Nesta dissertação nós revisamos aspectos gerais de teorias de gauge, os princípios da formulação de rede da cromodinâmica quântica (QCD) e algumas propriedades de quarkônios pesados, i.e. estados ligados de um quark pesado e seu antiquark. Como um exemplo de simulações de Monte Carlo de modelos de rede, apresentamos aplicações nos casos do oscilador harmônico e teorias de gauge SU(2). Nós estudamos o efeito de incorporar o propagador de gluon de simulações na rede em um modelo de potencial para a descrição do quarkônio, no caso do botômomio e do charmônio. Nós usamos em ambos os casos uma abordagem numérica para calcular as massas dos estados de quarkônio. O espectro resultante é comparado em ambos os casos com cálculos usando o potencial de Coulomb mais linear (ou potencial Cornell). / In this dissertation we review general aspects of gauge theories, the principles of the lattice formulation of quantum chromodynamics (QCD) and some properties of heavy quarkonia, i.e. bound states of a heavy quark and its antiquark. As an illustration of Monte Carlo simulations of lattice models, we present applications in the case of the harmonic oscillator and SU(2) gauge theory. We study the effect of incorporating the gluon propagator from lattice simulations into a potential model for the description of quarkonium, in the case of bottomonium and charmonium. We use a numerical approach to evaluate masses of quarkonium states. The resulting spectrum is compared in both cases to calculations using the Coulomb plus linear (or Cornell) potential.

Nesta tese, discutimos em detalhes a técnica das Regras de Soma da QCD (RSQCD) e suas aplicações em sistemas hadrônicos situados na região de massa do charmônio. Em particular, calculamos a massa, as constantes de decaimento e acoplamento, bem como a largura de decaimento dos estados $Y(4260)$,$Y(3940)$ e $Z_c^+(3900)$. Além disso, consideramos a existência do parceiro estranho deste último, o $Z^+_{cs}(3970)$, e calculamos sua largura de decaimento de modo a prever seu valor em futuros experimentos. Usamos modelos ditos exóticos para descrever tais estados. Para o $Y(4260)$ e o $Y(3940)$ usamos correntes de mistura charmônio - tetraquarks. Para os estados carregados usamos uma corrente de tetraquarks. Como resultado das aplicações das RSQCD nesses sistemas, obtivemos valores de massa e largura compatíveis com os valores experimentais medidos pelas colaborações BESIII, Belle, Babar e CLEO-c. Dessa forma, podemos afirmar que os modelos utilizados fornecem uma boa interpretação para esses estados. Investigamos também, aplicando técnicas de teorias efetivas, os estados carregados $Z^+_c(4025)$ e novamente o $Z_c^+(3900)$, além dos estados no setor do bottom $Z^+_b(10610)$ e $Z_b^+(10650)$. Usamos as Lagrangianas da Simetria Oculta de Calibre Local (HGS) e também as regras da Simetria de Spin do Quark Pesado (HQSS) para determinarmos as interações $D\\bar{D}^*$, $D^*\\bar{D}^*$, $B\\bar{B}^*$ e $B^*\\bar{B}^*$ via troca de mésons vetoriais pesados e devido à troca de dois píons correlacionados e não correlacionados entre si. Determinamos o potencial para cada interação e, com isso, procuramos por pólos na solução da matriz $T$ na equação de Bethe-Salpeter, cujo kernel é dado pelo potencial. Como resultado desses estudos, obtivemos para as interações no setor do charme, estados ligados cuja massa e largura estão em razoável acordo com os estados carregados $Z^+_c(4025)$ e $Z_c^+(3900)$. Para as interações no setor do bottom, obtemos um estado fracamente ligado próximo do limiar de massa $B\\bar{B}^*$ cuja largura e massa são compatíveis com a estrutura $Z_b^+(10610)$ observada pela Colaboração Belle. Obtivemos um cusp no limiar de massa $B^*\\bar{B}^*$ próximo do valor da estrutura $Z_b^ (10650)$ / In this thesis, we discuss in details the QCD Sum Rules (QCDSR) technique and its application to the study of hadronic systems situated in the charmonium mass region. In particular, we applied QCDSR to calculate hadronic properties such as the mass, the coupling contants as well as the total decay width of the $Y(4260)$, $Y(3940)$ and $Z_c^+(3900)$ charmoniumlike states. We have also predicted the decay width of the strange partner of the $Z_c^+(3900)$, called $Z_{cs}^+(3970)$, to be searched in future experiments. In order to describe these states, we used exotic models. For $Y(4260)$ and $Y(3940)$ states we used mixed charmonium-tetraquarks interpolating currents. For the charged states we used tetraquark currents. As a result of the application of QCDSR to these systems, we obtained masses and decay widths in good agreement with the experimental values measured by BESIII, Babar, and CLEO-c collaborations. Therefore, the currents we used within QCDSR approach provide a good interpretation for these states. Furthermore, applying effective field theories techniques, we also investigated the charged states $Z_c^+(4025)$ and $Z_c^+(3900)$, in addition to $Z^+_b(10610)$ and $Z_b^+(10650)$ in the bottom sector. Specifically, we used hidden local symmetry Lagrangians (HGS) together with heavy quark spin symmetry rules (HQSS) in order to study the interactions $D\\bar{D}^*$, $D^*\\bar{D}^*$, $B\\bar{B}^*$ and $B^*\\bar{B}^*$ by means of the heavy vector exchange and also from the exchange of two pions, interacting and noninteracting among themselves. We obtained the potencial for each interaction, then we used them as a kernel of the Bethe-Salpeter equation in order to look for poles in the $T$-matrix. Our aim was to relate these poles with the charmoniumlike states of interest. As a result, in the charm sector, we obtained bound states whoses masses and widths are in a good agreement with the charged states we have studied. With respect to the bottom sector, we have found a loosely bound state very close to the $B\\bar{B}^*$ threshold with mass and width compatible with the structure $Z_b(10610)$ observed by Belle colaboration. We have obtained a cusp in the $B^*\\bar{B}^*$ threshold very close to the mass of the $Z_b^+(10650)$ state.

