This thesis concerns with numerical methods for a theoretical description of high energy particle scattering experiments. It focuses on fixed order perturbative calculations, i.e. on matrix elements and scattering cross sections at leading and next-to-leading order. For the leading order a number of algorithms for the matrix element generation and the numeric integration over the phase space are studied and implemented in a computer code, which allows to push the current limits on the complexity of the final state and the precision. For next-to-leading order calculations necessary steps towards a fully automated treatment are performed. A subtraction method that allows a process independent regularization of the divergent virtual and real corrections is implemented, and a new approach for a semi-numerically evaluation of one-loop amplitudes is investigated.

Critical thinking (CT) is one of the desirable skills to be taught in school. It is not only considered an important 21st century skill for living in a democratic society, but also important for a deep understanding of domain-specific content. Despite its importance, studies show that students often lack the ability to think critically. Moreover, there is a lack of clear theory, supported by empirical findings, for developing domain-specific teaching-learning sequences to promote students’ CT. This makes teaching CT challenging for teachers. To address this gap, the presented study has two goals: to identify design principles for instruction that promotes critical thinking and to develop an exemplary instructional unit in particle physics on this basis. Particle physics is chosen because of its abstractness and complexity, as well as student interest in the subject. Another basis is a definition of CT that can be readily applied in the context of teaching physics. For this purpose, Halpern’s classification of CT strategies and their measurable outcomes is used. Furthermore, a distinction is made between general CT skills that provide a framework for CT, such as understanding the need to define terms precisely, and domain-specific CT skills that represent the application of general CT skills in a specific domain and require domain-specific expertise, such as distinguishing between the concepts of mass and matter in the context of particle physics. This study examines the development of both general and domain-specific CT. The teaching-learning sequences about antimatter (10 to 12 lessons) are developed for students in grades 10, 11, and 12 using the Design-Based Research (DBR) approach. Analysis of the data from pilot studies provides guidance for further development of the antimatter course and the creation of a teacher package that supports teachers both methodologically and in terms of content when implementing the antimatter course. In the main study, the course is implemented in 3 classes in different federal states of Germany. To evaluate the effectiveness of the course in promoting students’ CT, the perspectives of students as well as of teachers are examined. To evaluate the effectiveness of the course from the students’ perspective, the video and audio data, the students’ works, students’ interviews or questionnaires are inductively analyzed using the constant comparative method to identify the students’ learning processes. The results show that students apply content knowledge, apply CT skills, and demonstrate a disposition toward CT. This corresponds to a developed CT. Further analysis is conducted to relate the design skeleton facets of the course (materials, activity structure, and participant structure) to the learning processes, using the conjecture map framework to support the results from the constant comparative method. A Particle Physics Critical Thinking (PPCT) test is also developed to triangulate the results. The results of administering the PPCT test as a posttest are consistent with the qualitative findings on the effectiveness of the course. A questionnaire is developed for teachers to elicit their perceptions of the relevance, practicality, and effectiveness of the course in promoting students’ CT. The results show a positive perception. Combining all the results shows that the antimatter course is an effective course in promoting CT. The design principles applied contribute to the theory of designing effective CT instruction. Furthermore, data analysis reveals the challenges students face in critical thinking and provides teachers with heuristics for designing a domain-specific course. Based on the findings, a model for teaching CT is developed. This work leads to implications for teaching, in addition to other research questions. These include, for example, developing domain-specific CT instruction using 6 principles empirically tested in this study, considering heuristics for designing domain-specific CT instruction, and using the course materials for the purpose of developing CT. In addition, the PPCT can guide the development of other domain-specific CT tests.:Abstract i Kurzfassung iii Table of Contents v 1 Introduction 1 1.1 Importance of critical thinking and its teaching 1 1.2 Research goals 2 1.3 Structure of the work 4 Part I Theory 7 2 What is critical thinking? 9 2.1 Definition of critical thinking 9 2.2 Commonalities between different definitions 20 2.3 Nature of critical thinking: general and domain-specific 28 2.3.1 Nature of critical thinking in physics 30 2.4 Students’ challenges in critical thinking 32 2.4.1 Verbal reasoning skill 33 2.4.2 Argument analysis skill 33 2.4.3 Thinking as hypothesis testing skill 34 2.4.4 Likelihood and uncertainty analysis skill 35 2.4.5 Decision making and problem solving skill 36 2.5 Teachers’ perspective on critical thinking and teaching critical thinking 37 2.5.1 Teachers’ perspective on critical thinking 38 2.5.2 Teachers’ perspective on teaching critical thinking 41 2.5.3 Rationale for developing supportive materials for teachers 41 3 Teaching critical thinking 43 3.1 Challenges of teaching critical thinking 44 3.1.1 Teaching critical thinking as a general or domain-specific skill . 