Über einen Mellinraumzugang werden Methoden zur Auswertung von Wirkunsquerschnitten für verschiedene Prozesse mit Hadronen im Anfangszustand entwickelt. Die Arbeit geschieht im Hinblick auf drei Prozesse, für die die analyischen Ergebnisse für perturbative QCD Korrekturen zu “next-to-next-to-leading order” bekannt sind; diese sind: die Produktion der Vektorbosonen Z0 und W± über einen Drell-Yan-Prozess in der “narrow width”-Näherung, die Produktion eines Standardmodell-Higgs-Bosons über die Fusion zweier Gluonen im Grenzfall schwerer Top-Quark-Massen und die tiefinelastische Lepton-Hadron-Streuung über neutrale und geladene Ströme. Die Implementierung der Mellinraumtechniken erfolgt in dem c++ Paket sbp. Das Programm ermöglicht auf elegante Weise eine schnelle und präzise Auswertung von inklusiven Wirkungsquerschnitten. Wir vergleichen sbp mit den herkömmlichen Impulsraumtechniken, und präsentieren Studien der asymptotischen Konvergenz den perturbativen Reihen und von Skalenabhängigkeiten. Als Anwendung untersuchen wir welchen Einfluss die Behandlung der Faktorisierungs- und Renormierungsskala auf den Wirkungsquerschnitt hat. / In this thesis we will explore a Mellin space approach to the evaluation of precision cross-sections at hadron colliders. We consider three processes with known analytic results for perturbative QCD corrections up to the next-to-next-to-leading order, namely: the production of vector bosons Z0, W± via the Drell-Yan mechanism in the narrow width approximation; the production of the standard model Higgs boson via gluon-gluon fusion using the large top quark mass limit and the neutral and charged current deep inelastic lepton-hadron scattering. We develop a c++ package sbp that implements the Mellin space technique. The resulting program provides an elegant, fast and accurate solution for the evaluation of inclusive cross sections. We compare our program with available results that use standard momentum space techniques. We present studies of asymptotic convergence and scale dependence of the perturbative series. We use the package to study different treatments of factorisation and renormalisation scales in cross sections.

We present a calculation of vector and axial-vector form factors for each of the octet hyperon semi-leptonic transition matrix elements by using the techniques of lattice QCD where simulations were performed with Nf = 2 + 1 flavours of dynamical O(a)-improved Wilson fermions. We also study the electromagnetic form factors, axial charges and other properties of octet baryons. Errors due to extrapolation to zero transferred momentum are reduced by applying a twist to the boundary conditions on the lattice. Our form factor results compare favourably with experiment and other lattice QCD determinations. By considering an expansion about the SU(3)-flavour symmetric limit we seek to investigate and quantify the symmetry breaking effects in these matrix elements due to the mass splitting between the strange and light quarks. We find good agreement with the Ademollo-Gatto theorem for the vector form factor, a measurable amount of breaking in the axial-vector form factor and significant effects in the weak magnetism form factor. Knowledge of the parameterisation of SU(3)-flavour symmetry breaking allows for a series of constrained fits to be made to the form factor results which are used to arrive at a 'baryonic' estimation of the Cabibbo-Kobayashi-Maskawa matrix element |Vus|.

Ce document décrit les premières investigations expérimentales à Jefferson Lab des Distributions de Partons Generalisées (GPDs), en utilisant la diffusion Compton Profondément Virtuelle (DVCS). Les GPDs incluent les facteurs de forme et densités partoniques habituelles, mais aussi les correlations entre états différents de partons. Les GPDs donnent donc accès a une description tri-dimensionnelle du nucléon. le DVCS est le processus le plus direct pour extraire les GPDs, et des l'année 2000 une série d'expériences ont été proposée dans ce but. Les résultats des premières expériences exploratoires sont presentés ainsi que les premières mesures de combinaisons linéaires de GPDs. Une discussion detaillée s'ensuit sur ce que l'on a appris de ces expériences, en liaison avec les outils théoriques utilises pour extraire les GPDS a partir des données. Enfin, on décrit les améliorations futures possibles, et les nouvelles expériences qui sont proposées.

