From cbb6c6dcc1ab2656694616b59702e3608d2d9564 Mon Sep 17 00:00:00 2001 From: david Date: Tue, 17 Sep 2019 11:21:41 +0200 Subject: [PATCH] Initial BSc commit --- figures/antikt-comparision.png | Bin 0 -> 432795 bytes figures/cms_coordinates.png | Bin 0 -> 184953 bytes figures/sm_wikipedia.svg | 447 +++++++++++++++++++++++++++++++++ structure.md | 144 +++++++++++ structure.pdf | Bin 0 -> 89878 bytes thesis.md | 416 ++++++++++++++++++++++++++++++ thesis.pdf | Bin 0 -> 685430 bytes thesis.tex | 357 ++++++++++++++++++++++++++ 8 files changed, 1364 insertions(+) create mode 100644 figures/antikt-comparision.png create mode 100644 figures/cms_coordinates.png create mode 100644 figures/sm_wikipedia.svg create mode 100644 structure.md create mode 100644 structure.pdf create mode 100644 thesis.md create mode 100644 thesis.pdf create mode 100644 thesis.tex diff --git a/figures/antikt-comparision.png b/figures/antikt-comparision.png new file mode 100644 index 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+ + u + + ≃2.2 MeV/c² + + ½ + up + + + + down + + + d + + ≃4.7 MeV/c² + −⅓ + ½ + down + + + + charm + + + c + + ≃1.28 GeV/c² + + ½ + charm + + + + strange + + + s + + ≃96 MeV/c² + −⅓ + ½ + strange + + + + top + + + t + + ≃173.1 GeV/c² + + ½ + top + + + + bottom + + + b + + ≃4.18 GeV/c² + −⅓ + ½ + bottom + + + + + Leptons + LEPTONS + + + electron + + + e + + ≃0.511 MeV/c² + −1 + ½ + electron + + + + electron neutrino + + + νe + + <2.2 eV/c² + 0 + ½ + electronneutrino + + + + muon + + + μ + + ≃105.66 MeV/c² + −1 + ½ + muon + + + + muon neutrino + + + νμ + + <0.17 MeV/c² + 0 + ½ + muonneutrino + + + + tau + + + τ + + ≃1.7768 GeV/c² + −1 + ½ + tau + + + + tau neutrino + + + ντ + + <18.2 MeV/c² + 0 + ½ + tauneutrino + + + + + Gauge Bosons + GAUGE BOSONS + VECTOR BOSONS + + + gluon + + + g + + 0 + 0 + 1 + gluon + + + + photon + + + γ + + 0 + 0 + 1 + photon + + + + Z boson + + + Z + + ≃91.19 GeV/c² + 0 + 1 + Z boson + + + + W boson + + + W + + ≃80.39 GeV/c² + ±1 + 1 + W boson + + + + + Scalar Bosons + SCALAR BOSONS + + + Higgs + + + H + + ≃124.97 GeV/c² + 0 + 0 + higgs + + + + + Tensor Bosons + TENSOR BOSONS + HYPOTHETICAL + + + Graviton + + + G + + 0 + 0 + 2 + graviton + + + + \ No newline at end of file diff --git a/structure.md b/structure.md new file mode 100644 index 0000000..5751c05 --- /dev/null +++ b/structure.md @@ -0,0 +1,144 @@ +# Abstract + +# Theoretical background + +## Standard model + + - issues + +### q* + + - common conclusion from composite models + +## LHC + +. + +. + +. + +### CMS + +. + +. + +. + +#### Jets + +. + +. + +. + +# Search for excited quarks + +. + +. + +. + +## Method of analysis + + - dominant background: QCD (gg-gg e.g. - two jets) + - division in QCD bg and signal + +### Signal/Background modelling + + - expected: bg smooth falling + +## Event selection + +- division in pre/post selection +- preselection for trigger efficiency and general physical cuts +- post selection to apply different taggers + +### Preselection + +. + +. + +. + +### Tagger + + - Cut on softdropmass + +#### Tau21 + +. + +. + +. + +#### DeepBoosted + +. + +. + +. + +### Optimization + +. + +. + +. + +## Data MC Comparision + +. + +### Sideband + +. + +## Uncertainties (?) + +. + +. + +. + +# Results + +. + +. + +. + +## 2016 + +. + +. + +. + +### previous research + +. + +. + +. + +## 2016 + 2017 + 2018 + +. + +. + +. + +# Summary diff --git a/structure.pdf b/structure.