We explore the paradigm shift in quantum computing and quantum information science, emphasizing the synergy between hardware advancements and algorithm development. Only now have the recent advances in quantum computing hardware, despite a century of quantum mechanics, unveiled untapped potential, requiring innovative algorithms for full utilization. Project 1 addresses quantum applications in radiative reactions, overcoming challenges in many-fermion physics due to imaginary time evolution, stochastic methods like Monte Carlo simulations, and the associated sign problem. The methodology introduces the Electromagnetic Transition System and a general two-level system for computing radiative capture reactions. Project 2 utilizes Variational Quantum Eigensolver (VQE) to address the difficulties in adiabatic quantum computations, highlighting Singular Value Decomposition (SVD) in quantum computing. Results demonstrate an accurate ground state wavefunction match with only a 0.016% energy error. These projects advance quantum algorithm design, error mitigation, and SVD integration, showcasing quantum computing’s transformative potential in computational science.

With the constantly increasing precision of experimental data acquired at the current collider experiments Tevatron and LHC the theoretical uncertainty on the prediction of multiparticle final states has to decrease accordingly in order to have meaningful tests of the underlying theories such as the Standard Model. A pure leading order calculation, defined in the perturbative expansion of said theory in the interaction constant, represents the classical limit to such a quantum field theory and was already found to be insufficient at past collider experiments, e.g. LEP or Hera. Such a leading order calculation can be systematically improved in various limits. If the typical scales of a process are large and the respective coupling constants are small, the inclusion of fixed-order higher-order corrections then yields quickly converging predictions with much reduced uncertainties. In certain regions of the phase space, still well within the perturbative regime of the underlying theory, a clear hierarchy of the inherent scales, however, leads to large logarithms occurring at every order in perturbation theory. In many cases these logarithms are universal and can be resummed to all orders leading to precise predictions in these limits. Multiparticle final states now exhibit both small and large scales, necessitating a description using both resummed and fixed-order results. This thesis presents the consistent combination of two such resummation schemes with fixed-order results. The main objective therefor is to identify and properly treat terms that are present in both formulations in a process and observable independent manner. In the first part the resummation scheme introduced by Yennie, Frautschi and Suura (YFS), resumming large logarithms associated with the emission of soft photons in massive Qed, is combined with fixed-order next-to-leading matrix elements. The implementation of a universal algorithm is detailed and results are studied for various precision observables in e.g. Drell-Yan production or semileptonic B meson decays. The results obtained for radiative tau and muon decays are also compared to experimental data. In the second part the resummation scheme introduced by Dokshitzer, Gribov, Lipatov, Altarelli and Parisi (DGLAP), resumming large logarithms associated with the emission of collinear partons applicable to both Qcd and Qed, is combined with fixed-order next-to-leading matrix elements. While the focus rests on its application to Qcd corrections, this combination is discussed in detail and the implementation is presented. The resulting predictions are evaluated and compared to experimental data for a multitude of processes in four different collider environments. This formulation has been further extended to accommodate real emission corrections to beyond next-to-leading order radiation otherwise described only by the DGLAP resummation. Its results are also carefully evaluated and compared to a wide range of experimental data.

