commit cbb6c6dcc1ab2656694616b59702e3608d2d9564 Author: david Date: Tue Sep 17 11:21:41 2019 +0200 Initial BSc commit diff --git a/figures/antikt-comparision.png b/figures/antikt-comparision.png new file mode 100644 index 0000000..c0cd01d Binary files /dev/null and b/figures/antikt-comparision.png differ diff --git a/figures/cms_coordinates.png b/figures/cms_coordinates.png new file mode 100644 index 0000000..409d298 Binary files /dev/null and b/figures/cms_coordinates.png differ diff --git a/figures/sm_wikipedia.svg b/figures/sm_wikipedia.svg new file mode 100644 index 0000000..94b99a6 --- /dev/null +++ b/figures/sm_wikipedia.svg @@ -0,0 +1,447 @@ + + + + Standard Model of Elementary Particles + + Basic tiles are 240x240px usually spaced 250px apart. + + + + + image/svg+xml + + + Wikimedia Commons + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Standard Model of Elementary Particles + + + Forces + + + + + + + Fermions + + three generations of matter(fermions) + + I + II + III + + + + + Bosons + + interactions / force carriers(bosons) + + + + mass, charge, spin + mass + charge + spin + + + + Quarks + QUARKS + + + up + + + u + + ≃2.2 MeV/c² + ⅔ + ½ + up + + + + down + + + d + + ≃4.7 MeV/c² + −⅓ + ½ + down + + + + charm + + + c + + ≃1.28 GeV/c² + ⅔ + ½ + charm + + + + strange + + + s + + ≃96 MeV/c² + −⅓ + ½ + strange + + + + top + + + t + + ≃173.1 GeV/c² + ⅔ + 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 0000000..9cb07f0 Binary files /dev/null and b/structure.pdf differ diff --git a/thesis.md b/thesis.md new file mode 100644 index 0000000..e97171f --- /dev/null +++ b/thesis.md @@ -0,0 +1,416 @@ +--- +author: David Leppla-Weber +title: Search for excited quark states decaying to qW/qZ +lang: en-GB +header-includes: | + \usepackage[onehalfspacing]{setspace} + \usepackage{siunitx} + \usepackage{tikz-feynman} + \pagenumbering{gobble} +abstract: | + This is my very long abstract. + + Blubb +documentclass: article +geometry: +- top=2.5cm +- left=3cm +- right=2.5cm +- bottom=2.5cm +papersize: a4 +mainfont: Times New Roman +fontsize: 12pt +toc: true +--- +\newpage +\pagenumbering{arabic} + +# Introduction + +\newpage + +# Theoretical background + +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 processes of +quantum chromodynamics and the theory of q*, which will be the main topic of this thesis. + +## 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. Each of those exists in six so called flavours. +Furthermore, quarks and leptons can also be divided into three generations, each of which contains two particles. +In the lepton category, each generation has one charged lepton and one neutrino, that has no charge. Also, the mass of +the neutrinos is not yet known, so far, only an upper bound has been established. A full list of particles known to the +standard model can be found in [@fig:sm]. Furthermore, all fermions have an associated anti particle with reversed +charge. Therefore it is not clear, whether it makes sense to differ between particle and anti particle for chargeless +particles such as photons and neutrinos. + +![Elementary particles and some of their properties.](./figures/sm_wikipedia.svg){width=50% #fig:sm} + +The gauge bosons, namely the photon, $W^\pm$ bosons, $Z^0$ boson, and eight gluons, are mediators of the different +forces of the standard model. + +The photon is responsible for the electromagnetic force and therefore interacts with all +electrically charged particles. It itself carries no electromagnetic charge and has no mass. Possible interactions are +either scattering or absorption. + +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: + +\begin{equation} + V_{CKM} = + \begin{pmatrix} + |V_{ud}| & |V_{us}| & |V_{ub}| \\ + |V_{cd}| & |V_{cs}| & |V_{cb}| \\ + |V_{td}| & |V_{ts}| & |V_{tb}| + \end{pmatrix} + = + \begin{pmatrix} + 0.974 & 0.225 & 0.004 \\ + 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. + +The strong interaction or 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, +although they don't carry just one colour but rather a combination of a colour and an anticolour, 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 at a certain point +more energetically efficient to form a new quark - antiquark pair than separating 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. An effect called Hadronisation. + +### Quantum Chromodynamic background {#sec:qcdbg} + +In this thesis, a decay that produces two jets will be analysed. Therefore it will be hard to distinguish the signal +processes from any QCD effects. Those also produce two jets in the endstate, as can be seen in [@fig:qcdfeynman]. They +are also happening very often in a proton proton collision. This is caused by the structure of the proton. It