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9cb07f00b15dd572b3dbc15ab5157021009f01c6 GIT binary patch literal 89878 zcmb5VV~j3P+of5y?Rv_#ZCj^o`;@Iywr$(CZQHi3dB5qNPAA_aJ+ptU{rAq=*UHMB zO{OR+PRB&g217QtG`t4G24Do(8(G2d^1?94n%bE=TL9QNIRXFUz%Yng+Blm!0vNVVs;DO$}{f+&7xlCLJ>w(Y8NnG$Ljs=Rt|)bq{;U7iqc8Qk?^U zjd22Tf;OLSX}rPf@f8w1Gm?Y62~YWFnBXh?A#%;0&bnmHF$uZgHAF?x9s#=GvQPy^ z_(RIb^d@l_{qROaW>GRvc9x&?lb?6mp2r{tHDS`MYk%z%Yh)IaeX`9nkzmQ@nI}d1 z=X96TZMETQ;u7OUCv<0s5&#*{gyB)|7(Oc)n(BgiBW;QK1zT`JCB!~c2&p&Arr1|vBsiG8)127h3Vz2gksOokZ 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ze`>)2S|6eC4<9%`fQ1ExMMQ+5TwI(W5hz3y!YRxR;Sd$%fbj$VcbCU`q!HGpj%EN3 zPRPGV=>G=`r5aUHMHM9WU!FsK@fzzjpyN^7+E>^XuN6JsmbA+NbvG#d)4ki3teOdA zY|LqB@Sd)^&$qj}=iMisLQgY2qlG#iuo=l>~%r|bCq}Q1=82b2u`edT|#PRwc z)dx>&UnKei69dT;1Gp1|(AE7Bu(FG?_IC>I8h%dM=XK9g;CrqwYrkGcu_0YT7Rlp_de)@WTF(<)0 zPZHIVZZ5rm=;iG;Enn38_B`Zz~0ft{&DAUJ<5`U Mu^AXdqg processes), this analysis will focus on the processes q\*->qW and q\*->qZ. +In this case, due to jet substructure studies, it is possible to establish a discriminator between QCD background and +jets originating in a W/Z decay. They still make up roughly 20 % of the signal events to study and therefore seem like a +good choice. + +To find signal events in the data, this thesis looks at the dijet invariant mass distribution. It is assumed to only consist +of QCD background and signal events, other backgrounds are neglected. If the q\* particle exists, this distribution +should show a peak at its invariant mass. This peak will be looked for with statistical methods explained later on. + +## Signal/Background modelling + +To be able to first make sure the setup is working as intended, simulated samples are of background and signal are used. +For that, Monte Carlo simulations are used. The different particle interactions that take in a proton - proton collision +are simulated using the probabilities provided by the Standard Model. Later on, also detector effects 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 and assuming a cross section of $\SI{1}{\per\pico\barn}$. + +The invariant mass distribution of the QCD background sample is fitted using the following function with three +parameters p0, p1, p2: +\begin{equation} +\frac{dN}{dm_{jj}} = \frac{p_0 \cdot ( 1 - m_{jj} / \sqrt{s} )^{p_2}}{ (m_{jj} / \sqrt{s})^{p_1}} +\end{equation} +Whereas $m_{jj}$ is the invariant mass of the dijet and $p_0$ is a normalisation parameter. Two and four parameter +functions have also been studied but found to not fit the background as good as this one. + +The signal is fitted using a double sided crystal ball function. A gaussian and a poisson have also been studied but +found to not fit the signal sample very well. + +\newpage + +# Preselection and data quality + +To separate the background from the signal, several cuts have to be introduced. The selection of events is divided in +two parts. The first one (the preselection) adds some cuts for trigger efficiency as well as general physics motivated +cuts. It is not expected to already provide a good separation of background and signal. In the second part, different +taggers will be used as a discriminator between QCD background and signal events. After the preselection, it is made +sure, that the simulated samples represent the real data