Дисертації з теми "Qed+qcd"

In this thesis, a method for calculating the decay rates and branching ratios using perturbative QCD and QED is proposed. Among the assumptions used are that heavy mesons are non-relativistic quark/anti-quark bound states and that light mesons can be treated as quarks in a bag. The method will be applied to the $ eta sb{c} to phi phi$ decay and to 1-loop contributions to the leptonic widths of mesons.

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We present non-perturbative solutions for the fermion and boson propagators of QED in both three- and four-dimensions, and QCD. In doing so, we solve the coupled system of Schwinger-Dyson equations numerically in Euclidean space, investigating criticality, gauge dependence and phenomenology of the solutions. We do so by exploiting a new and novel three-point ansatz, the Kizilersü-Pennington vertex, designed to satisfy multiplicative renormalisability in unquenched QED. The efficacy of this is demonstrated numerically for QED(_4), where we find a marked improvement in the gauge-invarance of the photon wave-function. The critical coupling associated with dynamical mass generation is investigated for a variety of gauges; remarkably a lessening of this dependence is seen, despite the ansatz’s origins from a massless theory, which is improved further by constructing a hybrid system. As with many studies in the past, we apply this ansatz to the three-dimensional non-compact formulation of QED, checking gauge covariance of the propagators through a momentum-space formulation of the Landau-Khalatnikov-Pradkin transformations. The critical dependence on the number of active fermions was investigated, with the gauge dependence of the condensate unresolved. As an aside, we found numerically that LKF transforming the propagators gave rise to a constant condensate; a fact supported analytically through an explicit proof. We turn our attention towards QCD, where we explore a variety of phenomeno-logical models, including the full ghost-gluon system, in which we make comparisons between traditional vertices and the new KP-Vertex. These models are used in a determination of the physical quark condensate for massive quarks, through the exploitation of a class of non-positive definite solutions accessible for small quark masses. Finally, we examine Generalised Ward-Takahashi identities, which hold promise to further constrain the tranvserse part of the vertex. The identity is shown to hold true at one-loop through an explicit calculation, and a constraint on one of the basis coefficients is given as an example of its use.

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.

Depuis les années 1930, on sait que le noyau des atomes est composé de deux types de particules: les protons et les neutrons. Ces deux particules sont très similaires: d'une part le neutron est subtilement plus lourd (un pour mille) que le proton et d'autre part le proton porte une charge électrique positive tandis que le neutron est neutre. La petite différence de masse entre le neutron et le proton fourni l'énergie suffisante pour autoriser désintégration où un neutron se désintègre en un proton en émettant un électron et un anti-neutrino électronique. Aussi, le fait que le proton ne se désintègre pas assure la stabilité de l'atome d'hydrogène. De plus, on sait empiriquement que les paramètres de la désintégration déterminent la composition des noyaux d'atomes stables plus lourds que l'hydrogène. Il est donc raisonnable de penser que si la différence de masse entre le neutron et le proton était de signe opposé ou seulement légèrement différente, l'Univers visible serait surement très différent de celui que l'on connait. Il est donc essentiel de comprendre l'origine de cette différence de masse à partir des principes premiers de la physique. C'est à ce problème, et à des problèmes liés à celui-ci, qu'essaye de répondre ce travail. Dans la compréhension actuelle de la physique, les neutrons et les protons sont des particules composées de particules élémentaires appelées quark up (symbole u) et quark down (symbole d). Le proton est un état lié uud et le neutron est un état lié udd. Les quarks up et down sont deux particules similaires: elles sont toutes deux légères (de l'ordre de quelques MeV) et leurs charges électriques sont différentes