A CromoDinâmica Quântica (QCD) é a teoria quântica de campos que descreve as interações fortes entre quarks, que são os constituintes fundamentais das partículas do núcleo atômico. Devido ao caráter peculiar destas interações, o estudo da QCD não pode ser realizado pelos métodos usuais em teorias quânticas de campos, baseados em expansões perturbativas. O estudo não-perturbativo da QCD a partir de primeiros princípios torna-se possível através da formulação de rede da teoria, que equivale a um modelo de mecânica estatística clássica, para o qual podem ser realizadas simulações numéricas através de métodos de Monte Carlo. A área de simulações numéricas da QCD representa uma das maiores aplicações atuais da computação de alto desempenho, sendo realizada nos principais centros computacionais do mundo. As grandes exigências do trabalho de pesquisa nesta área contribuíram inclusive para o desenvolvimento de novas arquiteturas computacionais. O uso de processamento paralelo é vital nessas simulações, principalmente nos casos em que está envolvida a simulação da chamada QCD completa, onde se consideram os efeitos dos quarks dinâmicos. Vários pacotes contendo implementações de algoritmos para o estudo da QCD começam a ser disponibilizados por grupos de pesquisa na área. Nosso foco neste trabalho é voltado para o pacote MILC. Além de fazer uma descrição detalhada da forma de utilização deste pacote, realizamos aqui um acompanhamento da evolução dos métodos empregados, desde o Método de Monte Carlo aplicado no algoritmo de Metropolis até a elaboração do algoritmo RHMC, introduzido recentemente. Fazemos uma comparação de e_ciência entre o RHMC e o algoritmo R, que foi o mais utilizado por décadas. / Quantum ChromoDinamics (QCD) is the quantum field theory that describes the strong interactions between quarks, which are the fundamental constituents of particles in the atomic nucleus. Due to the peculiar characteristic of these interactions, the study of QCD cannot be carried out by usual methods in quantum field theory, which are based on pertubative expansions. The non-pertubative study of QCD from first principles becomes possible through the lattice formulation of the theory, which is equivalent to a classical statistical mechanics model, which in turn can be carried out by numerical simulations using Monte Carlo methods. The field of numerical simulations of QCD is one of the main applications of high performance computing, and is perfomed in most major computational centers around the world. The demanding requirements needed in this field led also to the development of new computational architectures. The use of parallel processing is vital in these types of simulations, especially in cases that involve what is known as full QCD, where the effects of dynamic quarks are taken into account. Several packages with algorithms implemented for the study of QCD have been recently made available by research groups in this field. The focus of this work is the MILC package. Here we make a detailed description of how to use this package and a follow up of the used methods, from the Monte Carlo method applied in the Metropolis algorithm up to the development of the RHMC algorithm, recently introduced. Comparisons are made between the e_ciency of RHMC and the R algorithm, which was the most used in the past decades.