45 3.1.2 Teaching critical thinking implicitly or explicitly 46 3.1.3 Valuing disposition alongside teaching critical thinking 48 3.2 Design of critical thinking (CT) instruction 49 3.2.1 First component of CT instruction: Critical thinking model 50 3.2.2 Second component of CT instruction: Appropriate instructional design theory 52 3.2.3 A proposal for CT instruction 56 3.3 Evaluation of CT instruction 57 3.3.1 Evaluation criteria 58 3.3.2 Evaluation approaches 63 4 Design-based research 69 4.1 Design-based research (DBR) and its features 69 4.2 Conducting DBR in education: Design and evaluation of an instruction 71 4.2.1 Analysis and exploration phase 73 4.2.2 Design and construction phase 74 4.2.3 Evaluation and reflection phase 79 4.3 Summary 89 Part II Empirical Study 91 5 Research questions 93 6 Design and methodology of the study 95 6.1 Design and development of instruction according to Design-based research 96 6.1.1 Analysis and exploration phase 97 6.1.2 Design and construction phase 100 6.1.3 Evaluation and reflection phase 111 6.2 Evaluation of effectiveness of instruction 114 6.2.1 Constant comparative method for qualitative evaluation 114 6.2.2 Description of instruments for quantitative evaluation 119 6.3 Relating design skeleton facets to valued outcomes 133 6.4 Description of instrument for evaluating teachers’ perspective 134 7 Evaluation of effectiveness of the antimatter course 139 7.1 Participants 139 7.2 Evaluation of structure fidelity of implementation 141 7.2.1 Adherence 141 7.2.2 Duration 145 7.3 Results of qualitative data analysis 146 7.3.1 Likelihood and uncertainty analysis skill in the positron discovery context 147 7.3.2 Argument analysis skill in the Big Bang context 162 7.3.3 Verbal reasoning in the context of analysing the scenario of scene of “Illuminati” 173 7.3.4 Thinking as hypothesis testing in the antimatter trap context 184 7.4 Conclusion on the effectiveness of antimatter course 200 7.5 Development of critical thinking skills: a model proposal 202 7.5.1 Model proposal on developing likelihood and uncertainty analysis skill 202 7.5.2 Model proposal on developing argument analysis skill 204 7.5.3 Model proposal on developing verbal reasoning skill 205 7.5.4 Model proposal on developing thinking as hypothesis testing skill 206 7.5.5 An underlying model on developing critical thinking 207 8 Relating design skeleton facets to valued outcomes 213 8.1 Design skeleton facets of antimatter course 213 8.1.1 Materials 214 8.1.2 Activity structure 214 8.1.3 Participant structure 215 8.2 Relation of design skeleton facets to valued outcomes 218 8.2.1 Materials 218 8.2.2 Activity structure 220 8.2.3 Participant structure 221 8.3 Conclusion and discussion 225 9 Teacher perception of the antimatter course 227 9.1 Participants 227 9.2 Perceived relevance 228 9.3 Perceived practicality 232 9.4 Perceived effectiveness 234 9.5 Conclusion and discussion 239 10 Triangulation of findings 241 10.1 Participants 241 10.2 Evaluation of general critical thinking skills 242 10.3 Evaluation of domain-specific critical thinking skills 244 10.4 Conclusion and discussion 244 Part III Conclusion 247 11 Summary and discussion 249 11.1 Empirical study 249 11.2 Contribution to theory 253 11.2.1 Theory of instructional design 254 11.2.2 Evaluation of critical thinking instruction 256 11.2.3 Model on developing critical thinking 257 11.3 Limitations 257 12 Outlook 259 12.1 Implications for teaching critical thinking 259 12.2 Future research 263 Appendix 265 Research instruments 267 A Student information and prior knowledge questionnaire 267 B Particle Physics Critical Thinking (PPCT) test 270 C Student questionnaire 289 D Teacher information 290 E Teacher questionnaire 291 Antimatter course materials 292 F Worksheet 1: Critical Thinking 292 G Worksheet 2: Illuminati 295 H Worksheet 3: Anderson’s cloud chamber photograph 296 I Worksheet 4: Big Bang 298 J Worksheet 5: Search systematically 299 K Worksheet 6: Trapping antimatter 302 L Worksheet 7: Individual work “Illuminati” 305 M Worksheet 8: Group work “Illuminati” 306 List of tables 309 List of figures 313 References 315 Acknowledgements 329 Statement of Authorship 331 / Kritisches Denken (KD) ist eine der wünschenswerten Fähigkeiten, die in der Schule vermittelt werden sollten. Es gilt nicht nur als wichtige Kompetenz des 21. Jahrhunderts für das Leben in einer demokratischen Gesellschaft, sondern auch als wichtig für ein tiefes Verständnis von fachspezifischen Inhalten. Trotz dieser Bedeutung zeigen Studien, dass es den Lernenden oft an der Fähigkeit fehlt, kritisch zu denken. Zudem fehlt es an einer klaren, durch empirische Befunde gestützten Theorie für die Entwicklung von fachspezifischen Lehr-Lern-Sequenzen zur Förderung der KD-Fähigkeiten von SchülerInnen. Dies macht den KD-Unterricht zu einer Herausforderung für Lehrkräfte. Um diese Lücke zu schließen, verfolgt die vorgelegte Studie zwei Ziele: Die Identifikation von Gestaltungsprinzipien für einen Unterricht, der die Fähigkeit zum kritischen Denken fördert, und die Entwicklung einer exemplarischen Unterrichtseinheit in Teilchenphysik auf dieser Grundlage. Die Teilchenphysik wurde aufgrund ihrer Abstraktheit und Komplexität sowie des Interesses der Schüler ausgewählt. Eine weitere Grundlage ist eine Definition von KD, die sich gut im Rahmen des Physikunterrichts anwenden lässt. Hierzu wurde Halperns Klassifizierung von KD-Strategien und ihre messbaren Ergebnisse verwendet. Darüber hinaus wird unterschieden zwischen allgemeinen KD-Fähigkeiten, die einen Rahmen für KD bilden, wie z. B. das Verständnis für die Notwendigkeit, Begriffe genau zu definieren, und domänenspezifischen KD-Fähigkeiten, die die Anwendung allgemeiner KD-Fähigkeiten in einer bestimmten