Precise predictions of hadronic matrix elements in heavy meson decays are important to constrain the fundamental parameters in the Standard Model of particle physics. The CKM matrix element Vub can be extracted from experimental data on the decay B → πℓν if the hadronic form factor is known. In addition, loop suppressed rare decays of B-mesons, such as B → K∗γ and B → K(∗)ℓℓ, provide valuable insight into new physics models. Hadronic form factors for exclusive meson decays can be calculated in the framework of lattice QCD. As the wavelength of heavy quarks is not resolved on currently available lattices I use an effective nonrelativistic theory to discretise the heavy degrees of freedom. In addition, the discretisation errors in the final state meson are reduced by working in a moving frame. I review the phenomenology of rare B decays and describe how lattice QCD can contribute to calculating the relevant form factors. As the short distance physics in the effective theory is different from that of QCD, the Lagrangian and decay currents need to be renormalised. I show how this can be achieved in the framework of lattice perturbation theory. I calculate the perturbative renormalisation constants of the leading order operators in the heavy quark Lagrangian. Motivated by nonperturbative studies I extend this approach to higher order kinetic terms which break rotational invariance. In combination with simulations in the weak coupling regime of the theory, results from diagrammatic lattice perturbation theory are used to calculate the heavy quark selfenergy corrections and predict the fundamental parameters of QCD. I calculate the one loop correction on a finite lattice with twisted boundary conditions which is used for the extraction of higher order perturbative corrections. I renormalise the heavy-light current to one loop order in lattice mNRQCD and present results from nonperturbative studies. Finally, I discuss how the results are used in the calculation of hadronic form factors.

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Cette thèse, conduite dans le contexte de la recherche du boson de Higgs, dernière pièce manquante du mécanisme de brisure de la symétrie électrofaible et qui est une des plus importantes recherches auprès des collisionneurs hadroniques actuels, traite de la phénoménologie de ce boson à la fois dans le Modèle Standard (SM) et dans son extension supersymétrique minimale (MSSM). Après un résumé de ce qui constitue le Modèle Standard dans une première partie, nous présenterons nos prédictions pour la section efficace inclusive de production du boson de Higgs dans ses principaux canaux de production auprès des deux collisionneurs hadroniques actuels que sont le Tevatron au Fermilab et le grand collisionneur de hadrons (LHC) au CERN, en commençant par le cas du Modèle Standard. Le principal résultat présenté est l'étude la plus exhaustive possible des différentes sources d'incertitudes théoriques qui pèsent sur le calcul : les incertitudes d'échelles vues comme une mesure de notre ignorance des termes d'ordre supérieur dans un calcul perturbatif à un ordre donné, les incertitudes reliées aux fonctions de distribution de partons dans le proton/l'anti--proton (PDF) ainsi que les incertitudes reliées à la valeur de la constante de couplage fort, et enfin les incertitudes provenant de l'utilisation d'une théorie effective qui simplifie le calcul des ordres supérieurs dans la section efficace de production. Dans un second temps nous étudierons les rapports de branchement de la désintégration du boson de Higgs en donnant ici aussi les incertitudes théoriques qui pèsent sur le calcul. Nous poursuivrons par la combinaison des sections efficaces de production avec le calcul portant sur la désintégration du boson de Higgs, pour un canal spécifique, montrant quelles en sont les conséquences intéressantes sur l'incertitude théorique totale. Ceci nous amènera à un résultat significatif de la thèse qui est la comparaison avec l'expérience et notamment les résultats des recherches du boson de Higgs au Tevatron. Nous irons ensuite au-delà du Modèle Standard dans une troisième partie où nous donnerons quelques ingrédients sur la supersymétrie et sa mise en application dans le MSSM où nous avons cinq bosons de Higgs, puis nous aborderons leur production et désintégration en se focalisant sur les deux canaux de production principaux par fusion de gluon et fusion de quarks $b$. Nous présenterons les résultats significatifs quant à la comparaison avec aussi bien le Tevatron que les résultats très récents d'ATLAS et CMS au LHC qui nous permettront d'analyser l'impact de ces incertitudes sur l'espace des paramètres du MSSM, sans oublier de mentionner quelques bruits de fond du signal des bosons de Higgs. Tout ceci va nous permettre de mettre en avant le deuxième résultat très important de la thèse, ouvrant une nouvelle voie de recherche pour le boson de Higgs standard au LHC. La dernière partie sera consacrée aux