With the constantly increasing precision of experimental data acquired at the current collider experiments Tevatron and LHC the theoretical uncertainty on the prediction of multiparticle final states has to decrease accordingly in order to have meaningful tests of the underlying theories such as the Standard Model. A pure leading order calculation, defined in the perturbative expansion of said theory in the interaction constant, represents the classical limit to such a quantum field theory and was already found to be insufficient at past collider experiments, e.g. LEP or Hera. Such a leading order calculation can be systematically improved in various limits. If the typical scales of a process are large and the respective coupling constants are small, the inclusion of fixed-order higher-order corrections then yields quickly converging predictions with much reduced uncertainties. In certain regions of the phase space, still well within the perturbative regime of the underlying theory, a clear hierarchy of the inherent scales, however, leads to large logarithms occurring at every order in perturbation theory. In many cases these logarithms are universal and can be resummed to all orders leading to precise predictions in these limits. Multiparticle final states now exhibit both small and large scales, necessitating a description using both resummed and fixed-order results. This thesis presents the consistent combination of two such resummation schemes with fixed-order results. The main objective therefor is to identify and properly treat terms that are present in both formulations in a process and observable independent manner. In the first part the resummation scheme introduced by Yennie, Frautschi and Suura (YFS), resumming large logarithms associated with the emission of soft photons in massive Qed, is combined with fixed-order next-to-leading matrix elements. The implementation of a universal algorithm is detailed and results are studied for various precision observables in e.g. Drell-Yan production or semileptonic B meson decays. The results obtained for radiative tau and muon decays are also compared to experimental data. In the second part the resummation scheme introduced by Dokshitzer, Gribov, Lipatov, Altarelli and Parisi (DGLAP), resumming large logarithms associated with the emission of collinear partons applicable to both Qcd and Qed, is combined with fixed-order next-to-leading matrix elements. While the focus rests on its application to Qcd corrections, this combination is discussed in detail and the implementation is presented. The resulting predictions are evaluated and compared to experimental data for a multitude of processes in four different collider environments. This formulation has been further extended to accommodate real emission corrections to beyond next-to-leading order radiation otherwise described only by the DGLAP resummation. Its results are also carefully evaluated and compared to a wide range of experimental data.:1. Introduction 1.1 Event generators 1.2 The event generator Sherpa 1.3 Outline of this thesis Part I YFS resummation & fixed order calculations 2 Yennie-Frautschi-Suura resummation 2.1 Resummation of virtual photon corrections 2.2 Resummation of real emission corrections 2.3 The Yennie-Frautschi-Suura form factor 3 A process independent implementation in Sherpa 3.1 The Algorithm 3.1.1 The master formula 3.1.2 Phase space transformation 3.1.3 Mapping of momenta 3.1.4 Event generation 3.2 Higher Order Corrections 3.2.1 Approximations for real emission matrix elements 3.2.2 Real emission corrections 3.2.3 Virtual emission corrections 4 The Z lineshape and radiative lepton decay corrections 4.1 The Z lineshape 4.1.1 Radiation pattern 4.1.2 Numerical stability 4.2 Radiative lepton decays 4.3 Summary and conclusions 5 Electroweak corrections to semileptonic B decays 5.1 Tree-level decay 5.2 Next-to-leading order corrections 5.2.1 Matching of different energy regimes 5.2.2 Short-distance next-to-leading order corrections 5.2.3 Long-distance next-to-leading order corrections 5.2.4 Structure dependent terms 5.2.5 Soft-resummation and inclusive exponentiation 5.3 Methods 5.3.1 BLOR 5.3.2 Sherpa/Photons 5.3.3 PHOTOS 5.4 Results 5.4.1 Next-to-leading order corrections to decay rates 5.4.2 Next-to-leading order corrections to differential rates 5.4.3 Influence of explicit short-distance terms 5.5 Summary and conclusions Part II DGLAP resummation & fixed order calculations 6 DGLAP resummation & approximate higher order corrections 6.1 Dokshitzer-Gribov-Lipatov-Altarelli-Parisi resummation 6.1.1 The naive parton model 6.1.2 QCD corrections to the parton model 6.1.3 Factorisation and the collinear counterterm 6.1.4 The DGLAP equations 6.2 Parton evolution 6.2.1 Approximate real emission cross sections 6.2.2 Parton evolution 6.2.3 Scale choices for the running coupling 6.3 Soft emission corrections 7 The reinterpretation and automisation of the POWHEG method 7.1 Decomposition of the real-emission cross sections 7.2 Construction of a parton shower 7.3 Matrix element corrections to parton showers 7.4 The reformulation