Domäne darstellen und domänenspezifisches Fachwissen erfordern, wie z. B. die Unterscheidung zwischen den Konzepten von Masse und Materie im Kontext der Teilchenphysik. Diese Studie untersucht die Entwicklung sowohl der allgemeinen als auch der domänenspezifischen KD. Die Lehr-Lern-Sequenzen über Antimaterie (10 bis 12 Unterrichtsstunde) werden für SchülerInnen der Klassenstufen 10, 11 und 12 mit Hilfe des Design-Based Research (DBR) Ansatzes entwickelt. Die Analyse der Daten aus den Pilotstudien liefert Anhaltspunkte für die Weiterentwicklung des Antimateriekurses und die Entwicklung eines Lehrerpakets, das Lehrkräfte methodisch und inhaltlich bei der Umsetzung des Antimateriekurses unterstützt. In der Hauptstudie wird der Kurs in 3 Klassen in verschiedenen Bundesländern Deutschlands durchgeführt. Um die Wirksamkeit des Antimateriekurses bei der Förderung des KD der SchülerInnen zu evaluieren, werden sowohl die Perspektiven der SchülerInnen als auch die der LehrerInnen untersucht. Um die Wirksamkeit des Kurses aus der Perspektive der SchülerInnen zu evaluieren, werden die Video- und Audiodaten, die Schülerarbeiten, das Schülerinterview und der Fragebogen induktiv mit der Constant Comparative Methode analysiert, um die Lernprozesse der SchülerInnen zu identifizieren. Die Ergebnisse zeigen, dass die SchülerInnen inhaltliches Wissen und KD-Fähigkeiten anwenden und eine Disposition zeigen, die gemeinsam einer entwickelten KD entsprechen. Zusätzlich werden mit Hilfe von sog. „Conjecture Maps“ die Gestaltungsfacetten des Kurses (Materialien, Aktivitätsstruktur und Teilnehmerstruktur) mit den Lernprozessen in Beziehung gesetzt, um die Ergebnisse aus der Constant Comparative Methode zu stützen. Ein Particle Physics Critical Thinking (PPCT) Test wurde ebenfalls entwickelt, um die Ergebnisse zu triangulieren. Die Ergebnisse der Durchführung des PPCT-Tests als Posttest stimmen mit den qualitativen Erkenntnissen über die Wirksamkeit des Kurses überein. Ferner wurde ein Fragebogen für Lehrkräfte entwickelt, um ihre Einschätzung der Relevanz, Praktikabilität und Wirksamkeit des Kurses bei der Förderung des KD der SchülerInnen zu erheben. Dieser zeigte eine positive Wahrnehmung. Die Kombination aller Ergebnisse zeigt, dass der Antimateriekurs ein effektiver Kurs zur Förderung des KD ist. Die angewandten Gestaltungsprinzipien tragen zur Theorie der Gestaltung eines wirksamen KD-Unterrichts bei. Darüber hinaus zeigt die Datenanalyse die Herausforderungen auf, denen sich die SchülerInnen beim kritischen Denken gegenübersehen, und liefert den Lehrkräften Heuristiken für die Gestaltung eines domänenspezifischen Kurses. Auf der Grundlage der Ergebnisse wird ein Modell für den KD-Unterricht entwickelt. Diese Arbeit führt neben weiteren Forschungsfragen auch zu Implikationen für den Unterricht. Dazu gehören z. B. die Entwicklung eines domainspezifischen KD-Unterrichts unter Verwendung von 6 Prinzipien, die in dieser Studie empirisch getestet wurden, die Berücksichtigung von Heuristiken für die Gestaltung eines domainspezifischen KD-Unterrichts, und die Verwendung der Kursmaterialien zum Zweck der Entwicklung von KD. Darüber hinaus kann der PPCT Test die Entwicklung anderer domainspezifischer KD-Tests anleiten.:Abstract i Kurzfassung iii Table of Contents v 1 Introduction 1 1.1 Importance of critical thinking and its teaching 1 1.2 Research goals 2 1.3 Structure of the work 4 Part I Theory 7 2 What is critical thinking? 9 2.1 Definition of critical thinking 9 2.2 Commonalities between different definitions 20 2.3 Nature of critical thinking: general and domain-specific 28 2.3.1 Nature of critical thinking in physics 30 2.4 Students’ challenges in critical thinking 32 2.4.1 Verbal reasoning skill 33 2.4.2 Argument analysis skill 33 2.4.3 Thinking as hypothesis testing skill 34 2.4.4 Likelihood and uncertainty analysis skill 35 2.4.5 Decision making and problem solving skill 36 2.5 Teachers’ perspective on critical thinking and teaching critical thinking 37 2.5.1 Teachers’ perspective on critical thinking 38 2.5.2 Teachers’ perspective on teaching critical thinking 41 2.5.3 Rationale for developing supportive materials for teachers 41 3 Teaching critical thinking 43 3.1 Challenges of teaching critical thinking 44 3.1.1 Teaching critical thinking as a general or domain-specific skill . 45 3.1.2 Teaching critical thinking implicitly or explicitly 46 3.1.3 Valuing disposition alongside teaching critical thinking 48 3.2 Design of critical thinking (CT) instruction 49 3.2.1 First component of CT instruction: Critical thinking model 50 3.2.2 Second component of CT instruction: Appropriate instructional design theory 52 3.2.3 A proposal for CT instruction 56 3.3 Evaluation of CT instruction 57 3.3.1 Evaluation criteria 58 3.3.2 Evaluation approaches 63 4 Design-based research 69 4.1 Design-based research (DBR) and its features 69 4.2 Conducting DBR in education: Design and evaluation of an instruction 71 4.2.1 Analysis and exploration phase 73 4.2.2 Design and construction phase 74 4.2.3 Evaluation and reflection phase 79 4.3 Summary 89 Part II Empirical Study 91 5 Research questions 93 6 Design and methodology of the study 95 6.1 Design and development of instruction according to Design-based research 96 6.1.1 Analysis and exploration phase 97 6.1.2 Design and construction phase 100 6.1.3 Evaluation and reflection phase 111 6.2 Evaluation of effectiveness of instruction 114 6.2.1 Constant comparative method for qualitative evaluation 114 6.2.2 Description of instruments for quantitative evaluation 119 6.3 Relating design skeleton facets to valued outcomes 133 6.4 Description of instrument for evaluating teachers’ perspective 134 7 Evaluation of effectiveness of the antimatter course 139 7.1 Participants 139 7.2 Evaluation of structure fidelity of implementation 141 7.2.1 Adherence 141 7.2.2 Duration 145 7.3 Results of qualitative data analysis 146 7.3.1 Likelihood and