does not +only consist of the three quarks, called valence quarks, but also of a lot of quark-antiquark pairs connected by +gluons, called the sea quarks. Therefore in a proton - proton collision, interactions of gluons and quarks are the main +processes causing a very strong QCD background. + +\begin{figure} +\centering +\feynmandiagram [horizontal=v1 to v2] { + q1 [particle=\(q\)] -- [fermion] v1 -- [gluon] g1 [particle=\(g\)], + v1 -- [gluon] v2, + q2 [particle=\(q\)] -- [fermion] v2 -- [gluon] g2 [particle=\(g\)], +}; +\feynmandiagram [horizontal=v1 to v2] { + g1 [particle=\(g\)] -- [gluon] v1 -- [gluon] g2 [particle=\(g\)], + v1 -- [gluon] v2, + g3 [particle=\(g\)] -- [gluon] v2 -- [gluon] g4 [particle=\(g\)], +}; +\caption{Two examples of QCD processes resulting in two jets.} \label{fig:qcdfeynman} +\end{figure} + +### Shortcomings of the Standard Model + +While being very successful in describing mostly all of the effects we can observe in particle colliders so far, the +Standard Model still has several shortcomings. + +- **Gravity**: as already noted, the standard model doesn't include gravity as a force. +- **Dark Matter**: observations of the rotational velocity of galaxies can't be explained by the matter known, dark + matter up to date is our best theory to explain those. +- **Matter-antimatter assymetry**: The amount of matter vastly outweights the amount of + antimatter in the observable universe. This can't be explained by the standard model, which predicts a similar amount + of matter and antimatter. +- **Symmetries between particles**: Why do exactly three generations of fermions exist? Why is the charge of a quark + exactly one third of the charge of a lepton? How are the masses of the particles related? Those questions cannot be + answered by the standard model. +- **Hierarchy problem**: + +## 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. 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. + +\begin{figure} +\centering +\feynmandiagram [large, horizontal=qs to v] { + a -- qs -- b, + qs -- [fermion, edge label=\(q*\)] v, + q1 [particle=\(q\)] -- v -- w [particle=\(W\)], + q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)], +}; +\caption{Feynman diagram showing a possible decay of a q* particle to a W boson and a quark with the W boson also +decaying to two quarks.} \label{fig:qsfeynman} +\end{figure} + +This thesis will search data collected by the CMS in the years 2016, 2017 and 2018 for the single excited quark state +q\* which can decay to a quark and any boson. An example of a q\* decaying to a quark and a W boson can be seen in +[@fig:qsfeynman]. 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 [@sec:qcdbg]. To reconstruct the mass of the q\* particle, the dijet +invariant mass, the mass of the two jets in the final state, can be calculated by adding their four momenta, vectors +consisting of the energy and momentum of a particle, together. From the four momentum it's easy to derive the mass by +solving $E=\sqrt{p^2 + m^2}$ for m. + +\newpage + +# Experimental Setup + +Following on, the experimental setup used to gather the data analysed in this thesis will be described. + +## Large Hadron Collider + +The Large Hadron Collider is the world's largest and most powerful particle accelerator [@website]. It has a perimeter +of 27 km and can collide protons at 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 luminosity L is a quantity to be able to calculate the number of events per second generated in a LHC collision by +$N_{event} = L\sigma_{event}$ with $\sigma_{event}$ being the cross section of the event. +The luminosity of the LHC for a Gaussian beam distribution can be described as follows: + +\begin{equation} + L = \frac{N_b^2 n_b f_{rev} \gamma_r}{4 \pi \epsilon_n \beta^*}F +\end{equation} + +Where $N_b$ is the number of particles per bunch, $n_b$ the number of bunches per beam, $f_{rev}$ the revolution +frequency, $\gamma_r$ the relativistic gamma factor, $\epsilon_n$ the normalised transverse beam emittance, $\beta^*$ +the beta function at the collision point and F the geometric luminosity reduction factor due to the crossing angle at +the interaction point: +\begin{equation} + F = \left(1+\left( \frac{\theta_c\sigma_z}{2\sigma^*}\right)^2\right)^{-1/2} +\end{equation} + +At the maximum luminosity of $10^{34}\si{\per\square\centi\metre\per\s}$, $N_b = 1.15 \cdot 10^{11}$, $n_b = 2808$, +$f_{rev} = \SI{11.2}{\kilo\Hz}$, $\beta^* = \SI{0.55}{\m}$, $\epsilon_n = \SI{3.75}{\micro\m}$ and $F = 0.85$. + +To quantify the amount of data collected by one of the experiments at LHC, the integrated luminosity is introduced as +$L_{int} = \int L dt$. In 2016 the CMS captured data of a total integrated luminosity of $\SI{35.92}{\per\femto\barn}$. +In 2017 it collected $\SI{41.53}{\per\femto\barn}$ and in 2018 $\SI{59.74}{\per\femto\barn}$. + +## Compact Muon Solenoid + +The data used in this thesis was captured by the Compact Muon Solenoid (CMS). It is one of the biggest experiments at +the Large Hadron Collider. It can detect all elementary particles of the standard model except neutrinos. For that, it +has an onion like setup. The particles produced in a collision first go through a tracking system. They then pass an +electromegnetic as well as a hadronic calorimeter. This part is surrounded by a supercondcting solenoid that generates a +magenetic field of 3.8 T. Outside of the solenoid are big muon chambers. + +### Coordinate conventions + +Per convention, the z axis points along the beam axis, the y axis upwards and the x axis horizontal towards the LHC +centre. Furthermore, the azimuthal angle $\phi$, which describes the angle in the x - y plane, the polar angle $\theta$, +which describes the angle in the y - z plane and the pseudorapidity $\eta$, which is defined as $\eta = +-ln\left(tan\frac{\theta}{2}\right)$ are introduced. The coordinates are visualised in [@fig:cmscoords]. + +![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 +](./figures/cms_coordinates.png){#fig:cmscoords width=60%} + +### The tracking system + +The tracking system is built of two parts, first a pixel detector and then silicon strip sensors. It is used to +reconstruct the tracks of charged particles, measuring their charge sign, direction and momentum. It is as close to the +collision as possible to be able to identify secondary vertices. + +### The electromagnetic calorimeter + +The electromagnetic calorimeter measures the energy of photons and electrons. It is made of tungstate crystal. +When passed by particles, it produces light in proportion to the particle's energy. This light is measured by +photodetectors that convert this scintillation light 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 (particles formed of quarks) and muons. They too leave some energy in the ECAL. + +### The hadronic calorimeter + +The hadronic calorimeter (HCAL) is used to detect high energy hadronic particles. It surrounds the ECAL and is made of +alternating layers of active and absorber material. While the absorber material with its high density causes the hadrons +to shower, the active material then detects those showers and measures their energy, similar to how the ECAL works. + +### The solenoid + +The solenoid, giving the detector its name, is one of the most important feature. It creates a magnetic field of 3.8 T +and therefore makes it possible to measure momentum of charged particles by bending their tracks. + +### 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. The system is divided into a barrel part and two endcaps. Together +they cover $0 < |\eta| < 2.4$. The muons are the only detected particles, that can pass all the other systems +without a significant energy loss. + +### 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 +the track and its clusters is then no more used for the detection of other particles. This is first done for muons and +then for charged hadrons, so a muon can't give rise to a wrongly identified charged hadron. Due to Bremsstrahlung photon +emission, electrons are harder to reconstruct, for them a specific track reconstruction algorithm is used [TODO]. +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 momentums. 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. + +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 [@fig:antiktcomparision]. + +![ +Comparision of the $k_t$, Cambridge/Aachen, SISCone and anti-$k_t$ algorithms clustering a sample parton-level event +with many random soft "ghosts". Taken from +](./figures/antikt-comparision.png){#fig:antiktcomparision} + +\newpage + +# Method of analysis + +As described in …, 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->qg 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 0000000..ad4e419 Binary files /dev/null and b/thesis.pdf differ diff --git a/thesis.tex b/thesis.tex new file mode 100644 index 0000000..9969b4f --- /dev/null +++ b/thesis.tex @@ -0,0 +1,357 @@ +% Options for packages loaded elsewhere +\PassOptionsToPackage{unicode}{hyperref} +\PassOptionsToPackage{hyphens}{url} +% +\documentclass[ + 12pt, + british, + a4paper, +]{article} +\usepackage{lmodern} +\usepackage{amssymb,amsmath} +\usepackage{ifxetex,ifluatex} +\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex + \usepackage[T1]{fontenc} + \usepackage[utf8]{inputenc} + \usepackage{textcomp} % provide euro and other symbols +\else % if luatex or xetex + \usepackage{unicode-math} + \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}