well. + +## Preselection + +From a decaying q\* particle, we expect two jets in the endstate. Therefore a cut of number of jets $\ge$ 2 is added. +More jets are also possible because of jets originating in QCD effects such as gluon - gluon interactions. The second +cut is on $\Delta\eta$. The q\* particle is expected to be very heavy and therefore almost stationary. Its decay +products should therefore be close to back to back, which means a low $\Delta\eta$. To maintain comparability, the +same cut as in previous research of $\Delta\eta \le 1.3$ will be used. The last cut in the preselection is on the dijet +invariant mass: $m_{jj} \ge \SI{1050}{\giga\eV}$. It is important for a high trigger efficiency. To summarise, the +following cuts are applied during preselection: + +1. Number of jets $\ge$ 2 +1. $\Delta\eta \le 1.3$ +1. $m_{jj} \ge \SI{1050}{\giga\eV}$ + +## Data - Monte Carlo Comparision + +To ensure high data quality, the MC QCD background sample is now being compared to the actual data of the corresponding +year collected by the CMS detector. This is done for the years 2016, 2017 and 2018. The distributions are normalised on +the invariant mass distribution. For most distributions, no significant difference is seen between data and simulation. +In 2018, way more events have a high number of primary vertices in the real data than in the simulated sample. This is +being investigated by a CMS workgroup already but should not affect this analysis. + +### Sideband + +The sideband is introduced to make sure there are no unwanted side effects of the used cuts. It adds a cut, that makes +sure, no data in the sideband is used for the actual analysis. As sideband, the region where the mass of one of the two +jets with the highest transverse momentum ($p_t$) is more than 105 GeV. Because the decay of a q\* to a vector boson is +being investigated, one of the two jets should have a mass between 105 GeV and 35 GeV. Therefore events with jets that +are heavier than 105 GeV will not be used for this analysis which makes them a good sideband to use. + +# Event substructure selection + +This selection is responsible for distinguishing between QCD and signal events by using a tagger to identify jets coming +from a vector boson. Two different taggers will be used to later compare the results. The decay analysed includes either +a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a cut on the +softdropmass of a jet. The softdropmass 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. The softdropmass +of at least one of the two leading jets is expected to be within $\SI{35}{\giga\eV}$ and $\SI{105}{\giga\eV}$. + +## N-Subjettiness + +The N-subjettiness $\tau_n$ is defined as + +\begin{equation} \tau_N = \frac{1}{d_0} \sum_k p_{T,k} \cdot \text{min}\{ \Delta R_{1,k}, \Delta R_{2,k}, …, \Delta +R_{N,k} \} \end{equation} + +with k going over the constituent particles in a given jet, $p_{T,k}$ being their transverse momenta and $\Delta R_{J,k} += \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}$ being the distance of a candidate subjet J and a constituent particle k in the +rapidity-azimuth plane. It quantifies to what degree a jet can be regarded as a jet composed of $N$ subjets. +It has been shown, that $\tau_{21} = \tau_2/\tau_1$ is a good discriminator between QCD events +and events originating from the decay of a