uncertainty analysis skill in the positron discovery context 147 7.3.2 Argument analysis skill in the Big Bang context 162 7.3.3 Verbal reasoning in the context of analysing the scenario of scene of “Illuminati” 173 7.3.4 Thinking as hypothesis testing in the antimatter trap context 184 7.4 Conclusion on the effectiveness of antimatter course 200 7.5 Development of critical thinking skills: a model proposal 202 7.5.1 Model proposal on developing likelihood and uncertainty analysis skill 202 7.5.2 Model proposal on developing argument analysis skill 204 7.5.3 Model proposal on developing verbal reasoning skill 205 7.5.4 Model proposal on developing thinking as hypothesis testing skill 206 7.5.5 An underlying model on developing critical thinking 207 8 Relating design skeleton facets to valued outcomes 213 8.1 Design skeleton facets of antimatter course 213 8.1.1 Materials 214 8.1.2 Activity structure 214 8.1.3 Participant structure 215 8.2 Relation of design skeleton facets to valued outcomes 218 8.2.1 Materials 218 8.2.2 Activity structure 220 8.2.3 Participant structure 221 8.3 Conclusion and discussion 225 9 Teacher perception of the antimatter course 227 9.1 Participants 227 9.2 Perceived relevance 228 9.3 Perceived practicality 232 9.4 Perceived effectiveness 234 9.5 Conclusion and discussion 239 10 Triangulation of findings 241 10.1 Participants 241 10.2 Evaluation of general critical thinking skills 242 10.3 Evaluation of domain-specific critical thinking skills 244 10.4 Conclusion and discussion 244 Part III Conclusion 247 11 Summary and discussion 249 11.1 Empirical study 249 11.2 Contribution to theory 253 11.2.1 Theory of instructional design 254 11.2.2 Evaluation of critical thinking instruction 256 11.2.3 Model on developing critical thinking 257 11.3 Limitations 257 12 Outlook 259 12.1 Implications for teaching critical thinking 259 12.2 Future research 263 Appendix 265 Research instruments 267 A Student information and prior knowledge questionnaire 267 B Particle Physics Critical Thinking (PPCT) test 270 C Student questionnaire 289 D Teacher information 290 E Teacher questionnaire 291 Antimatter course materials 292 F Worksheet 1: Critical Thinking 292 G Worksheet 2: Illuminati 295 H Worksheet 3: Anderson’s cloud chamber photograph 296 I Worksheet 4: Big Bang 298 J Worksheet 5: Search systematically 299 K Worksheet 6: Trapping antimatter 302 L Worksheet 7: Individual work “Illuminati” 305 M Worksheet 8: Group work “Illuminati” 306 List of tables 309 List of figures 313 References 315 Acknowledgements 329 Statement of Authorship 331

Diese Arbeit beschreibt die Suche nach assoziierter Produktion eines Higgsbosons und eines Top-Quark Paares in Proton-Proton Kollisionen bei einer Schwerpunktsenergie von 13 TeV. Für diese Analyse wurden Ereignisse analysiert, die exakt zwei Leptonen mit gleichem Ladungsvorzeichen oder exakt drei Leptonen enthalten und daher auf die Higgs Zerfallsmoden in H->WW, H->ZZ und H->tautau sensitiv sind. Die Daten wurden mit dem ATLAS Detektor am Large Hadron Collider (LHC) in den Jahren 2015-17 aufgezeichnet. Der grösste Untergrund in beiden Kanälen stammt aus assoziierter Produktion von Vektorbosonen mit einem Top-Quark Paar (ttW und tt(Z/gamma)), Dibosonproduktion und Ereignisse, die Photonen und Hadronen, die fehlerhaft als Leptonen identifiziert wurden, erhalten oder Leptonen, die aus Zerfällen von Hadronen stammen. Der Leptonuntergrund wurde mit einer neuen Methode abgeschätzt, die auf separaten Kategorien für jeden Produktionsmodus des Leptonuntergrundes basiert. Der Beitrag jeder Kategorie wird in verschiedenen Kontrollregionen aus dem Vergleich von Daten mit der Simulation bestimmt. Das Verhältnis des gemessenen ttH Wirkungsquerschnitts zu der Vorhersage des Standardmodells und die Normierungsfaktoren des Untergrundes werden gleichzeitig in einem Profile-Likelihood-Fit bestimmt. Das Verhältnis des gemessenen zum erwarteten ttH Wirkungsquerschnitts, unter der Annahme einer Higgsbosonmasse von 125 GeV, wurde zu 0.88(+0.54/-0.51) mit einer beobachteten (erwarteten) Signifikanz von 1.80 (2.52) Standardabweichungen gemessen. Das entspricht einem geschätzten Wirkungsquerschnitt für die ttH Produktion von 446(+241/-227) fb, in Übereinstimmung mit der Standardmodellvorhersage von 507(+35/-50) fb. / This thesis describes the search for the associated production of a Higgs boson and a top-quark pair in proton-proton collisions with a center-of-mass energy of 13 TeV. The analysis focuses on events containing two leptons with same-sing electric charge or exactly three leptons in the final state. With these requirements, the analysis is sensitive to the H->WW, H->ZZ and H->tautau Higgs decay modes. The used data was recorded with the ATLAS detector at the Large Hadron Collider (LHC) during the 2015-17 period. The primary sources of background were found to be ttW, tt(Z/gamma), Diboson processes and events containing fake or non-prompt leptons coming from hadron decays, photon conversions and electron charge mis-identification. The estimation of the hadron decay and photon conversion fake backgrounds was performed using a novel semi-data driven technique where Monte Carlo background categories are created for each fake process of interest. A profile likelihood fit to data is then used to extract a normalization factor for each fake category, which are used to correct the Monte Carlo predictions. The ratio of the measured ttH signal cross-section to the Standard Model expectations and a normalization factor for the ttW process are extracted simultaneously from the same fit. The measured to expected cross-section ratio for a Standard Model Higgs boson of mass 125 GeV was found to be 0.88(+0.54/-0.51) with an observed (expected) significance of 1.80 (2.52) standard deviations. This corresponds to an estimated ttH cross-section of 446(+241/-227) fb, in agreement with the Standard Model prediction of 507(+35/-50) fb.