perspectives de ce travail et notamment donnera quelques résultats préliminaires dans le cadre d'une étude exclusive, d'un intérêt primordial pour les expérimentateurs. / This thesis has been conducted in the context of one of the utmost important searches at current hadron colliders, that is the search for the Higgs boson, the remnant of the electroweak symmetry breaking. We wish to study the phenomenology of the Higgs boson in both the Standard Model (SM) framework and its minimal Supersymmetric extension (MSSM). After a review of the Standard Model in a first part and of the key reasons and ingredients for the supersymmetry in general and the MSSM in particular in a third part, we will present the calculation of the inclusive production cross sections of the Higgs boson in the main channels at the two current hadron colliders that are the Fermilab Tevatron collider and the CERN Large Hadron Collider (LHC), starting by the SM case in the second part and presenting the MSSM results, where we have five Higgs bosons and focusing on the two main production channels that are the gluon gluon fusion and the bottom quarks fusion, in the fourth part. The main output of this calculation is the extensive study of the various theoretical uncertainties that affect the predictions: the scale uncertainties which probe our ignorance of the higher–order terms in a fixed order perturbative calculation, the parton distribution functions (PDF) uncertainties and its related uncertainties from the value of the strong coupling constant, and the uncertainties coming from the use of an effective field theory to simplify the hard calculation. We then move on to the study of the Higgs decay branching ratios which are also affected by diverse uncertainties. We will present the combination of the production cross sections and decay branching fractions in some specific cases which will show interesting consequences on the total theoretical uncertainties. We move on to present the results confronted to experiments and show that the theoretical uncertainties have a significant impact on the inferred limits either in the SM search for the Higgs boson or on the MSSM parameter space, including some assessments about SM backgrounds to the Higgs production and how they are affected by theoretical uncertainties. One significant result will also come out of the MSSM analysis and open a novel strategy search for the Standard Higgs boson at the LHC. We finally present in the last part some preliminary results of this study in the case of exclusive production which is of utmost interest for the experimentalists.

Für verschiedene Richtgrößen, die untersucht werden, um Hinweise auf Neue Physik jenseits des Standardmodells der Teilchenphysik zu finden, stellt die Gitter-QCD stellt derzeit den einzigen Ab-initio-Zugang für die Berechnung von nichtperturbativen hadronischen Beiträgen dar. Zu diesen Observablen gehören die anomalen magnetischen Momenten der Leptonen und das Laufen der elektroschwachen Kopplungskonstanten. Wir bestimmen den führenden QCD-Beitrag zum anomalen magnetischen Moment des Myons mit Hilfe einer Gitter-QCD-Rechnung auf Ensemblen, die Nf=2+1+1 dynamische Twisted-Mass-Fermionen berücksichtigen. Durch die Betrachtung aktiver up, down, strange and charm Quarks können erstmalig Gitter-QCD-Daten für die Myonanomalie direkt mit phänomenologischen Resultaten verglichen werden, da letztere bei der derzeitigen Genauigkeit sensitiv auf die ersten beiden Quarkgenerationen sind. Unlängst wurde darauf hingewiesen, dass es auch möglich sein könnte Beiträge Neuer Physik durch verbesserte Messungen der anomalen magnetischen Momente des Elektrons und des Tauons nachzuweisen. Aus diesem Grund berechnen wir auch deren führende QCD-Beiträge, was gleichzeitig eine Überprüfung des Wertes für das Myon liefert. Zusätzlich nutzen wir die gewonnenen Daten, um den führenden hadronischen Beitrag zum Laufen der Feinstrukturkonstante zu berechnen. Darüber hinaus zeigen wir, dass sogar für den schwachen Mischungswinkel der führende QCD-Beitrag mit Hilfe dieser Daten berechnet werden kann. Dadurch identifizieren wir eine neue grundlegende Observable für die Suche nach Neuer Physik, deren hadronische Beiträge mit Hilfe der Gitter-QCD beschafft werden können. Mit den Resultaten dieser Arbeit ist es uns gelungen ungeeignete Herangehensweisen der phänomenologisch notwendigen Flavourseparation auszuschließen und somit direkt die derzeit präziseren phänomenologischen Bestimmungen dieser bedeutsamen physikalischen Größe zu unterstützen. / For several benchmark quantities investigated to detect signs for new physics beyond the standard model of elementary particle physics, lattice QCD currently constitutes the only ab initio approach available at small momentum transfers for the computation of non-perturbative hadronic contributions. Among those observables are the lepton anomalous magnetic moments and the running of the electroweak coupling constants. We compute the leading