boosted vector boson. + +The $\tau_{21}$ cut is applied to the one of the two highest $p_t$ jets passing the softdropmasswindow. If both of them +pass, it is applied to the one with higher $p_t$. + +## DeepBoosted + +The deep boosted tagger uses a trained neural network to identify decays originitating in a vector boson. It is supposed +to give better efficiencies than the older N-Subjettiness method. + +## Optimization + +To figure out the best value to cut on the discriminators introduced by the two taggers, a value to quantify how good a +cut is has to be introduced. For that, the significance calculated by $\frac{S}{\sqrt{B}}$ will be used. S stands for +the amount of signal events and B for the amount of background events in a given interval. This value assumes a gaussian +error on the background so it will be calculated for the 2 TeV masspoint where enough background events exist to justify +this assumption. The value therefore represents how good the signal can be distinguished from the background in units of +the standard deviation of the background. As interval, a 10 % margin around the masspoint is chosen. + +As a result, the $\tau_{21}$ cut is placed at $\le 0.35$ and the VvsQCD cut is placed at $\ge 0.83$. + +\newpage + +# Signal extraction + +## Uncertainties + +\newpage + +# Results + + +## 2016 + +### previous research + + +## 2016 + 2017 + 2018 + + +# Summary diff --git a/thesis.pdf b/thesis.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ad4e41930b8a8f286b5cd3936cd2aeea8f1b12fd GIT binary patch literal 685430 zcmd3PbzBu)*S2(ngmfIFn{((8q`O<`2I)@eF6k}_k&u)Q=`Km78$?>VzJoVB_wzhA z@AtibeLwxAoaYtpP4eZ@u65f`rvU-W8ZH#m4~ z?rC;726wR72bg-=wvKb+N~hGD1|0!&fV|f^NbD_#Ihlr-7<@h^e7%wxhMEC6)?`W{ z?7%e+iUB3TXR`oR_%9!R$oIU&ipN3K+6nj$U(~s_%{(=kgF&qDErPh!b%`N?_*r9< z=tcPv<~FjLz-aL3=U&RZd|NrOo8%Jgvz;nVKQQ1eOf*yKJaFsO zcHe*^r@rhD6-Bii(CzVMu@a*o7Vj56sf2h_`5C161mUROBsM&_mn=8};7Vw7p~>y3j%0o#_NuYe4nCRh3VZTG$c`$dTWNy?akj3he3?|h#p)-U+IVMA6^NY^!=ipZFCS2 zaBk>UBEAUmJ;D@4?Dc?BO`jNyz;L5^n=N4FgH#>DTJ^*fZt2&;&`QIzgpzqjyn+x6 zCX1`5CbB;@;Fa{sGG~w6V1sCwcf{3IgCaWAcOBz7BG#-V^-61)sXw%KV4uF@&8Z$P z;Hn_7o%I%zIA&N>l*a1v*xN4m$SgMfC}bfUn`L}buK5OoDMf*)2%V_*!>|e>}%AL>@|c$ zf|jEp361jgx0tMlzGUwKCvw;2{`T+kn_9YEk5s*IZ-g}Fv{lyR#moK+3X09XN z?WE+#=NHGyt}daK1}%nmK;A=PPH!%hvwMvVy9N<+8owYu2%58SWY`xnlqa}mC@n~<`C5( zg!k|KM6Sw8m!stz-?R~>c~L2JBf|nZ57BDvjDUs!vs(gl<>fX0dS~zX0K_2j(QeXy zagOL$T|CAasx&B_k8l*TA*EAF8jCny;mxwl^Y_@qN ztimKHGdQa@Uh+6D>VeymrgK-h~ER41x^MN2O*u0HQwDc z7g5#+F9Y6s-)v;TS+Hzwe0|3up!EJ2<&q7hgsoE>vZ|jZmok2NJ1D_7^jK4W$z7=i z`;#>NyQ%`>eVT zJEUJYo++^miIEbafM3TZn*On6tNF?MZHXt)>nLTqN5LYXES-#;?ecA>pOo7<3pev- zrIOEQ2Rg*ee996f5v}+nyZ5BzNE#8SRsMNN;K|1SZe9Wcva+6<;mwpp7kYV5XR69(87HQy-u2;4xd#st>EL!4mS9KbcLa#3 zGZ)hE(5R0sW2dh@EIa^wr&BmaUlEy)rSM(DhVzR1ipKiH@n*MAPnn__kiz2LFpJiA zB&hqr8KS7ZA$!wTO3YdzdezYsA>-awx9iAoiLX^B<&KvY-ST{|`X=6pG6#yaMX`g0 zpj+&aOW5@=!>lX9xP$HKW(0ZdHK>m@^qM!8j+aSoHs`Cqdma((hYB7k?xyei6TQ_d zlgp;880Q!79fMiM8OEgXWe^?wEPKxsUMU0oCEJu0jE%?Z2&to>XXzt0SwOPZ9QpOM zPi#csbyLlZTSp3=l$#VnML*Y5lH1697Aba3FuiO1BjD>T(n3j z{+6}mspU8g(H=dHOj)gF(|k*(7$@44kV86a`8?x2+*INNF>(NYkjjbJ~jVl{kfQ1upKtbE7Y|^*9Q~qt`we_pz z+5PZ1fg{iiesUH%NCnu5W*bgI0h>DlT?AW18Qp7M>5Iq!$_qH~!OkY;V)U;hLQ{Z@9fh+Q3h$a6%Lm=k0)Pn!-z z$8;$CdGqXeF~ZbY{h9iB4v~BWp6hzWM~OaRK8nJEc?s^~LPR^a&wU4RSzC<=BCNCZ ztev>h09xKkjq1_f=MMe?1>PrXlXjnI*!kAzq`w8gy7`unWt=x`n_NShEA{}!R|V>_ z;vial?d{_#8mLt;u?1-x!jw@J7AGA>A21F@CycCC&i zOe;@z`$pr2)05%Z#O?