Diese Arbeit präsentiert die Messung der Produktion eines einzelnen top quarks im s-channel. Dazu wird der 13 TeV ATLAS Datensatz, welcher von 2015 bis 2018 aufgenommen wurde und insgesamt 139 fb^−1 integrierte Luminositat hat, analysiert. Die große Schwierigkeit dieser Analyse ist die überwältigende Menge an Untergrund. Nach einer optimisierten Auswahl von Ereignissen stammen nur 3 % der Ereignisse von dem gesuchten Prozess. Demzufolge muss der Untergrund so gut wie möglich von dem Signal getrennt werden. In dieser Analyse wird die Matrixelement Methode verwendet. Diese Methode wendet das Neyman-Pearson Lemma, das die optimale Teststatistik beschreibt, auf dieses Teilchenphysik Experiment an. Die Likelihood Funktionen werden durch eine Faltung der Matrixelemente, die die harte Streuung beschreiben, mit den Transferfunktionen, die für die Modelierung der Detektoreffekte zuständig sind, berechnet. Wegen begrenzter Rechenkapazitäten kann dabei nur die erste Ordnung der Näherung in die Berechnung einbezogen werden. Diese Arbeit stellt außerdem Studien vor, die das Ziel haben diese Methode zu verbessern. Dazu wurden die Transferfunktion neu bestimmt. Außerdem wird ein Neuronales Netzwerk zur Identifizierung des Signals angewendet. Um das Resultat zu extrahieren wurde eine statistisches Modell der diskriminierenden Variable der Matrixelement Methode erstellt und mit Hilfe des profile likelihood Fits wurde der Parameter μ, der als Quotient aus dem gemessenen s-channel Wirkungsquerschnitt zu dem vom Standard Modell vorhergesagten Wirkungsquerschnitt definiert ist, bestimmt. Das Resultat der Analyse ist μ = 1.28 ^+0.36_− 0.31. Dies stimmt mit der Standard Modell Vorhersage überein. Die gemessene Signifikanz beträgt 4.19 σ. Dies ist die höchste jemals gemessene Signifikanz für die s-channel Produktion eines einzelnen top quarks in Proton-Proton Kollisionen. / This thesis presents the measurement of the single top s-channel production with the ATLAS detector. The analysis is based on data collected between 2015 and 2018, at a center-of-mass energy of 13 TeV and with an integrated luminosity of 139 fb^−1. The main challenge of this analysis is the overwhelming background. After an optimized selection of events the signal amounts to only approximately 3 % of all events in the signal region. This necessitates the best possible separation of signal and background. In this thesis, the Matrix Element is utilized. The underlying principle for this method is the Neyman-Pearson lemma which states the optimal test statistic. The likelihoods are computed by a convolution of the matrix elements describing the hard scattering process and the transfer functions which model the detector effects. Due to limited computing resources, only the leading order approximation can be calculated. This thesis further investigates methodologies aimed at enhancing the effectiveness of the signal separation process. For that reason, the transfer functions are updated and a study in which a neural network uses the event likelihoods of the Matrix Element Method as in- put to produce a different discriminating variable is shown. To extract the final result, a statistical analysis of the discriminating variable result- ing from the Matrix Element Method is preformed. A statistical model is built and the profile likelihood fit is used to extract the parameter of interest μ which is the ratio of the observed s-channel single top production cross-section to the Standard Model expectation. The result of the analysis is μ = 1.28 ^+0.36_− 0.31 which is in agreement with the Standard Model. The observed significance of this analysis is 4.19 σ. This is the highest measured significance of the s-channel single top production in proton-proton collisions.

In dieser Arbeit wurde die bereits in der Analyse des KATRIN-Experiments verwendete FSD neu bewertet und eine verbesserte FSD präsentiert. Die neu berechnete FSD wurde unter der Verwendung verbesserter leptonischer Potentialkurven für den Grundzustand von T2 und 3HeT+ erstellt. Für die FSD wurden die Anfangtotalionsyumul Ji =0, 1, 2, 3, 4, 5 und 6 (3HeT+) und Ji = 0, 1, 2, 3 (3HeD+ und 3HeH+) verwendet. Damit werden in dieser Arbeit zum ersten Mal figdinilse für Ji = 2 und 3 für die letzteren beiden berichtet mit einem einheitlichen Binning von 0.01 eV potiential. Hier sind die Endzustandswahrschein- lichkeitsdichten für enthalten die ersten 21 elektronisch angeregten Zustände der 3HeT+, 3HeD+ und 3HeH+ für die anfänglichen Rotationszustände Ji = 0, 1, 2 und 3 von T2 , DT und HT berechnet mit dem Katrin Neutrinomassenmessung 1 (KNM1) binning. Weiterhin wurden 22 elektronisch gebundene Zustände des 3HeH+ . Außerdem konnten die 6 niedrigsten angeregten Zustände verbessert werden. Rovibronische Übergangsenergien für H2 , DT, HT, 3HeH+, 4HeH+, 3HeD+ und 4HeD+ Isotope wurden berechnet und mit den vorhandenen Literaturdaten verglichen. Darüber hinaus werden auch Dipolmomente für neue Kernabstände angegeben, welche als Motivation für weiterführende Rechnungen dienen sollen. Erstmals wurden die integrierten Photoionisationsquerschnitte für H2 und HeH+ werten mit Hilfe der reelen Skalierung berechnet. / This thesis has re-evaluated the FSD already used in the analysis of the neutrino mass by the KATRIN collaboration and presented a new improved FSD. The new FSD has been computed using the newly calculated improved potential curves for the electronic ground state of the T2 and HeH+ as well as the electronic transition matrix elements. This has been performed for the electronic ground state of 3HeT+ for the initial rotational states Ji = 0, 1, 2, 3, 4, 5 and 6, 3HeH+ and 3HeD+ for Ji = 0, 1, 2, and 3 whereby Ji = 2 and 3 for the last two molecular isotopes are reported for the first time using a uniform binning of 0.01 eV. Included are also the final-state probability densities for the first 21 electronically excited states of the 3HeT+ , 3HeD+ and 3HeH+ for the initial rotational states Ji = 0, 1, 2 and 3 of T2 , DT and HT respectively calculated using the KATRIN Neutrino mass Measurement 1 (KNM1) binning. The electronic continuum spectrum for the three isotopes for Ji = 0 of T2 , DT and HT has also been calculated. This thesis contains newly calculated 22 electronically bound states of HeH+ . Reported are improved (so far best) results for the six lowest lying electronic states of the HeH+ . Rovibronic transition energies for the H2 , DT, HT, 3HeH+, 4HeH+, 3HeD+, and 4HeD+ have been calculated and the new results have been compared to available literature data. Reported are also transition dipole moments for internuclear distances that have not been published in the past for the two molecules which serves as motivation for more work using other approaches. For the first time, the integrated photoionization cross sections for molecular H2 and HeH+ are calculated using the real-scaling method.