QCD contribution to the muon anomalous magnetic moment by performing lattice QCD calculations on ensembles incorporating Nf=2+1+1 dynamical twisted mass fermions. Considering active up, down, strange, and charm quarks, admits for the first time a direct comparison of the lattice data for the muon anomaly with phenomenological results because both the latter as well as the experimentally obtained values are sensitive to the complete first two generations of quarks at the current level of precision. Recently, it has been noted that improved measurements of the electron and tau anomalous magnetic moments might also provide ways of detecting new physics contributions. Therefore, we also compute their leading QCD contributions, which simultaneously serve as cross-checks of the value obtained for the muon. Additionally, we utilise the obtained data to compute the leading hadronic contribution to the running of the fine structure constant, which enters all perturbative QED calculations. Furthermore, we show that even for the weak mixing angle the leading QCD contribution can be computed from this data. In this way, we identify a new prime observable in the search for new physics whose hadronic contributions can be obtained from lattice QCD. With the results obtained in this thesis, we are able to exclude unsuitable phenomenologically necessary flavour separations and thus directly assist the presently more precise phenomenological determinations of this eminent quantity.

Wir präsentieren die Analyse der Daten, die in den Jahren 2002-2004 mit dem 27.56 GeV Positronenstrahl des HERA Speicherrings am DESY und dem internen transversal polarisierten Wasserstofftarget (''fixed target'') des HERMES Experiments aufgenommen wurden. Ereignisse mit einem gestreuten Positron und einem erzeugter Pion wurden selektiert. Die ausschließliche Erzeugung eines einzelnen Pions, e p -> e'' n pi+, wird durch die Anforderung gewährleistet, daß die fehlende Masse des Ereignisses der Masse des Neutrons, das nicht gemessen wird, entspricht. Der Streuquerschnitt für diesen Prozess hängt von der Bjorken-Skalenvariable, den Vierer-Impulsübertrag und den Transversalimpulsübertrag, deren durchschnittliche Werte für unsere Datensätze bei =0.12, =2.3 GeV^2, =-0.18 GeV^2 liegen, sowie zwei azimuthale Winkel: der Winkel phi zwischen den Streu- und Produktionsebene (die Schnittlinie der Ebenen enthält das virtuelle Photon), und der Winkel phi_S zwischen der Streuebene und dem Polarisationsvector des Targets. Die Asymmetrie, auch Transversal-Target-Einzelspin-Azimuthalasymmetrie genannt, wird als das Verhältnis der Differenz zur Summ der Streuquerschnitte für die positive und negative Targetpolarisation definiert. Es wird durch sechs azimuthale Sinus-Modulationen charakterisiert, deren Amplituden von -1 bis 1 varieren können. Wir messen die Asymmetrie eines Datensatzes von 2093 Ereignissen mit einem Signal-Rausch-Verhältnis von 1:1. Im Durchschnitt wurden geringe oder mit Null übereinstimmende Amplitudenwerte gefunden, abgesehen von der Amplitude von der sin(phi_S) Modulation, allerdings innerhalb der großen exprimentellen Unsicherheiten. Ein direkter und genauerer Vergleich der Daten mit der Theorie verlangt größere Statistik und verbesserte Fähigkeiten des Detektor als für die vorliegende Messung vorhanden waren. / We present the analysis of data taken in the years 2002-2004 with the 27.56 GeV positron beam of the HERA storage ring at DESY and the internal transversely polarised hydrogen fixed target of the HERMES experiment. Events with a scattered positron and a produced pion are selected. Exclusive production of single pions, e p -> e'' n pi+, is ensured by requiring the missing mass in the event to be equal to the mass of the neutron, which is not detected. The cross section for this process depends on the Bjorken scaling variable, the four-momentum transfer, and the transverse four-momentum transfer, whose average values for our sample are =0.12, =2.3 GeV^2, =-0.18 GeV^2, respectively, and two azimuthal angles: the angle phi between the scattering and production planes (their common line contains the virtual photon), and the angle phi_S between the scattering plane and the target polarisation vector. The asymmetry, also called transverse-target single-spin azimuthal asymmetry, is defined as the ratio of the difference to the sum of the cross sections for positive and negative target polarisation. It is characterised by six azimuthal sine modulations, whose amplitudes can vary from -1 to 1. We measure the asymmetry from a sample of 2093 events with a signal-to-background ratio of 1:1. At average kinematics, the values of the amplitudes are found to be small or consistent with zero, except for the amplitude of the sin(phi_S) modulation, however, within their large statistical uncertainties. A direct and more precise data-to-theory comparison requires larger statistics and improved detector capabilities than available for the present measurement.