_tx#bsHD088OLEi7oY(Huti;0in341%CBP+Tt#_br{s<_lF zUnrHQy*j3#bNT9HwHI=z{R+3{HHv&ehMR$`OV611(LBa`bf?9(Laz6^Bkn#!MW%#B zL}R0bF-oWtPKXn%3y$M5iL;~(!_G{6GY9s$BGabj9tSAfDeNcC*i*C&(r!%9t-x{w zWBDXy^uT8{7Q@t5ymNE{TrHl)L5gQ=<=zsIJ`nqkQKwtbF17i>gwszlJo+3vk}1ra zXFTCWN|FJnx;FkUs7Ct5BGPQN8L^XuA*k&BGVtg>axfHh;ImTlHq$i~$yGBxqkO_T z{kXo*tEHqacVN+>sWBL`gONb;^qKT-sg_f=DSJ&YPptYk8s^t{n7%i{4Hsr+eCvkv zWZz>wmn>uPcBGtnhZzCBl|^r~*m!v)Ivve|Vx#E$dy|dUO2_;g23o3q#%jh{R=Nr4LttQfc_}Ne*W2>|KF)}e;C9uOe@Viq?(3W61%v0|h_F6; 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\defaultfontfeatures{Scale=MatchLowercase} + \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1} + \setmainfont[]{Times New Roman} +\fi +% Use upquote if available, for straight quotes in verbatim environments +\IfFileExists{upquote.sty}{\usepackage{upquote}}{} +\IfFileExists{microtype.sty}{% use microtype if available + \usepackage[]{microtype} + \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts +}{} +\makeatletter +\@ifundefined{KOMAClassName}{% if non-KOMA class + \IfFileExists{parskip.sty}{% + \usepackage{parskip} + }{% else + \setlength{\parindent}{0pt} + \setlength{\parskip}{6pt plus 2pt minus 1pt}} +}{% if KOMA class + \KOMAoptions{parskip=half}} +\makeatother +\usepackage{xcolor} +\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, + pdfcreator={LaTeX via pandoc}} +\urlstyle{same} % disable monospaced font for URLs +\usepackage[top=2.5cm,left=3cm,right=2.5cm,bottom=2.5cm]{geometry} +\usepackage{listings} +\newcommand{\passthrough}[1]{#1} +\lstset{defaultdialect=[5.3]Lua} +\lstset{defaultdialect=[x86masm]Assembler} +\setlength{\emergencystretch}{3em} % prevent overfull lines +\providecommand{\tightlist}{% + \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} +\setcounter{secnumdepth}{5} +\usepackage[onehalfspacing]{setspace} +\usepackage{siunitx} +\usepackage{tikz-feynman} +\tikzfeynmanset{compat=1.0.0} +\pagenumbering{gobble} +\ifxetex + % Load polyglossia as late as possible: uses bidi with RTL langages (e.g. Hebrew, Arabic) + \usepackage{polyglossia} + \setmainlanguage[variant=british]{english} +\else + \usepackage[shorthands=off,main=british]{babel} +\fi +\usepackage[]{biblatex} + +\title{Search for excited quark states decaying to qW/qZ} +\author{David Leppla-Weber} +\date{} + +\begin{document} +\maketitle +\begin{abstract} +This is my very long abstract. + +Blubb +\end{abstract} + +{ +\setcounter{tocdepth}{3} +\tableofcontents +} +\newpage +\pagenumbering{arabic} + +\hypertarget{introduction}{% +\section{Introduction}\label{introduction}} + +\newpage + +\hypertarget{theoretical-background}{% +\section{Theoretical background}\label{theoretical-background}} + +This chapter presents a short summary of the theoretical background +relevant to this thesis. It first gives introduction to the standard +model itself and some of the issues it raises. It then goes on to +explain the processes of quantum chromodynamics and the theory of q*, +which will be the main topic of this thesis. + +\hypertarget{standard-model}{% +\subsection{Standard model}\label{standard-model}} + +The Standard Model of physics proofed very successful in describing +three of the four fundamental interactions currently known: the +electromagnetic, weak and strong interaction. The fourth, gravity, could +not yet be successfully included in this