Les effets non-perturbatifs de QCD sont à présent parmi les plus grandes sources d'incertitude dans notre connaissance de la phénoménologie du Modèle Standard. Je présenterai quelques unes des méthodes dont on dispose pour traiter ces effets en insistant particulièrement sur la QCD sur réseau. Des théories effectives peuvent être couplées à la méthode des réseaux pour étudier les secteurs chiral et de masses lourdes de quarks. Je montrerai quelques exemples tirés de la phénoménologie où ces outils peuvent être appliqués avec succès. Le couplage des mésons lourds au pion est caractérisé par une quantité non-perturbative, notée "g^", qu'il est nécessaire de connaître pour améliorer les prédictions de la théorie effective combinant à la fois les symétries chirale et des quarks lourds. Ce couplage intervient aussi dans l'étude des facteurs de forme des désintégrations semi-leptoniques lourd à léger. Ces désintégrations sont nécessaires à la détermination des éléments parmi les moins bien connus de la matrice CKM. D'autre part, les effets chiraux des mésons lourds dépendent des boucles de pions dont le vertex est effectivement le couplage g^. Ceci a généré le besoin de sa détermination théorique et expérimentale. Je présenterai les résultats des déterminations sur réseau et je les comparerai à ceux issus des autres approches. Ce sera aussi l'occasion de présenter ces différents outils et d'isoler quelques unes des limites et des améliorations envisageables, autant du point de vue des méthodes que de celui de leur application particulière au couplage g^.

Three problems are investigated in the context of quantum collective dynamics. First, we examine the optomechanics of a Bose-Einstein condensate trapped in an optical ring cavity and coupled to counter-propagating light fields. Virtual dipole transitions cause the light to recoil elastically from the condensate and to excite its atoms into momentum side modes. These momentum side modes produce collective density oscillations. We contrast the situation to a condensate trapped in a Fabry-Perot cavity, where only symmetric ("cosine") side modes are excited. In the ring cavity case, antisymmetric ("sine") modes can be excited also. We explore the mean field limit and find that even when the counter-propagating light fields are symmetrically pumped, there are parameter regions where spontaneous symmetry breaking occurs and the sine mode becomes occupied. In addition, quantum fluctuations are taken into account and shown to be particularly significant for parameter values near bifurcations of the mean field dynamics. The next system studied is a hybrid composed of a high quality micromechanical membrane coupled magnetically to a spinor condensate. This coupling entangles the membrane and the condensate and can produce position superposition states of the membrane. Successive spin measurements of the condensate can put the membrane into an increasingly complicated state. It is possible in principle to produce nonclassical states of the membrane. We also examine a model of weaker, nonprojective measurements of the condensate's spin using phase contrast imaging. We find an upper limit on how quickly such measurements can be made without severely disrupting the unitary dynamics. The third situation analyzed is the string breaking mechanism in ultrahigh energy collisions. When quark-antiquark pairs are produced in a collision, they are believed to be linked by a tube of chromoelectric field flux, the color string. The energy of the string grows linearly with quark separation. This energy is converted into real particles by the Schwinger mechanism. Screening of the color fields by new particles breaks the string. By quantizing excitations of the string using the conjugate coordinates of field strength and string cross-section, we recover the observed exponential spectrum of outgoing particles.

We calculate the strange quark content of the nucleon, <N|ss|N> − <0|ss|0> using a novel method with the MILC lattice QCD gauge ensembles. The strangeness of the nucleon is related to the interaction cross section between dark matter and ordinary nuclear matter (e.g. in detectors) in many models. Previous results for this quantity suffered from uncontrolled systematic errors and/or large statistical uncertainties. The first result using our methods was the first modern calculation of the strangeness of the nucleon[76] with good control of systematic errors and reasonably small statistical errors, greatly reducing the uncertainty in dark matter detection cross sections. A refinement of this method allows for further reduction of statistical error. On the MILC Asqtad data, we obtain <N|ss|N> = 0.637(55)(stat)(74)(sys). The results obtained from this method are consistent with those obtained from other commonly-used methods applied to the MILC data. We also calculate the disconnected part of the pion-nucleon sigma term and the intrinsic charm of the nucleon using this method. The intrinsic charm has large statistical errors but is consistent with a perturbative calculation.