Orientador: Arlene Cristina Aguilar / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós-Graduação em Física, 2012

In this thesis we consider the phenomenology of the theory of strong interactions, Quantum Chromodynamics (QCD), with particular reference to the ongoing experimental program at the Large Hadron Collider in CERN. The current progress in precision measurement of Standard Model processes at the LHC experiments must be matched with corresponding precision in theoretical predictions, and to this end we present calculations at next-to-next-to-leading order in perturbation theory of observable quantities involving quarks and gluons, the strongly interacting particles of the SM. Such calculations form the most important class of corrections to observables and are vital if we are to untangle signals of New Physics from LHC data. We consider in particular the amplitudes for five parton interactions at 1- and 2-loop order and present full (in the 1-loop case) and partial (in the 2-loop case) analytic results in terms of rational functions of kinematic invariants multiplying a basis of master integrals. We address the problem of the solution of a system of integration-by-parts identities for Feynman integrals and demonstrate how some current difficulties may be overcome. We consider also the properties of the top quark, and present the NNLO, real-virtual contributions to the calculation of its decay rate. The results are presented as helicity amplitudes so that the full behaviour of the top spin is retained. These amplitudes constitute a necessary ingredient in the complete calculation of top quark pair production and decay at NNLO which will be an important theoretical input to many experimental analyses. Turning to a more phenomenological study, we consider the extraction of two important SM parameters, the top mass and the strong coupling constant, from measurements of top pair production at the ATLAS and CMS experiments. We compare with NNLO theory predictions and use a least-squares method to extract the values of the parameters simultaneously. We find best fit values of the parameters which are compatible with previous extractions performed using top data with the current world averages published by the Particle Data Group. We consider the issue of PDF choice and the circumstances in which a heavy quark can be considered a constituent of the proton. In particular, we look at the production of a Higgs boson in association with bottom quarks in four and five flavour schemes, in which the b may or may not be included in the initial state. We show that theoretical predictions in both schemes are well-motivated and appropriate in different scenarios, and moreover that results in the schemes are consistent provided a judicious choice of the renormalisation and factorisation scales is made. We suggest a typical scale choice motivated by considerations of consistency and find it to be somewhat lower than the typical hard scale of the process.

One of the important issues of Quantum Chromodynamics (QCD) - the fundamental theory of strong interaction, is the understanding of the role of the quark-gluon interactions in the processes involving nuclear targets. One direction in such studies is to explore the onset of the quark gluon degrees of freedom in nuclear dynamics. The other direction is using the nuclear targets as a “micro-labs” in studies of the QCD processes involving protons and neutrons bound in the nucleus. In the proposed research, we work in both directions considering high energy photo- and electro-production reactions involving deuteron and 3 He nuclei. In the first half of the research, we study the high energy break-up of the 3 He nucleus, caused by a incoming photon, into a proton-deuteron pair at the large center of mass scattering angle. The main motivation of the research is the theoretical interpretation of recent experimental data which revealed the unprecedentedly large exponent s −17 , for the energy dependence of the differential cross section. In the present research, we extend the theoretical formalism of the hard QCD rescattering model to calculate energy and angular dependences of the absolute cross section of the γ 3 He → pd reaction in high momentum transfer limit. The second half of the research explores the deep-inelastic scattering of a polarized electron off the polarized deuteron and 3 He nuclei, to explore the quark-gluon structure of polarized neutron. The main reason of using deuteron is that it is the most simple and best understood nucleus. While the reason of using polarized 3 He as an effective polarized neutron target is that because of the Pauli-principle, the two protons in the target are in the opposite spin states and thus the neutron has all the polarization of the 3 He nucleus. However this approximation is exact only for the S-state and becomes less accurate with the increase of the internal momentum of the bound nucleons in the nucleus. There are several planned experiments which will be performed during next few years at the kinematics in which the internal momenta of the probed neutron cannot be neglected. Therefore, for the reliable interpretation of the data, all the nuclear effects, especially the effects related to the relativistic treatment of high momentum component of the nuclear wave function, should be taken into account. In this work, we developed a comprehensive theoretical framework for calculation of the all relevant nuclear effects that will allow the accurate extraction of the neutron data from deepinelastic scattering involving deuteron and 3 He targets.