theory. + +The Standard Model divides all particles into spin-\(\frac{n}{2}\) +fermions and spin-n bosons, where n could be any integer but so far is +only known to be one for fermions and either one (gauge bosons) or zero +(scalar bosons) for bosons. The fermions are further divided into quarks +and leptons, both of which exist in three generations. + +\begin{itemize} +\tightlist +\item + issues +\end{itemize} + +\hypertarget{quantum-chromodynamics}{% +\subsection{Quantum Chromodynamics}\label{quantum-chromodynamics}} + +The quantum chromodynamics (QCD) describe the strong interaction of +particles. It applies to all particles carrying colour (e.g.~quarks). +The force is mediated by the gluons. Those bosons carry colour as well +and can therefore interact with themselves. As a result of this, +processes, where a gluon decays into two gluons are possible. +Furthermore the strong force, binding to colour carrying particles, +increases with their distance r making it impossible to separate two +bound particles and causing the effect of hadronisation, which describes +the process of hadrons forming out of individual, colour carrying, +particles. + +\hypertarget{excited-quark-states}{% +\subsection{Excited quark states}\label{excited-quark-states}} + +One category of theories that try to solve some of the shortcomings of +the standard model are the composite quark models. Those state, that +quarks consist of some particles unknown to us so far. A common +prediction of those models are excited quark states (q*, q**, +q***\ldots). This thesis will search data of the years 2016, 2017 and +2018 for the single excited quark state q* which decays to a quark and +any boson. As the boson will also quickly decay to for example two +quarks, those events will be hard to distinguish from the QCD background +described in \ldots. + +\feynmandiagram [horizontal=a to b] { + i1 -- [fermion] a -- [fermion] i2, + a -- [photon] b, + f1 -- [fermion] b -- [fermion] f2, +}; + +\hypertarget{experimental-setup}{% +\section{Experimental Setup}\label{experimental-setup}} + +Following on, the experimental setup used to gather the data analysed in +this thesis will be described. + +\hypertarget{large-hadron-collider}{% +\subsection{Large Hadron Collider}\label{large-hadron-collider}} + +The Large Hadron Collider is the world's largest and most powerful +particle accelerator \autocite{website}. It has a perimeter of 27 km and +can collide protons at a centre of mass energy of 13 TeV. It is home to +several experiments, the biggest of those are ATLAS and CMS. Both are +general-purpose detectors to investigate the particles that form during +particle collisions. + +\hypertarget{cms}{% +\subsection{CMS}\label{cms}} + +\hypertarget{the-particle-flow-algorithm}{% +\subsubsection{The Particle Flow +algorithm}\label{the-particle-flow-algorithm}} + +\hypertarget{jet-clustering}{% +\subsubsection{Jet clustering}\label{jet-clustering}} + +Because of the hadronisation it is not possible to uniquely identify the +originating particle of a jet. Nonetheless, several algorithms exist to +help with this problem. The algorithm used in this thesis is the +anti-\(k_t\) clustering algorithm. It arises from a generalization of +several other clustering algorithms, namely the \(k_t\), +Cambridge/Aachen and SISCone clustering algorithms. + +The anti-\(k_t\) clustering