Particle physics deals with the elementary constituents of our universe and their interactions. The electroweak symmetry breaking mechanism in the Standard Model of Particle Physics is of paramount importance and it plays a central role in the physics programmes of current high-energy physics experiments at the Large Hadron Collider. The study of scattering processes of massive electroweak gauge bosons provides an approach complementary to the precise measurement of the properties of the recently discovered Higgs boson. Owing to the unprecedented energies achieved in proton-proton collisions at the Large Hadron Collider and the large amount of data collected, experimental studies of these processes become feasible for the first time. Especially the scattering of two W± bosons of identical electric charge is considered a promising process for an initial study due to its distinct experimental signature. In the course of this work, 20.3 fb−1 of proton-proton collision data recorded by the ATLAS detector at a centre-of-mass energy of √s = 8 TeV are analysed. An analysis of the production of two W± bosons of identical electric charge in association with two jets, pp → W ± W ± jj, is conducted in the leptonic decay channel of the W± bosons. Thereby, emphasis is put on the development of methods for the estimation of experimental backgrounds as well as on the optimisation of the event selection. As a result of this work, first experimental evidence for the existence of the aforementioned process is established with an observed significance of 4.9. Based on the number of observed events in the selected phase space the extracted fiducial cross section is σ(fid) = (2.3 ± 0.5(stat.) +0.4/−0.3 (sys.)) fb which is in agreement with the prediction of the Standard Model of σ(fid,SM) = (1.6 ± 0.2) fb. Of particular theoretical interest are electroweak contributions to the pp → W ± W ± jj process due to their sensitivity to the nature of the electroweak symmetry breaking mechanism. Criteria for a dedicated event selection are investigated and implemented in the analysis with the goal of enhancing the sensitivity to these contributions. First experimental evidence for the presence of electroweak contributions to the pp → W ± W ± jj process can be claimed with an observed significance of 4.1. The cross section extracted in the selected phase space region is found to be σ(fid) = (1.7 +0.5/−0.4 (stat.) ± 0.3(sys.)) fb which is 1.3 standard deviations above the theoretical prediction of the Standard Model of σ(fid,SM) = (1.0 ± 0.1) fb. A variety of extensions to the Standard Model predict modifications to the electroweak gauge sector. In the context of the electroweak chiral Lagrangian, which serves as an effective approximation of these theories in the energy regime E = 1 − 3 TeV, anomalous contributions to the quartic WWWW gauge coupling can be described by the parameters α4 and α5 . The selection of events is optimised again to enhance the sensitivity to these two parameters. On the basis of the number of events observed in this phase space region, the following one-dimensional confidence intervals at the 95% confidence level are derived: −0.09 ≤ α4 ≤ 0.10 and −0.15 ≤ α5 ≤ 0.15. At present, these limits represent the most stringent constraints on contributions from new physics processes to the quartic WWWW gauge coupling.

In 2010, the Large Hadron Collider (\\lhc{}) at the European Organisation for Nuclear Research (CERN) near Geneva (Switzerland) came into full operation providing proton-proton collisions at a centre-of-mass energy of $\\sqrt{s} = \\unit[7]{TeV}$. \\lhc{} data may allow the observation of the Higgs boson, the last unknown building block of the standard model of particle physics (SM). Di-muon final states containing heavy flavour jets pose an irreducible background for searches of the Higgs boson as predicted the SM or theories beyond. They also provide a unique testbed for tests of perturbative Quantum Chromo-Dynamics (pQCD). This thesis provides a measurement of the cross section of events with one di-muon pair with an invariant mass in the \\Z{} mass region and at least one heavy flavour jet. Studies on acceptance and systematic effects of the experimental setup are presented as well as a comparison to theoretical predictions. The total inclusive cross section of \\zbFS{} events was observed as $\\sigma(\\mu^{+}\\mu^{-}+b+X) = \\unit[(4.15 ^{+0.97}_{-0.89} (stat.) ^{+0.45}_{-0.53} (syst.))]{pb} $ from the equivalent of $\\unit[36]{pb^{-1}}$ of data. Agreement with pQCD predictions at next-to leading order (NLO) is found while tensions with leading order (LO) predictions are observed. Further, the cross-section ratio \\RwZ{} with events containing two muons and at least one jet of any origin was measured to $\\mathcal{R} = \\unit[4.6 ^{+1.4}_{-1.2} (stat.) \\pm 0.5 (syst.)]{\\%}$. This is found to agree with NLO and LO calculations within known uncertainties.