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete β functions. The motivation of calculating the discrete β functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare the distribution of Fisher zeros for lattice gauge models with four and twelve light fermion flavors. We also briefly discuss the scaling of the zeros and its connection with the infrared fixed point (IRFP) and the mass anomalous dimension. Conventional numerical simulations suffer from the critical slowing down at the critical region, which prevents one from simulating large system. In order to reach the continuum limit in the lattice gauge theories, one needs either large volume or clever extrapolations. TRG is a new computational method that may calculate exponentially large system and works well even at the critical region. We formulate the TRG blocking procedure for the two dimensional O(2) (or XY ) and O(3) spin models and discuss possible applications and generalizations of the method to other spin and lattice gauge models. We start the thesis with the introduction and historical background of the RG in general.

Electromagnetic properties of the octet and decuplet baryons are calculated in quenched QCD on a 20 ³ x40 lattice with a lattice spacing of 0.128 fm using the fat - link irrelevant clover ( FLIC ) fermion action. FLIC fermions enable simulations to be performed efficiently at quark masses as low as 300 MeV. By combining FLIC fermions with an improved conserved vector current we ensure that discretization errors occur only at Ο ( α ² ) while maintaining current conservation. Magnetic moments, charge radii and magnetic radii are extracted from the electric and magnetic form factors for each individual quark sector. From these the corresponding baryon properties are constructed. Our results for the octet baryons are compared with the predictions of Quenched Chiral Perturbation Theory ( Q χ PT ) and experimental values where available. Results for the charge radii and magnetic moments of the octet baryons are in accord with the predictions of the Q χ PT, suggesting that the sum of higher order terms makes only a small contribution to the chiral expansion. The regime where chiral physics dominates remains to be explored. We establish the non - analytic behavior of the charge radii and magnetic moment in the case of octet baryons. The neutron charge radius suggests that the chiral regime is still far away. We establish substantial environment sensitivity in the quark behavior in the low mass region. We establish that the u and d quarks make substantial and important contribution to the magnetic moment of the Λ contradicting the predictions of the Simple Quark Model. We present the E0 and M1 form factors of the decuplet baryons and the charge radii and magnetic moments. We compare the decuplet baryon results with the lattice calculation of charge radii and magnetic moments of octet baryons. We establish that the environment sensitivity is far less pronounced in the case of the decuplet baryons compared to that in the octet baryons. A surprising result is that the charge radii of the decuplet baryons are generally smaller than that of the octet baryons. Magnetic moment of the Δ + shows a turn over in the low quark mass region, making it smaller than the proton magnetic moment. This is consistent with the expectations of the Quenched Chiral Perturbation Theory. A similar turn over is also noticed in the magnetic moment of the ∑ * [superscript 0], but not for Ξ * where only kaon loops can appear in Quenched QCD. We present results for the higher order moments of the decuplet baryons, i.e., the electric quadrupole moment E2 and the magnetic octupole moment M3. With these results we provide the first conclusive analysis which shows that decuplet baryons are deformed. The electric quadrupole moment of the The electric quadrupole moment of the Ω ‾ baryon is postive when the negative charge factor is included, and is equal to 0.014 ± 0.0005 fm ², indicating an oblate shape. / Thesis (Ph.D.)--School of Chemistry and Physics, 2006.