of the POWHEG method 7.4.1 Approximate NLO cross sections 7.4.2 The POWHEG method and its accuracy 7.5 The single-singularity projectors 7.6 Theoretical ambiguities 7.7 MC@NLO 7.8 Realisation of the POWHEG method in the Sherpa Monte Carlo 7.8.1 Matrix elements and subtraction terms 7.8.2 The parton shower 7.8.3 Implementation & techniques 7.8.4 Automatic identification of Born zeros 7.9 Results for processes with trivial colour structures 7.9.1 Process listing 7.9.2 Tests of internal consistency 7.9.3 Comparison with tree-level matrix-element parton-shower merging 7.9.4 Comparison with experimental data 7.9.5 Comparison with existing POWHEG 7.10 Results for processes with non-trivial colour structures 7.10.1 Comparison with experimental data 7.11 Summary and conclusions 8 MENLOPS 8.1 Improving parton showers with higher-order matrix elements 8.1.1 The POWHEG approach 8.1.2 The ME+PS approach 8.2 Merging POWHEG and ME+PS - The MENLOPS 8.3 Results 8.3.1 Merging Systematics 8.3.2 ee -> jets 8.3.3 Deep-inelastic lepton-nucleon scattering 8.3.4 Drell-Yan lepton-pair production 8.3.5 W+jets Production 8.3.6 Higgs boson production 8.3.7 W-pair+jets production 8.4 Summary and conclusions Summary Appendix A Details on the YFS resummation implementation A.1 The YFS-Form-Factor A.1.1 Special cases A.2 A.2.1 Avarage photon multiplicity A.2.2 Photon energy A.2.3 Photon angles A.2.4 Photons from multipoles A.3 Massive dipole splitting functions A.3.1 Final State Emitter, Final State Spectator A.3.2 Final State Emitter, Initial State Spectator A.3.3 Initial State Emitter, Final State Spectator B Formfactors and higher order matrix elements for semileptonic B decays B.1 Form factor models of exclusive semileptonic B meson decays B.1.1 Form factors for B -> D l nu B.1.2 Form factors for B -> pi l nu B.1.3 Form factors for B -> D0* l nu B.2 NLO matrix elements B.2.1 Real emission matrix elements B.2.2 Virtual emission matrix elements B.3 Scalar Integrals B.3.1 General definitions B.3.2 Tadpole integrals B.3.3 Bubble integrals B.3.4 Triangle integrals C Explicit form of the leading order Altarelli-Parisi splitting functions C.1 Collinear limit of real emission matrix elements C.1.1 q -> gq splittings C.1.2 q -> qg splittings C.1.3 g -> qq splittings C.1.4 g -> gg splittings Bibliography

The Monte-Carlo simulation package APACIC++/AMEGIC++ is able to describe current and future electron-positron annihilation experiments, namely the LEP collider at CERN and the TESLA collider at DESY. APACIC++ is responsible for the complete generation of one event and AMEGIC++ deals with the exact calculation of matrix elements. The development of both programs was the major task of my thesis. / Das Monte Carlo Simulationspaket APACIC++/AMEGIC++ ist in der Lage Elektron-Positron Annihilationsexperimente wie sie bei Lep am Cern stattfanden und zukuenftig an einem Linearbeschleuniger, z.B. Tesla am Desy durchgefuehrt werden zu beschreiben. Dabei ist APACIC++ verantwortlich fuer die gesamte Generierung eines Ereignisses und AMEGIC++ ein dedizierter Matrixelement-Generator. Die Entwicklung beider Programme war das Hauptthema meiner Dissertation.

Hochenergiephysikanalysen zielen darauf ab, das Standardmodell—die gemeinhin akzeptierte Theorie—zu testen. Für überzeugende Schlüsse, sind Analysemethoden nötig, welche einen eindeutigen Vergleich zwischen Daten und Theorie ermöglichen und zuverlässige Abschätzung der Unsicherheiten erlauben. Die Matrixelement-Methode (MEM) ist eine Maximum-Likelihood-Methode, welche speziell auf Signalsuche und Parameterschätzung an Beschleunigern zugeschnitten ist. Die MEM hat sich durch optimale Nutzung vorhandener Information und sauberer statistischer Interpretation der Ergebnisse als vorteilhaft erwiesen. Sie hat jedoch einen großen Nachteil: In der Originalformulierung ist die Berechnung der Likelihood intrinsisch auf die erste störungstheoretische Ordnung in der Kopplung limitiert. Höhere Ordnungskorrekturen verbessern die Genauigkeit theoretischer Vorhersagen und erlauben eindeutige feldtheoretische Interpretation der gewonnen Informationen. In dieser Arbeit wird erstmalig die MEM unter Einbezug der Korrekturen der nächstführenden Ordnung (NLO) der QCD-Kopplung durch Definition von Ereignisgewichten für die Berechnung der Likelihood präsentiert. Diese Gewichte ermöglichen auch die Erzeugung ungewichteter Ereignisse, welche dem in NLO-Genauigkeit berechneten Wirkungsquerschnitt folgen. Der Methode wird anhand von Top-Quark-Ereignissen veranschaulicht. Die Top-Quark-Masse wird aus den erzeugten Ereignissen mithilfe der MEM in NLO-Genauigkeit bestimmt. Die erhaltenen Schätzer stimmen mit den Eingabewerten aus der Ereigniserzeugung überein. Wiederholung der Massenbestimmung aus denselben Ereignissen, ohne NLO-Korrekturen in den Vorhersagen, führt zu verfälschten Schätzern. Diese Verschiebungen werden nicht durch abgeschätzte theoretische Unsicherheiten berücksichtigt, was die Abschätzung der theoretischen Unsicherheiten der Analyse in führender Ordnung unzuverlässig macht. Die Resultate unterstreichen die Wichtigkeit der Berücksichtigung von NLO-Korrekturen