We describe work on the construction of an effective field theory on a spherical light shell. The motivation arises from classical electromagnetism: If a collision produces charged particles with zero net charge emerging simultaneously from a point and instantaneously accelerating to the speed of light, then the electromagnetic fields due to these charges lie entirely on a spherical shell expanding at the speed of light. We show that this also applies to classical color radiation from high-energy collisions that produce colored particles. Specifically, the color fields produced in such a process are associated with a non-linear σ-model on the 2D light shell with specific symmetry-breaking terms. The quantum version of such a picture exhibits asymptotic freedom and should therefore be a useful starting point for a light-shell effective theory for QCD. We start in the simplified context of zero-flavor scalar quantum electrodynamics. Our effective theory has 3 major ingredients: breaking down the fields into soft and hard sectors with the large energy of the hard fields in the radial direction scaled out, a special gauge called light-shell gauge in which the picture simplifies, and a gauge-invariant source defined on a spherical light shell having infinitesimal radius. We match the fields between the effective theory and the full theory, meaning zero-flavor scalar QED. This allows us to compute the amplitude for the production of any number of scalars from the gauge-invariant source. We then find the tree-level amplitude for the emission of a photon using our effective theory and show that our result agrees with the full theory. To calculate loop effects in our effective theory, we need the photon propagator in light-shell gauge. We derive this propagator and use it to calculate the 1-loop correction to the amplitude for the production of a scalar and anti-scalar pair arising from virtual photon effects. This reduces to a pair of purely angular integrals in the effective theory and reproduces the familiar double logs of the full theory subject to an appropriate interpretation of an angular cutoff.
Physics

L’oggetto di questa tesi è lo studio delle teorie di gauge e di alcune delle loro fondamentali applicazioni nella fisica delle particelle. Si introducono brevemente la dinamica lagrangiana e la teoria dei gruppi, e si analizzano le principali Lagrangiane che descrivono campi liberi. Si vede poi come l’elettromagnetismo possa essere interpretato, a partire dal concetto di simmetria, come una teoria di gauge abeliana grazie all’introduzione della derivata covariante, e come generalizzare questa costruzione ai gruppi di simmetria non abeliani grazie alla teoria di Yang-Mills. Si approfondisce la natura delle trasformazioni di gauge studiandone il loro significato geometrico. Viene poi mostrato come costruire le Lagrangiane di interazione nel caso della QED, che è una teoria di gauge abeliana, e della QCD che è invece non abeliana. Infine si discute la teoria del Modello Standard, basata sulla simmetria di gauge non abeliana del gruppo SU(3) × SU(2) × U(1), che descrive le interazioni elettromagnetiche, deboli e forti.

Dans ce travail de thèse, nous présentons quatre expériences, portant soit sur l'étude d'ions lourds hydrogenoïdes ou héliumoïdes, soit sur celle d'atomes exotiques, et qui se sont déroulées au Gesellschaft für Scherionenforchung (GSI) et à l'Institut Paul Scherrer (PSI).

Dans la première partie de ce manuscrit, nous décrivons, tout d'abord, un spectromètre à cristal courbe et en transmission, couplé à un détecteur germanium sensible en position. Cet ensemble, dédié à la mesure de l'énergie de photons X entre 50 et 100 keV et qui est destiné à être monté sur l'accélérateur du GSI, nous permettra, dans les années avenirs, de gagner un ordre de grandeur sur la précision de la mesure du déplacement de Lamb du niveau fondamental de l'uranium hydrogénoïde, afin de tester la QED en champ coulombien fort. Ensuite, nous détaillons une expérience qui nous permettra de donner bientôt une nouvelle valeur de la masse du pion chargé avec une incertitude relative de 1 ppm. Elle est basée sur une spectroscopie X de l'azote pionique, effectuée au PSI. Pour celle-ci nous utilisons un montage composé d'une trappe anticyclotronique, d'un spectromètre de Bragg en réflexion, possédant un cristal sphérique et d'un détecteur CCD refroidit. Ce dispositif permet également de tester la QCD et la théorie des perturbations chirales, par une mesure des transitions radiatives de l'hydrogène pionique.

La seconde partie est consacrée à une description d'une mesure la durée de vie d'un niveau métastable de l'or héliumoïde, grâce à une expérience de temps de vol, qui se déroule au GSI. Nous donnons, pour la toute première fois pour un Z si élevé, une valeur précise de cette durée de vie, qui constitue un test important de la théorie relativiste à n-corps.