algorithm associates hard particles with +their soft particles surrounding them within a radius R in the \(\eta\) +- \(\phi\) plane forming cone like jets. If two jets overlap, the jets +shape is changed according to its hardness. A softer particles jet will +change its shape more than a harder particles. A visual comparision of +four different clustering algorithms can be seen in \ldots. + +\hypertarget{method-of-analysis}{% +\section{Method of analysis}\label{method-of-analysis}} + +As described in \ldots, an excited quark q* can decay to a quark and any +boson. The branching ratios are calculated to be as follows: + +The majority of excited quarks will decay to a quark and a gluon, but as +this is virtually impossible to distinguish from QCD effects (for +example from the qg-\textgreater qg processes), this analysis will focus +on the processes q\emph{-\textgreater qW and q}-\textgreater qZ. As the +vector bosons quickly decay mainly into two quarks, it will still be +hard to discriminate between signal and qcd background events, but due +to jet substructure studies it is well possible to establish a +discriminator. + +\begin{itemize} +\tightlist +\item + dominant background: QCD (gg-gg e.g.~- two jets) +\item + division in QCD bg and signal +\end{itemize} + +\hypertarget{signalbackground-modelling}{% +\subsection{Signal/Background +modelling}\label{signalbackground-modelling}} + +Following on, as background a QCD Monte Carlo sample will be used and as +signal a Monte Carlo sample of q* decaying to qW/qZ. + +The background is fitted using the following function with three +parameters p0, p1, p2: \begin{equation} +\frac{dN}{dm_{jj}} = \frac{p_0 \cdot ( 1 - m_{jj} / \sqrt{s} )^{p_2}}{ (m_{jj} / \sqrt{s})^{p_1}} \end{equation} +Whereas \(m_{jj}\) is the invariant mass of the dijet and \(p_0\) is a +normalisation parameter. Two and four parameter functions have also been +studied but found to not fit the background as good as this one. + +The signal is fitted using a double sided crystal ball function. A +gaussian and a poisson have also been studied but found to not fit the +signal sample very well. + +\hypertarget{event-selection}{% +\section{Event selection}\label{event-selection}} + +The selection of events is divided in two parts. First, the preselection +is optimized for high trigger efficiency and makes some physically +motivated cuts. After that, a jet substructure selection uses different +taggers to discriminate between QCD and signal events. + +\hypertarget{preselection}{% +\subsection{Preselection}\label{preselection}} + +The preselection introduces the following cuts: + +\begin{enumerate} +\def\labelenumi{\arabic{enumi}.} +\tightlist +\item + Number of jets \(\ge\) 2 +\item + \(\Delta\eta \le 1.3\) +\item + \(m_{jj} \ge \SI{1050}{\giga\eV}\) +\end{enumerate} + +In the final state, at least two jets are expected. One directly +originating from the decaying q* particle, the other one from the +decaying vector boson. The resonance mass of the q* particle is expected +to be very high, therefore it will be almost stationary and decay into +two particles that are approximately back to back. That is ensured by +the \(\Delta\eta\) cut. The last cut of the invariant dijet mass is to +improve trigger efficiency. + +\hypertarget{datamc-comparision}{% +\subsection{Data/MC Comparision}\label{datamc-comparision}} + +To