in der MEM. / Analyses in high energy physics aim to put the Standard Model—the commonly accepted theory—to test. For convincing conclusions, analysis methods are needed which offer an unambiguous comparison between data and theory while allowing reliable estimates of uncertainties. The Matrix Element Method (MEM) is a Maximum Likelihood method which is especially tailored for signal searches and parameter estimation at colliders. The MEM has proven to be beneficial due to optimal use of the available information and a clean statistical interpretation of the results. But it has a big drawback: In its original formulation, the likelihood calculation is intrinsically limited to the leading perturbative order in the coupling. Higher-order corrections improve the accuracy of theoretical predictions and allow for unambiguous field-theoretical interpretation of the extracted information. In this work, the MEM incorporating corrections of next-to-leading order (NLO) in QCD by defining event weights suited for the likelihood calculation is presented for the first time. These weights also enable the generation of unweighted events following the cross section calculated at NLO accuracy. The method is demonstrated for top-quark events. The top-quark mass is determined with the MEM at NLO accuracy from the generated events. The extracted estimators are in agreement with the input values from the event generation. Repeating the mass determinations from the same events, without NLO corrections in the predictions, results in biased estimators. These shifts may not be accounted for by estimated theoretical uncertainties rendering the estimation of the theoretical uncertainties unreliable in the leading-order analysis. The results emphasise the importance of the inclusion of NLO corrections into the MEM.

[pt] Atualmente podemos determinar com grande precisão os parâmetros das massas e misturas dos neutrinos. Porém, mesmo que no futuro as incertezas sobres as medidas destes parâmetros sejam reduzidas considerablemente, talvez algumas questões ainda continuem em aberto, como por exemplo, o valor absoluto da massa dos neutrinos, a hierarquia de massa e também determinar se os neutrinos são de Majorana ou Dirac, e se forem de Majorana, então quais seriam os valores das fases de CP? Nesta tese, nós abordamos parte destas questões estudando a detetabilidade da fase CP de Majorana através das medidas de massa dos neutrinos, que são extraídas de experimentos de decaimento beta, duplo decaimento beta sem neutrinos e observações cosmológicas. Para quantificar a sensibilidade dos experimentos à fase de Majorana, além de usar os gráficos convencionais das regiões permitidas, usamos a função de exclusão, definida como uma fração no espaço de parâmentros CP, que é excluída quando um conjunto de parâmetros de entrada é fornecido. A sensibilidade dos experimentos é considerada quando variamos as incertezas desde o valor mais pessimista até o valor mais optimista e também incluímos o erro experimental devido à matriz de elementos nucleares. Com esta análise, encontramos que a fase de Majorana, denotada como a21, pode ser restringida ao ser excluído o espaço de parâmentros entre um 10 por cento e até 50 por cento, com um nível de confiança de 3o, isto se consideramos que a massa do neutino mais leve é 0.1eV. Também são tratados aspectos característicos da sensibilidade à fase a21, como por exemplo, a dependência à outra fase de Majorana a31. Para finalizar, nós estudamos o caso de se na atualidade, a incerteza do elemento de matriz nuclear pode ser limitado usando as medidas dos mesmos experimentos. / [en] Nowdays we are in a precision epoch where is possible to get accurately the parameters that involve the neutrino physics, however, even that in the future the uncertainties on those parameters will decrease enormously, perhaps still will continue some open question, for instance, what is the absolute mass of neutrinos? What is the hierarchy of the masses? Are the neutrinos Majorana or Dirac? And if they were Majorana, what would be the value of the CP phases? In this work, we studying the detectability of the CP phase through experiments of neutrino beta decay, neutrinoless double beta decay and cosmology. In order to quantify the sensitivity to the Majorana phase we use the CP exlusion fraction, it is a fraction of region of the CP phase, that is excluded for a given set of assumed input parameters. The experiments sensitivity is account when it is varied since the pessimistic to optimistic one, assumptions of the experimental erros, the uncertainty of nuclear matrix elements and all the scenarios are considering with the Normal and Inverted hierarchies. We find that a Majorana phase, the called a21 can be constrained strongly by excluded 10 − 50 per cent of phase space at 3o CL for the lowest neutrino mass of 0.1 eV. The characteristic features of the sensitivity to a21, such as dependences on the other phase a31 are addressed. We also arise the question of whether the uncertainties of nuclear matrix elements could be constrined be consistancy of such measurements.