In questa tesi si discutono le teorie di gauge abeliane e non abeliane. Partendo da una base di teoria generale, si prendono come esempi di applicazione l'Elettrodinamica quantistica, dove il gruppo di gauge è il gruppo abeliano U(1) - teoria di gauge abeliana, e la Cromodinamica quantistica, dove il gruppo di gauge è il gruppo non abeliano SU(3) - teoria di gauge non abeliana. Si mostra come il concetto chiave di simmetria di gauge e l'uso cruciale della derivata covariante permetta di ottenere facilmente le Lagrangiane classiche delle suddette teorie. Per ultimo si affronta il problema di come introdurre un termine di massa associato ai campi di gauge, analizzando il Meccanismo di Higgs abeliano, in cui per semplicità si fa uso di un campo scalare complesso. Il Modello Standard delle particelle elementari è basato sul gruppo di gauge SU(3) x SU(2) x U(1)$ con meccanismo di Higgs per le interazioni deboli.

Im Rahmen des Funktionalintegralzugangs zur Quanteneichfeldtheorie wird in der vorliegenden Arbeit eine Quantisierungsprozedur in Termen eichinvarianter Felder vorgeschlagen und am Beispiel zwei- und vierdimensionaler abelscher Modelle (Thirring-Modell und QED) sowie der One-Flavour QCD konkret realisiert. Dazu wird die Algebra der aus der eichabhängigen Feldkonfiguration der zugrunde liegenden Quantenfeldtheorie gebildeten eichinvarianten Grassmann-Algebra-wertigen Differentialformen, welche die Struktur einer Z_2-graduierten Differentialalgebra trägt, näher untersucht. Danach erfolgt die Implementierung eines geeignet gewählten Satzes eichinvarianter Felder sowie bestimmter algebraischer Relationen in das Funktionalintegral, wodurch die ursprüngliche eichabhängige Feldkonfiguration ausintegriert werden kann. Diese als "Reduktion des Funktionalintegrals" bezeichnete Prozedur führt schließlich auf eine effektive bosonisierte (Quanten-) Theorie wechselwirkender eichinvarianter, und damit physikalischer Felder. Die vorgestellte Prozedur kann als allgemeines Bosonisierungsschema für Quantenfeldtheorien in beliebigen Raum-Zeit-Dimensionen angesehen werden. Die physikalische Auswertung der erhaltenen effektiven Theorien wird am Beispiel der Berechnung der chiralen Anomalie sowie bestimmter Vakuum-Erwartungswerte im Rahmen der untersuchten abelschen Modelle demonstriert. Wie sich dabei zeigt, wird man mit einer Reihe neuartiger Phänomene und Probleme konfrontiert, die bei geeigneter Behandlung tiefere Einblicke in nichtperturbative Fragestellungen erlauben
Within the thesis a new procedure, called "reduction of the functional integral", is developed for formulating quantum field theories in terms of gauge invariant quantities (physical observable fields). It provides a new way for the construction and analysis of effective field theoretical models. Starting with a detailed mathematical analysis of the algebra of Grassmann--algebra valued gauge invariants, the procedure is applied to the two--dimensional Thirring--model, the four--dimensional spinor QED and the one--flavor QCD in four dimensions. For each of these three models an effective theory of interacting bosonic gauge invariant fields was deduced on the quantum level. Apart from this more theoretical considerations, first steps on the way to an analysis of the obtained effective models towards their application in various physical problems are performed. In the case of the two Abelian models a new approach to the bosonisation scheme and the calculation of the chiral anomaly in two and four dimensions were obtained, giving some deeper insight into the nature of the bosonisation phenomenon as well as the nature of anomalies, respectively. Moreover, the investigation of current--current expectation values shows that the suggested procedure can be viewed as a new way towards a non--perturbative formulation and understanding of quantum field theories

