 1 TeV higher for the decay to qW and almost 0.8 TeV higher for
 the decay to qZ than what was concluded by the previous research
 \autocite{PREV_RESEARCH}.
 
-\begin{figure}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_Combinedtau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqW_Combineddb_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_Combinedtau_13TeV.pdf}
-  \end{minipage}
-  \begin{minipage}{0.5\textwidth}
-  \includegraphics{./figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf}
-  \end{minipage}
-\caption{Results of the cross section limits for the three combined years using the $\tau_{21}$ tagger (left) and the 
-deep boosted tagger (right).}
+\begin{figure}%
+  \centering
+  \subfloat[Decay to qW, using N-subjettiness tagger]{%
+  \label{fig:resCombinedtw}%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_Combinedtau_13TeV.pdf}}
+  \subfloat[Decay to qW, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqW_Combineddb_13TeV.pdf}%
+  \label{fig:resCombineddw}}\\
+  \subfloat[Decay to qZ, using N-subjettiness tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_Combinedtau_13TeV.pdf}%
+  \label{fig:resCombinedtz}}%
+  \subfloat[Decay to qZ, using deep boosted tagger]{%
+  \includegraphics[width=0.5\textwidth]{./figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV.pdf}%
+  \label{fig:resCombineddz}}%
+\caption{Results of the cross section limits for the combined dataset using the $\tau_{21}$ tagger and the deep boosted 
+tagger.}
 \label{fig:resCombined}
 \end{figure}
 
 \hypertarget{comparison-of-taggers}{%
 \subsection{Comparison of taggers}\label{comparison-of-taggers}}
 
-The previously shown results already show, that the deep boosted tagger
-was not able to significantly improve the results compared to the
-N-subjettiness tagger. For further comparison, in
+The results presented in Table~\ref{tbl:res2016} show, that the deep
+boosted tagger was not able to significantly improve the results
+compared to the N-subjettiness tagger. For further comparison, in
 Fig.~\ref{fig:limit_comp} the expected limits of the different taggers
 for the q* \(\rightarrow\) qW and the q* \(\rightarrow\) qZ decay are
 shown. It can be seen, that the deep boosted is at best as good as the
 N-subjettiness tagger. This was not the expected result, as the deep
 neural network was already found to provide a higher significance in the
 optimisation done in Sec.~\ref{sec:opt}. The higher significance should
-also result in lower cross section limits. Apparently, doing the
-optimization only on data of the year 2018, was not a good choice. To
-make sure, there is no mistake in the setup, also the expected cross
-section limits using only the high purity category of the two taggers
-with 2018 data are compared in Fig.~\ref{fig:comp_2018}. There, the
-cross section limits calculated using the deep boosted tagger are a bit
-lower than with the N-subjettiness tagger, showing, that the method used
-for optimisation was working but should have been applied to the
-combined dataset.
+also result in lower cross section limits. To make sure, there is no
+mistake in the setup, also the expected cross section limits using only
+the high purity category of the two taggers with 2018 data are compared
+in Fig.~\ref{fig:comp_2018}. There, the cross section limits calculated
+using the deep boosted tagger are a bit lower than with the
+N-subjettiness tagger, showing, that the method used for optimisation is
+working but the assumption of it also applying to the combined dataset
+did not hold.
 
-Recently, some issues with the training of the deep boosted tagger used
-in this analysis were also found, which might explain, why it didn't
-perform better in general.
+This can be explained by some training issues identified lately. The
+training of the DeepAK8 tagger was done for the data of year 2016. It
+therefore performs differently for the data of the other years. This
+caused the DeepAK8 tagger to perform significantly worse than it could
+have for several reasons. First, the optimization done for the data of
+year 2018 could therefore not be applied to the other datasets. Second,
+even for the data of 2016, a newer version of the background simulation
+was used, that, in combination with the samples used for the signal,
+turned out to be the worst case scenario for the used training.
+Recently, the training was improved to better perform across all
+datasets, but those changes could not be incorporated into this thesis
+due to it not being possible to do this in a reasonable timeframe.
 
 \begin{figure}
 \begin{minipage}{0.5\textwidth}
@@ -1471,7 +1573,7 @@ decay to qZ}
 \begin{figure}
 \hypertarget{fig:comp_2018}{%
 \centering
-\includegraphics[width=0.6\textwidth,height=\textheight]{./figures/limit_comp_2018.pdf}
+\includegraphics[width=0.7\textwidth,height=\textheight]{./figures/limit_comp_2018.pdf}
 \caption{Comparision of deep boosted and N-subjettiness tagger in the
 high purity category using the data from year
 2018.}\label{fig:comp_2018}
@@ -1484,57 +1586,48 @@ high purity category using the data from year
 \hypertarget{summary}{%
 \section{Summary}\label{summary}}
 
-In this thesis, a limit on the mass of the q* particle has been
-successfully established. This was done searching for its decay to qW
-and qW with the vector boson then decaying hadronically. By combining
-the data from the years 2016, 2017 and 2018, collected by the CMS
-experiment, the previously set limit could be significantly improved.
+In this thesis, a search for the q* particle decaying to q + W and q + Z
+was presented. Data of proton - proton collisions at the LHC of an
+integrated luminosity of \(\SI{137.19}{\per\femto\barn}\) collected by
+the CMS experiment at a centre-of-mass energy of
+\(\sqrt{s} = \SI{13}{\tera\eV}\) has been searched. Also a partial
+dataset of \(\SI{35.92}{\per\femto\barn}\) was analysed, to be able to
+compare the results to previous research. Monte Carlo simulations were
+used to estimate the QCD background and signal.
 