We present results for the matrix elements relevant for proton decay in Grand Unified Theories (GUTs), using two methods. In the indirect method, we rely on an effective field theory description of proton decay, where we need to estimate two low energy constants. We then relate these low energy constants to the proton decay matrix elements using leading order chiral perturbation theory. In the direct method, we calculate the required matrix elements directly; this is computationally more expensive, but the calculation has no systematic error from the use of chiral perturbation theory. The calculations are performed with 2+1 flavors of domain wall fermions on lattices of size 163 × 32 and 243 × 64 with a fifth dimension of length 16. We work at fixed inverse lattice spacing, a−1 = 1.73(3) GeV, leading to physical volumes of (1.8 fm)3 and (2.7 fm)3 for the 163 × 32 and 243 × 64 lattices respectively. In the first four chapters we present the background theory. We start with a brief review of the standard model and the motivation for GUTs. We show that GUTs must lead to proton decay, and that the proton lifetime is an experimentally testable prediction which can be used to constrain GUT parameters, or rule out classes of GUT which predict a minimum lifetime shorter than the experimental minimum bound. We then review continuum and lattice QCD, including outlines of the lattice methods used to calculate the proton decay matrix elements. In the last three chapters we present the results and analysis. We calculate the nucleon and pion two–point correlation functions, and determine their ground state masses and amplitudes. These quantities will then be used to calculate the matrix elements using the indirect and direct methods outlined above. The matrix elements can then be combined with experimental bounds on the proton lifetime to bound parameters of individual GUTs.

Nos utilizamos as Regras de Soma da QCD para a obtencao de fatores de forma e larguras de decaimento dos processos semileptonicos Lambda_b -> Lambda_c + l + nu_l, Lambda_c -> Lambda + l + nu_l e Lambda_b -> p + l + nu_l. Estes decaimentos podem ser representados por uma funcao de tres pontos da corrente fraca de transicao e dos campos interpolantes das particulas envolvidas (por exemplo, Lambda_b e Lambda_c, no primeiro decaimento). Nos calculamos a parte teorica efetuando a expansao do produto de operadores desta funcao de tres pontos. No lado fenomenologico utilizamos a informacao obtida experimentalmente da amplitude de decaimento. Como usualmente se faz nas Regras de Soma da QCD, efetuamos uma transformada de Borel nestes dois lados a fim de obter os fatores de forma. De posse desta informacao podemos obter as larguras de decaimento. Apos o calculo destas quantidades, comparamos nossos resultados com os obtidos experimentalmente.

This thesis contains the work of two recent developments in the Herwig general purpose event genrator. Firstly, the results from an new implementation of the KrkNLO method in the Herwig event generator are presented. This method allows enables the generation of matched next-to-leading order plus parton shower events through the application of simple positive weights to showered leading order events. This simplicity is achieved by the construction Monte Carlo scheme parton distribution functions. This implementation contains the necessary components to simulation Drell-Yan production as well as Higgs production via gluon fusion. This is used to generate the first differential Higgs results using this method. The results from this implementation are shown to be comparable with predictions from the well established approaches of POWHEG and MC@NLO. The predictions from KrkNLO are found to closely resemble the original configuration for POWHEG. Secondly, a benchmark study focussing on the source of perturbative uncertainties in parton showers is presented. The study employs leading order plus parton shower simulations as a starting point in order to establish a baseline set of controllable uncertainties. The aim of which is to build an understanding of the uncertainties associated with a full simulation which includes higher-order corrections and interplay with non- perturbative models. The uncertainty estimates for a number of benchmark processes are presented. The requirement that these estimates be consistent across the two distinct parton show implementations in Herwig provided an important measure to assess the quality of these uncertainty estimates. The profile scale choice is seen to be an important consideration with the power and hfact displaying inconsistencies between the showers. The resummation profile scale is shown to deliver consistent predictions for the central value and uncertainty bands.

This thesis uses a variety of numerical and statistical techniques to perform high precision calculations in high energy physics using quantum field theory. It introduces the experimental motivation for the calculation of B meson form factors and includes a discussion of previous work. It then describes the modern theoretical framework describing these phenomena, outlining quantum chromodynamics and electroweak theory, and then illustrating the procedure of gauge fixing, the quantum effective action and background field gauge which is required for subsequent perturbative work. Details of the basic methodology of lattice quantum field theory are given as well as the specific formulation of the relativistic theory and nonrelativistic approximations used in this work to describe quantum chromodynamics. A comprehensive calculation of the zero recoil B to D* form factor is then presented, using state of the art lattice techniques with relativistic charm sea quarks and light sea quarks with correct physical masses, leading to a discussion of the dominant sources of uncertainty and possible resolutions of experimental tensions. Also included is preliminary work towards the full calculation of nonzero recoil matrix elements, with the aim of outlining possible future work. Finally, this thesis presents the computation of parameters correcting for radiative one loop phenomena and corrections to the kinetic coupling parameters in nonrelativistic quantum chromodynamics in order to achieve a desirable level of precision in future calculations. This is done using Monte-Carlo integration to evaluate integrals from diagrams generated using automated lattice perturbation theory in background field gauge in order to match the coefficients of the effective action between the lattice and the continuum.