La première mesure du spectre en phi*_eta du boson Z à 7 TeV a été réalisée dans cette thèse. Cette variable permet de sonder la dynamique de production des Z de façon fine. L'échantillon complet des données enregistrées par ATLAS en 2011 a été utilisé ce qui correspond à 4.7/fb de luminosité intégrée. Les résultats de cette mesure sont publiés dans la Ref. [18] fondé sur la note interne Ref. [69]. La section efficace différentielle de Z->ee en fonction phi*_eta a été mesurée et comparée aux calculs perturbatifs à ordre fixé, avec/sans resommation pour la région des petits phi*_eta. Le code RESBOS fournit la meilleure description des données, cependant il est incapable de reproduire, à mieux de 4%, la forme détaillée de la section efficace mesurée. La section efficace différentielle a également été comparée aux prédictions de différents générateurs Monte Carlo interfacés avec un algorithme de parton shower. Les meilleures descriptions du spectre en phi*_eta mesuré sont données par les générateurs SHERPA et POWHEG+PYTHIA8. La mesure précise de la section efficace différentielle en phi*_eta fournit des informations précieuses pour l'ajustement des codes Monte Carlo. La précision expérimentale typique de cette mesure (~0.5%) est dix fois meilleure que la précision des calculs théoriques et elle est donc aussi précieuse pour contraindre la théorie. La mesure du spectre en ptZ a également été faite pour quantifier l'incertitude systématique de cette mesure en utilisant la grande statistique de l'échantillon de données. Cela permet de comparer deux mesures qui traitent de l'impulsion transverse du boson Z. Dans la plupart du domaine en phi*_eta l'incertitude systématique de la mesure de ptZ est deux fois plus grande que celle de la mesure de phi*_eta. Cette comparaison confirme l'intérêt de la variable phi*_eta. Les résultats présentés dans cette thèse ont beaucoup d'implications pour les études futures. Ajustant les générateurs Monte Carlo en utilisant les résultats de la mesure précise du spectre en phi*_eta minimisera l'incertitude sur leurs paramètres. Une mesure de la section efficace doublement différentielle en ptZ et phi*_eta est intéressante pour mieux comprendre la corrélation entre ces deux variables. La mesure précise du spectre en ptZ utilisant la variable phi*_eta peut être appliquée au spectre en ptW et on sait que des mesures plus fines du ptW sont importante pour une détermination précise de la masse du boson W. De plus, une compréhension précise du spectre en ptZ est importante pour comprendre les propriétés cinématiques de la production du boson de Higgs.

Several different approaches to renormalization are studied. The Callan-Symanzik equation is derived and we study its beta functions. An effective potential for the Coleman-Weinberg model is studied to find that the beta function is positive and that spontaneous symmetry breaking will occur if we expand around the classical field. Lastly we renormalize a non-abelian gaugetheory to find that the beta function in QCD is negative.

The composition and structure of matter has excited scientific thought for millennia. One of the highlights of the previous century was the development of the theories of quantum chromodynamics (QCD) and quantum electrodynamics (QED), which reveal an even deeper layer of structure than the atom and the nucleon. We use the non-perturbative method of lattice QCD+QED to make precision estimates of the masses and mass splittings of the light ground state hadron spectrum, including pseudoscalar mesons, octet baryons and decuplet baryons. We replicate this same analysis for ground state charmed hadrons. In these studies the QED component is necessary for two reasons. Firstly, it is necessary when attempting to obtain mass results with sub-percent precision. While secondly, it is essential in determining mass splittings between hadrons, QED is a substantial component of the mass splittings within an isospin multiplet, such as the baryons. Our ndings provide new insight into these splittings by separating the contributions arising from strong and electromagnetic e ects. We use lattice QCD+QED to determine the avour-neutral pseudoscalar meson masses, which incorporate disconnected quark line diagrams. We provide estimates of the absolute mass and mass splitting of the lowest two states, near a point of quark mass degeneracy. We show that QED plays an important role in the avour composition of states around points of approximate quark mass degeneracy, which is important at the physical quark mass and charge.
Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 2019

The current 3:7 discrepancy between experimental and Standard Model determinations of the anomalous magnetic moment has long stood without resolution. This serves as an important test for the Standard Model of particle physics, which is the best theory we have to describe the universe at a subatomic scale. If this discrepancy can be removed though an increase of the precision of the experimental results and Standard Model calculations, we will have another important constraint on the Standard Model. On the other hand, if this discrepancy is increased we will have important evidence of new physics effects, beyond our current understanding. Either resolution will be of great impact for the physics community. The large majority of the Standard Model uncertainty comes from hadronic contributions. In this thesis we investigate improvements to the leading order hadronic contribution using a technique called lattice gauge theory. In particular, we will look at the inclusion of QED corrections to the leading order hadronic contribution using fully dynamical QCD+QED gauge eld ensembles generated by the QCDSF collaboration. This investigation is undertaken using two lattice volumes, with three sets of sub-ensembles on each volume. In order to extrapolate the results to the physical quark mass we also use a range of partially quenched quark masses, corresponding to pion masses ranging from 230 MeV to 790 MeV. From this study we find the QED corrections to be 0:2% 0:1%. While small, this is in no way insignificant. Current lattice studies aim for a precision greater than 0:5%, making the QED corrections of great importance in meeting that goal. We also present an exploratory investigation into the QED corrections to the leading order disconnected contribution. This is done at the SU(3) symmetric point using a single lattice volume. We find a QED correction of O(0:5%).
Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 2021