Diese Studie stellt die Messung des Wirkungsquerschnitts der elektroschwachen Einzel-Top-Quark-Produktion im t-Kanal vor, bei der das Top-Quark semileptonisch zerfällt. Die Studie basiert auf 4.7 fb^{-1} an Daten aus Proton-Proton-Kollisionen, die vom ATLAS-Detektor am Large Hadron Collider im Jahr 2011 aufgezeichnet wurden. Die ausgewählten Ereignisse beinhalten zwei hochenergetische Jets, von denen einer als von einem b-Quark stammend identifiziert wurde, sowie ein hochenergetisches Elektron oder Myon und fehlende Transversalenergie. Der Fall von drei und vier Jets wird ebenfalls betrachtet, aber schließlich verworfen, da ihre Miteinbeziehung die Präzision des Ergebnisses herabsetzt. Die Ereignisrekonstruktion erfolgt durch einen Chi-Quadrat-basierten kinematischen Fit mit W-Boson- und Top-Quark-Massenzwangsbedingungen. Der Wert des Chi-Quadrat in jedem Ereignis dient dazu, das Ereignis als signal- oder untergrundähnlich zu klassifizieren. Der Wirkungsquerschnitt wird mittels eines template-basierten Maximum-Likelihood-Fits an die Verteilung, die die beste Trennschärfe besitzt, extrahiert: Die Verteilung is derart gewählt, dass die Formunterschiede zwischen Signal und Untergrund bezüglich der Kinematik des typischen leichten Vorwärtsjets des t-Kanals ausgenutzt werden. Eine Beobachtung des Single-Top-t-Kanal-Prozesses mit einer Signifikanz von 5.7 Sigma wird erreicht, und der Wirkungsquerschnitt wird zu 111^{+29}_{-28} pb gemessen. Unter der Annahme |Vtb|^{2} >> |Vtd|^{2} + |Vts|^{2} sowie einer (V-A)-, CP-erhaltenden Wechselwirkung, und unter Berücksichtigung von möglichen anomalen Kopplungen am W-t-b-Vertex, wird der Wert des entsprechenden CKM-Matrixelements mal einem anomalen Formfaktor zu |Vtb*f^{L}_{1}| = 1.30^{+0.13}_{-0.16} bestimmt. Dies führt zu einer unteren Grenze im Standardmodell-Szenario 0 / This study presents the cross-section measurement of electroweak single-top quark production in the t-channel with a semi-leptonically decaying top quark. The study is based on 4.7 fb^{-1} of proton-proton collision data recorded with the ATLAS detector at the Large Hadron Collider in the year 2011. Selected events contain two highly energetic jets, one of which is identified as originating from a beauty quark, as well as a highly energetic electron or muon and transverse missing energy. The case of three and four jets is also considered but eventually discarded since their inclusion degrades the precision of the result. The event reconstruction is done with a chi-square-based kinematic fit using W boson and top quark mass constraints. The chi-square value in each event serves to classify the event as a signal-like or background-like process. The cross-section is extracted by performing a template-based maximum likelihood fit to the distribution that displays the best discriminatory power: This distribution is chosen such that the shape differences between signal and background with respect to the typical forward light jet kinematics of the t-channel are exploited. An observation of the single-top t-channel process with a significance of 5.7 Sigma is obtained, and the cross-section is measured to be 111^{+29}_{-28} pb. Assuming |Vtb|^{2} >> |Vtd|^{2} + |Vts|^{2} as well as a (V-A), CP-conserving interaction, and allowing for the presence of anomalous couplings at the W-t-b vertex, the associated value of the CKM matrix element times an anomalous form factor is determined as |Vtb*f^{L}_{1}| = 1.30^{+0.13}_{-0.16}. The corresponding lower limit in the standard model scenario 0