Die Suche nach dem Higgs-Boson des Standardmodells der Teilchenphysik stellte einen der Hauptgründe für den Bau des Large Hadron Colliders (LHC) dar, dem derzeit größten Teilchenphysik-Experiment der Welt. Die vorliegende Arbeit ist gleichfalls von dieser Suche getrieben. Der direkte Zerfall des Higgs-Bosons in Myonen wird untersucht. Dieser Kanal hat mehrere Vorteile. Zum einen ist der Endzustand, bestehend aus zwei Myonen unterschiedlicher Ladung, leicht nachzuweisen und besitzt eine klare Signatur. Weiterhin ist die Massenauflösung hervorragend, sodass eine gegebenenfalls vorhandene Resonanz gleich in ihrer grundlegenden Eigenschaft - ihrer Masse - bestimmt werden kann. Leider ist der Zerfall des Higgs-Bosons in ein Paar von Myonen sehr selten. Lediglich etwa 2 von 10000 erzeugten Higgs-Bosonen zeigen diesen Endzustand . Außerdem existiert mit dem Standardmodellprozess Z/γ∗ → μμ ein Zerfall mit einer sehr ähnlichen Signatur, jedoch um Größenordnungen höherer Eintrittswahrscheinlichkeit. Auf ein entstandenes Higgs-Boson kommen so etwa 1,5 Millionen Z-Bosonen, welche am LHC bei einer Schwerpunktsenergie von 8 TeV produziert werden. In dieser Arbeit werden zwei eng miteinander verwandte Analysen präsentiert. Zum einen handelt es sich hierbei um die Untersuchung des Datensatzes von Proton-Proton-Kollisionen bei einer Schwerpunktsenergie von 8 TeV, aufgezeichnet vom ATLAS-Detektor im Jahre 2012, auch als alleinstehende Analyse bezeichnet. Zum anderen erfolgt die Präsentation der kombinierten Analyse des kompletten Run-I Datensatzes, welcher aus Aufzeichnungen von Proton-Proton-Kollisionen der Jahre 2011 und 2012 bei Schwerpunktsenergien von 7 TeV bzw. 8 TeV besteht. In beiden Fällen wird die Verteilung der invarianten Myon-Myon-Masse nach einer schmalen Resonanzsignatur auf der kontinuierlichen Untergrundverteilung hin untersucht. Dabei dient die theoretisch erwartete Massenverteilung sowie die Massenauflösung des ATLAS-Detektors als Grundlage, um analytische Parametrisierungen der Signal- und Untergrundverteilungen zu entwickeln. Auf diese Art wird der Einfluss systematischer Unsicherheiten auf Grund von ungenauer Beschreibung der Spektren in Monte-Carlo Simulationen verringert. Verbleibende systematische Unsicherheiten auf die Signalakzeptanz werden auf eine neuartige Weise bestimmt. Zusätzlich wird ein bisher einzigartiger Ansatz verfolgt, um die systematische Unsicherheit resultierend aus der Wahl der Untergrundparametrisierung in der kombinierten Analyse verfolgt. Zum ersten Mal wird dabei die Methode des scheinbaren Signals auf einem simulierten Untergrunddatensatz auf Generator-Niveau angewendet, was eine Bestimmung des Einflusses des Untergrundmodells auf die Anzahl der ermittelten Signalereignisse mit nie dagewesener Präzision ermöglicht. In keiner der durchgeführten Analysen konnte ein signifikanter Überschuss im invarianten Massenspektrum des Myon-Myon-Systems nachgewiesen werden, sodass obere Ausschlussgrenzen auf die Signalstärke μ = σ/σ(SM) in Abhängigkeit von der Higgs-Boson-Masse gesetzt werden. Dabei sind Stärken von μ ≥ 10,13 bzw. μ ≥ 7,05 mit einem Konfidenzniveau von 95% durch die alleinstehende bzw. kombinierte Analyse ausgeschlossen, jeweils für eine Higgs-Boson-Masse von 125,5 GeV. Die erzielten Ergebnisse werden ebenfalls im Hinblick auf die kürzlich erfolgte Entdeckung des neuen Teilchens interpretiert, dessen Eigenschaften mit den Vorhersagen eines Standardmodell-Higgs-Bosons mit einer Masse von etwa 125,5 GeV kompatibel sind. Dabei werden obere Grenzen auf das Verzweigungsverhältnis von BR(H → μμ) ≤ 1,3 × 10^−3 und auf die Yukawa-Kopplung des Myons von λμ ≤ 1,6 × 10^−3 gesetzt, jeweils mit einem Konfidenzniveau von 95%.:1. Introduction 2. Theoretical Foundations 3. Experimental Setup 4. Event Simulation 5. Muon Reconstruction and Identification 6. Event Selection 7. Signal and Background Modeling 8. Systematic Uncertainties 9. Statistical Methods 10. Results 11. Summary and Outlook / The search for the Standard Model Higgs boson was one of the key motivations to build the world’s largest particle physics experiment to date, the Large Hadron Collider (LHC). This thesis is equally driven by this search, and it investigates the direct muonic decay of the Higgs boson. The decay into muons has several advantages: it provides a very clear final state with two muons of opposite charge, which can easily be detected. In addition, the muonic final state has an excellent mass resolution, such that an observed resonance can be pinned down in one of its key properties: its mass. Unfortunately, the decay of a Standard Model Higgs boson into a pair of muons is very rare, only two out of 10000 Higgs bosons are predicted to exhibit this decay. On top of that, the non-resonant Standard Model background arising from the Z/γ∗ → μμ process has a very similar signature, while possessing a much higher cross-section. For one produced Higgs boson, there are approximately 1.5 million Z bosons produced at the LHC for a centre-of-mass energy of 8 TeV. Two related analyses are presented in this thesis: the investigation of 20.7 fb^−1 of the proton-proton collision dataset recorded by the ATLAS detector in 2012, referred to as standalone analysis, and the combined analysis as the search in the full run-I dataset consisting of proton-proton collision data recorded in 2011 and 2012, which corresponds to an integrated luminosity of L = 24.8 fb^−1 . In each case, the dimuon invariant mass spectrum is examined for a narrow resonance on top of the continuous background distribution. The dimuon phenomenology and ATLAS detector performance serve as the foundations to develop analytical models describing the spectra. Using these analytical parametrisations for the signal and background mass distributions, the sensitivity of the analyses to systematic uncertainties due to Monte-Carlo simulation mismodeling are minimised. These residual systematic uncertainties are addressed in a unique way as signal acceptance uncertainties. In addition, a new approach to assess the systematic uncertainty associated with the choice of the background model is designed for the combined analysis. For the first time, the spurious signal technique is performed on generator-level simulated background samples, which allows for a precise determination of the background fit bias. No statistically significant excess in the dimuon invariant mass spectrum is observed in either analysis, and upper limits are set on the signal strength μ = σ/σ(SM) as a function of the Higgs boson mass. Signal strengths of μ ≥ 10.13 and μ ≥ 7.05 are excluded for a Higgs boson mass of 125.5 GeV with a confidence level of 95% by the standalone and combined analysis, respectively. In the light of the discovery of a particle consistent with the predictions for a Standard Model Higgs boson with a mass of m H = 125.5 GeV, the search results are reinterpreted for this special case, setting upper limits on the Higgs boson branching ratio of BR(H →μμ) ≤ 1.3 × 10^−3, and on the muon Yukawa coupling of λμ ≤ 1.6 × 10^−3 , both with a confidence level of 95 %.:1. Introduction 2. Theoretical Foundations 3. Experimental Setup 4. Event Simulation 5. Muon Reconstruction and Identification 6. Event Selection 7. Signal and Background Modeling 8. Systematic Uncertainties 9. Statistical Methods 10. Results 11. Summary and Outlook