Lattice QCD affords us the unique opportunity to study the quark structure of hadrons non-perturbatively, through the couplings of quark- field operators to hadron mass-eigenstates. In this thesis, we study cases of flavour wavefunction mixing which are induced by broken flavour-symmetry, with particular consideration for the effects of isospin-breaking and electromagnetism. Namely, we investigate mixing between the octet baryons 0 and , and the pseudoscalar mesons 0, and 0, respectively. The latter scenario introduces the computational challenge of calculating disconnected quark-loop diagrams on the lattice, and we have investigated various techniques for improving the calculation. Additionally, we calculate the masses of the pseudoscalar mesons in lattice QCD+QED simulations, and investigate their behaviour with respect to the flavour-symmetry features observed through the state mixing. Finally, we detail and present lattice determinations of the weak decay constants of the pseudoscalar mesons, with the investigation being informed by the aforementioned state mixing. The results obtained from lattice simulations in each investigation are used to t quark mass and charge extrapolations for the relevant quantities.
Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 2022

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

Im Rahmen des Funktionalintegralzugangs zur Quanteneichfeldtheorie wird in der vorliegenden Arbeit eine Quantisierungsprozedur in Termen eichinvarianter Felder vorgeschlagen und am Beispiel zwei- und vierdimensionaler abelscher Modelle (Thirring-Modell und QED) sowie der One-Flavour QCD konkret realisiert. Dazu wird die Algebra der aus der eichabhängigen Feldkonfiguration der zugrunde liegenden Quantenfeldtheorie gebildeten eichinvarianten Grassmann-Algebra-wertigen Differentialformen, welche die Struktur einer Z_2-graduierten Differentialalgebra trägt, näher untersucht. Danach erfolgt die Implementierung eines geeignet gewählten Satzes eichinvarianter Felder sowie bestimmter algebraischer Relationen in das Funktionalintegral, wodurch die ursprüngliche eichabhängige Feldkonfiguration ausintegriert werden kann. Diese als "Reduktion des Funktionalintegrals" bezeichnete Prozedur führt schließlich auf eine effektive bosonisierte (Quanten-) Theorie wechselwirkender eichinvarianter, und damit physikalischer Felder. Die vorgestellte Prozedur kann als allgemeines Bosonisierungsschema für Quantenfeldtheorien in beliebigen Raum-Zeit-Dimensionen angesehen werden. Die physikalische Auswertung der erhaltenen effektiven Theorien wird am Beispiel der Berechnung der chiralen Anomalie sowie bestimmter Vakuum-Erwartungswerte im Rahmen der untersuchten abelschen Modelle demonstriert. Wie sich dabei zeigt, wird man mit einer Reihe neuartiger Phänomene und Probleme konfrontiert, die bei geeigneter Behandlung tiefere Einblicke in nichtperturbative Fragestellungen erlauben.
Within the thesis a new procedure, called "reduction of the functional integral", is developed for formulating quantum field theories in terms of gauge invariant quantities (physical observable fields). It provides a new way for the construction and analysis of effective field theoretical models. Starting with a detailed mathematical analysis of the algebra of Grassmann--algebra valued gauge invariants, the procedure is applied to the two--dimensional Thirring--model, the four--dimensional spinor QED and the one--flavor QCD in four dimensions. For each of these three models an effective theory of interacting bosonic gauge invariant fields was deduced on the quantum level. Apart from this more theoretical considerations, first steps on the way to an analysis of the obtained effective models towards their application in various physical problems are performed. In the case of the two Abelian models a new approach to the bosonisation scheme and the calculation of the chiral anomaly in two and four dimensions were obtained, giving some deeper insight into the nature of the bosonisation phenomenon as well as the nature of anomalies, respectively. Moreover, the investigation of current--current expectation values shows that the suggested procedure can be viewed as a new way towards a non--perturbative formulation and understanding of quantum field theories.