ensure high data quality, the MC QCD background sample is now being +compared to the actual data of the corresponding data. This is done for +all three years of data available in Run2. + +\hypertarget{event-substructure-selection}{% +\section{Event substructure +selection}\label{event-substructure-selection}} + +This selection is responsible for distinguishing between QCD and signal +events by using a tagger to identify jets coming from a vector boson. +Two taggers different taggers will be used to later compare the results. +For each tagger, a softdropmass is introduced. + +\hypertarget{sideband}{% +\subsection{Sideband}\label{sideband}} + +The sideband is introduced to make sure there are no unwanted side +effects of the used cut. It adds a cut, that makes sure, no data in the +sideband is used for the actual analysis. Later on, a cut on the +softdropmass will be used. The sideband is the softdropmass cut +reversed. + +\hypertarget{n-subjettiness}{% +\subsection{N-Subjettiness}\label{n-subjettiness}} + +The N-subjettiness \(\tau_n\) is defined as + +\begin{equation} \tau_N = \frac{1}{d_0} \sum_k p_{T,k} \cdot \text{min}\{ \Delta R_{1,k}, \Delta R_{2,k}, …, \Delta +R_{N,k} \} \end{equation} + +with k going over the constituent particles in a given jet, \(p_{T,k}\) +being their transverse momenta and +\(\Delta R_{J,k} = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2}\) being the +distance of a candidate subjet J and a constituent particle k in the +rapidity-azimuth plane. It has been shown, that +\(\tau_{21} = \tau_2/\tau_1\) is a good discriminator between QCD events +and events originating from the decay of a boosted vector boson. + +\hypertarget{deepboosted}{% +\subsection{DeepBoosted}\label{deepboosted}} + +The deep boosted tagger uses a trained neural network to identify decays +originitating in a vector boson. It is supposed to give better +efficiencies than the older N-Subjettiness method. + +\hypertarget{optimization}{% +\subsection{Optimization}\label{optimization}} + +To figure out the best value to cut on the discriminators introduced by +the two taggers, a value to quantify how good a cut is has to be +introduced. For that, the significance calculated by +\(\frac{S}{\sqrt{B}}\) will be used. S stands for the amount of signal +events and B for the amount of background events in a given interval. +This value assumes a gaussian error on the background so it will be +calculated for the 2 TeV masspoint where enough background events exist +to justify this assumption. The value therefore represents how good the +signal can be distinguished from the background in units of the standard +deviation of the background. As interval, a 10 \% margin around the +masspoint is chosen. + +As a result, the \(\tau_{21}\) cut is placed at \(\le 0.35\) and the +VvsQCD cut is placed at \(\ge 0.83\). + +\hypertarget{signal-extraction}{% +\section{Signal extraction}\label{signal-extraction}} + +\hypertarget{uncertainties}{% +\subsection{Uncertainties}\label{uncertainties}} + +\hypertarget{results}{% +\section{Results}\label{results}} + +\hypertarget{section}{% +\subsection{2016}\label{section}} + +\hypertarget{previous-research}{% +\subsubsection{previous research}\label{previous-research}} + +\hypertarget{section-1}{% +\subsection{2016 + 2017 + 2018}\label{section-1}} + +\printbibliography[title=Summary] + +\end{document}