-For the analysis, the following selection was applied to the data:
+A selection was introduced to reduce background events and enhance
+signal sensitivity. This selection required at least two jets, a
+\(\Delta\eta \ge 1.3\) between the two highest \(p_t\) jets, an
+invariant mass of the two highest \(p_t\) jets greater than
+\(\SI{1050}{\giga\eV}\) and a soft-drop mass of at least one jet between
+\(\SI{35}{\giga\eV}\) and \(\SI{105}{\giga\eV}\).
 
-\begin{itemize}
-\tightlist
-\item
-  \#jets \(\ge\) 2
-\item
-  \(\Delta\eta < 1.4\)
-\item
-  \(m_{jj} \ge \SI{1050}{\giga\eV}\)
-\item
-  \(\SI{35}{\giga\eV} < m_{SDM} < \SI{105}{\giga\eV}\)
-\end{itemize}
+Two taggers, the DeepAK8 and the N-subjettiness tagger, have been used
+to identify jets originating from the decay of a vector boson. For both
+of them, two categories were introduced. A high purity category, aiming
+for maximal signal sensitivity in the low TeV region of the invariant
+mass spectrum and a low purity category, aiming for better statistics in
+the high TeV region. For the DeepAK8 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.
 
-For the deep boosted tagger, a high purity category of \(VvsQCD > 0.95\)
-and a low purity category of \(VvsQCD \le 0.95\) was used. For the
-N-subjettiness tagger the high purity category was \(\tau_{21} < 0.35\)
-and the low purity category \(0.35 < \tau_{21} < 0.75\). These values
-were obtained by optimizing for the highest possible significance of the
-signal.
+A combined fit to the dijet invariant mass distribution of background
+plus 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. Because no significant deviation from the
+Standard Model was observed, new exclusion limits for the mass of the q*
+particle were 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.
-
-The optimization process used to find the optimal values for the
-discriminant provided by the taggers, was found to not be optimal. It
-was only done using 2018 data, with which the deep boosted tagger showed
-a higher significance than the N-subjettiness tagger. Apparently, the
-assumption, that the same optimization would apply to the data of the
-other years as well, did not hold. Using the combined dataset, the deep
-boosted tagger showed no better cross section limits than the
-N-subjettiness tagger, which are directly related to the significance
-used for the optimization. Therefore, with a better optimization and the
-fixed training issues of the deep boosted tagger, it is very likely,
-that the result presented could be further improved.
+The DeepAK8 tagger performed worse than was expected. This can be
+explained with some training issues identified lately. Therefore, with
+an updated training, it is expected that the presented results can be
+further improved.
 
 \newpage
 
@@ -1542,9 +1635,11 @@ that the result presented could be further improved.
 
 \printbibliography
 
-\newpage
-\hypertarget{appendix}{%
-\section*{Appendix}\label{appendix}}
+\appendix
+
+\hypertarget{expected-and-observed-cross-section-limits}{%
+\section{Expected and observed cross section
+limits}\label{expected-and-observed-cross-section-limits}}
 
 \begin{longtable}[]{@{}lllll@{}}
 \caption{Cross Section limits using 2016 data and the N-subjettiness
diff --git a/thesis.toc b/thesis.toc
index b24f7ea..f30d932 100644
--- a/thesis.toc
+++ b/thesis.toc
@@ -10,10 +10,10 @@
 \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 {3.2.2}The tracking system}{8}{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 {3.2.5}The solenoid}{9}{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}% 
@@ -22,17 +22,18 @@
 \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 {subsection}{\numberline {5.2}Data - Monte Carlo Comparison}{15}{subsection.5.2}% 
+\contentsline {subsubsection}{\numberline {5.2.1}Sideband}{15}{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}% 
 \contentsline {subsection}{\numberline {6.3}Optimization}{22}{subsection.6.3}% 
-\contentsline {section}{\numberline {7}Signal extraction}{23}{section.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}{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}% 
+\contentsline {section}{\numberline {7}Signal extraction}{24}{section.7}% 
+\contentsline {subsection}{\numberline {7.1}Systematic Uncertainties}{24}{subsection.7.1}% 
+\contentsline {section}{\numberline {8}Results}{26}{section.8}% 
+\contentsline {subsection}{\numberline {8.1}Partial dataset}{26}{subsection.8.1}% 
+\contentsline {subsubsection}{\numberline {8.1.1}Comparison with existing results}{26}{subsubsection.8.1.1}% 
+\contentsline {subsection}{\numberline {8.2}Combined dataset}{28}{subsection.8.2}% 
+\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{30}{subsection.8.3}% 
+\contentsline {section}{\numberline {9}Summary}{32}{section.9}% 
+\contentsline {section}{\numberline {A}Expected and observed cross section limits}{34}{appendix.A}%