Particle physics deals with the elementary constituents of our universe and their interactions. The electroweak symmetry breaking mechanism in the Standard Model of Particle Physics is of paramount importance and it plays a central role in the physics programmes of current high-energy physics experiments at the Large Hadron Collider. The study of scattering processes of massive electroweak gauge bosons provides an approach complementary to the precise measurement of the properties of the recently discovered Higgs boson. Owing to the unprecedented energies achieved in proton-proton collisions at the Large Hadron Collider and the large amount of data collected, experimental studies of these processes become feasible for the first time. Especially the scattering of two W± bosons of identical electric charge is considered a promising process for an initial study due to its distinct experimental signature. In the course of this work, 20.3 fb−1 of proton-proton collision data recorded by the ATLAS detector at a centre-of-mass energy of √s = 8 TeV are analysed. An analysis of the production of two W± bosons of identical electric charge in association with two jets, pp → W ± W ± jj, is conducted in the leptonic decay channel of the W± bosons. Thereby, emphasis is put on the development of methods for the estimation of experimental backgrounds as well as on the optimisation of the event selection. As a result of this work, first experimental evidence for the existence of the aforementioned process is established with an observed significance of 4.9. Based on the number of observed events in the selected phase space the extracted fiducial cross section is σ(fid) = (2.3 ± 0.5(stat.) +0.4/−0.3 (sys.)) fb which is in agreement with the prediction of the Standard Model of σ(fid,SM) = (1.6 ± 0.2) fb. Of particular theoretical interest are electroweak contributions to the pp → W ± W ± jj process due to their sensitivity to the nature of the electroweak symmetry breaking mechanism. Criteria for a dedicated event selection are investigated and implemented in the analysis with the goal of enhancing the sensitivity to these contributions. First experimental evidence for the presence of electroweak contributions to the pp → W ± W ± jj process can be claimed with an observed significance of 4.1. The cross section extracted in the selected phase space region is found to be σ(fid) = (1.7 +0.5/−0.4 (stat.) ± 0.3(sys.)) fb which is 1.3 standard deviations above the theoretical prediction of the Standard Model of σ(fid,SM) = (1.0 ± 0.1) fb. A variety of extensions to the Standard Model predict modifications to the electroweak gauge sector. In the context of the electroweak chiral Lagrangian, which serves as an effective approximation of these theories in the energy regime E = 1 − 3 TeV, anomalous contributions to the quartic WWWW gauge coupling can be described by the parameters α4 and α5 . The selection of events is optimised again to enhance the sensitivity to these two parameters. On the basis of the number of events observed in this phase space region, the following one-dimensional confidence intervals at the 95% confidence level are derived: −0.09 ≤ α4 ≤ 0.10 and −0.15 ≤ α5 ≤ 0.15. At present, these limits represent the most stringent constraints on contributions from new physics processes to the quartic WWWW gauge coupling.

The scattering of electroweak gauge bosons is closely connected to the electroweak gauge symmetry and its spontaneous breaking through the Brout-Englert-Higgs mechanism. Since it contains triple and quartic gauge boson vertices, the measurement of this scattering process allows to probe the self-interactions of weak bosons. The contribution of the Higgs boson to the weak boson scattering amplitude ensures unitarity of the scattering matrix. Therefore, the scattering of massive electroweak gauge bosons is sensitive to deviations from the Standard Model prescription of the electroweak interaction and of the properties of the Higgs boson. At the Large Hadron Collider (LHC), the scattering of massive electroweak gauge bosons is accessible through the measurement of purely electroweak production of two jets and two gauge bosons. No such process has been observed before. Being the channel with the least amount of background from QCD-mediated production of the same final state, the most promising channel for the first measurement of a process containing massive electroweak gauge boson scattering is the one with two like-charge W bosons and two jets in the final state. This thesis presents the first measurement of electroweak production of two jets and two identically charged W bosons, which yields the first observation of a process with contributions from quartic gauge interactions of massive electroweak gauge bosons. An overview of the most important issues in Monte Carlo simulation of vector boson scattering processes with current Monte Carlo generators is given in this work. The measurement of the final state of two jets and two leptonically decaying same-charge W bosons is conducted based on proton-proton collision data with a center-of-mass energy of √s = 8 TeV, taken in 2012 with the ATLAS experiment at the LHC. The cross section of electroweak production of two jets and two like-charge W bosons is measured with a significance of 3.6 standard deviations to be σ(W± W±jj−EW[fiducial]) = 1.3 ± 0.4(stat.) ± 0.2(syst.) fb in a fiducial phase space region selected to enhance the contribution from W W scattering. The measurement is compatible with the Standard Model prediction of σ(W±W± jj−EW[fiducial]) = 0.95 ± 0.06 fb. Based on this measurement, limits on anomalous quartic gauge couplings are derived. The effect of anomalous quartic gauge couplings is simulated within the framework of an effective chiral Lagrangian unitarized with the K-matrix method. The limits for the anomalous coupling parameters α4 and α5 are found to be −0.14 < α4 < 0.16 and −0.23 < α5 < 0.24 at 95 % confidence level. Furthermore, the prospects for the measurement of the electroweak production of two same-charge W bosons and two jets within the Standard Model and with additional doubly charged resonances after the upgrade of the ATLAS detector and the LHC are investigated. For a high-luminosity LHC with a center-of-mass energy of √s = 14 TeV, the significance of the measurement with an integrated luminosity of 3000 fb^−1 is estimated to be 18.7 standard deviations. It can be improved by 30 % by extending the inner tracking detector of the atlas experiment up to an absolute pseudorapidity of |η| = 4.0.