Orientadora: Arlene Cristina Aguilar / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-31T04:21:18Z (GMT). No. of bitstreams: 1 Figueiredo_ClaraTeixeira_M.pdf: 3320128 bytes, checksum: 24dc162fc60ec8d9e4cdb7690324c5fa (MD5) Previous issue date: 2016 / Resumo: Neste trabalho, descrevemos os mecanismos de geração de uma massa dinâmica para o gluon no regime não perturbativo da QCD. Além disso, analisamos o impacto que essa geração de massa do gluon aliada ao comportamento do ghost, que permanece não massivo no região não perturbativa, causa em outras funções de Green fundamentais da QCD. A partir das equações de Schwinger-Dyson, apresentamos um formalismo teórico generalizado para lidar com a geração de massa para o gluon em teorias de Yang-Mills. A construção central se baseia na ação combinada das identidades de Ward satisfeitas pelos vértices não perturbativos (dentro do esquema PT-BFM) e uma identidade especial, chamada identidade de seagull, nos diagramas que compõem a equação de Schwinger-Dyson do propagador de gluon. O resultado dessas considerações é que o gluon permanece rigorosamente não massivo, desde que os vértices não contenham polos. Quando tais polos são incorporados aos vértices da teoria, os termos se combinam de tal forma que a aniquilação total de divergências quadráticas permanece e, ao mesmo tempo, aparecem contribuições residuais que provocam a saturação do propagador de gluon no infravermelho profundo. Esses polos se comportam como excitações de estado ligado não massivas e podem ser estudados a partir das equações de Bethe-Salpeter. As análises realizadas previamente dentro desse contexto consideravam apenas a possibilidade de polo no vértice de três gluons, desprezando efeitos advindo de possíveis polos nos demais vértices. Aqui, nós obtemos a contribuição da presença de um polo no vértice gluon-ghost para a equação dinâmica que descreve a criação de tais polos. Por fim, nota-se que o fato do gluon ganhar um massa dinâmica e o ghost permanecer não massivo impacta algumas das funções de Green da teoria, em particular o propagador de gluon e o vértice de três gluons. Assim, verificamos que o comportamento divergente dos loops de ghost induz simultaneamente um máximo no propagador de gluon e um mínimo em seu termo cinético. Além disso, esses loops provocam uma mudança de sinal e uma divergência negativa no infravermelho em um dos fatores de forma do vértice de três gluons, calculado em uma configuração cinemática especial / Abstract: In this work, we describe the mechanisms at work in the gluon dynamical mass generation in the nonperturbative regime of QCD. In addition, we obtain some effects of this mass generation allied to the behavior of the ghost, which remain massless in the nonperturbative region, in other fundamental Green's functions of QCD. From the Schwinger-Dyson equations, we present a general theoretical formalism to deal with mass generation in Yang-Mills theories. The central construction relies on the combined action of the Ward identities satisfied by the nonperturbative vertices (within the PT-BFM scheme) and a special identity, called seagull identity, in the diagrams that comprise the Schwinger-Dyson equation for the gluon propagator. The result of these considerations is that the gluon remains rigorously massless, given that the vertices do not contain poles. When such poles are incorporated to the vertices of the theory, the terms are combined in a way that the total annihilation of the quadratic divergences remains and, at the same time, residual contributions appear, which provoke the gluon propagator saturation in the deep infrared. These poles behave as massless bound-state excitations and can be studied using the Bethe-Salpeter equations. The analyses carried out previously within this context considered only the possibility of a pole in the three-gluon vertex, neglecting effects from possible poles in the remaining vertices. Here, we obtain the contribution of the presence of a pole in the gluon-ghost vertex for the dynamical equation that describes the creation of such poles. Finally, we note that the fact that the gluon gains a dynamical mass and the ghost remains massless impacts some of the Green's functions of the theory, in particular, the gluon propagator and the three-gluon vertex. Thus, we verify that the divergent behavior of the ghost loops induces simultaneously a maximum in the gluon propagator and a minimum in the kinetic term of this propagator. Besides, these loops generate a change in sign and a negative divergence in the infrared in one of the form factor of the three gluon vertex, calculated in a specific kinematic configuration / Mestrado / Física / Mestra em Física / 2014/16247-8 / 147440/2014-9 / FAPESP / CNPQ

A CromoDinâmica Quântica (QCD) é a teoria quântica de campos que descreve as interações fortes entre quarks, que são os constituintes fundamentais das partículas do núcleo atômico. Devido ao caráter peculiar destas interações, o estudo da QCD não pode ser realizado pelos métodos usuais em teorias quânticas de campos, baseados em expansões perturbativas. O estudo não-perturbativo da QCD a partir de primeiros princípios torna-se possível através da formulação de rede da teoria, que equivale a um modelo de mecânica estatística clássica, para o qual podem ser realizadas simulações numéricas através de métodos de Monte Carlo. A área de simulações numéricas da QCD representa uma das maiores aplicações atuais da computação de alto desempenho, sendo realizada nos principais centros computacionais do mundo. As grandes exigências do trabalho de pesquisa nesta área contribuíram inclusive para o desenvolvimento de novas arquiteturas computacionais. O uso de processamento paralelo é vital nessas simulações, principalmente nos casos em que está envolvida a simulação da chamada QCD completa, onde se consideram os efeitos dos quarks dinâmicos. Vários pacotes contendo implementações de algoritmos para o estudo da QCD começam a ser disponibilizados por grupos de pesquisa na área. Nosso foco neste trabalho é voltado para o pacote MILC. Além de fazer uma descrição detalhada da forma de utilização deste pacote, realizamos aqui um acompanhamento da evolução dos métodos empregados, desde o Método de Monte Carlo aplicado no algoritmo de Metropolis até a elaboração do algoritmo RHMC, introduzido recentemente. Fazemos uma comparação de e_ciência entre o RHMC e o algoritmo R, que foi o mais utilizado por décadas. / Quantum ChromoDinamics (QCD) is the quantum field theory that describes the strong interactions between quarks, which are the fundamental constituents of particles in the atomic nucleus. Due to the peculiar characteristic of these interactions, the study of QCD cannot be carried out by usual methods in quantum field theory, which are based on pertubative expansions. The non-pertubative study of QCD from first principles becomes possible through the lattice formulation of the theory, which is equivalent to a classical statistical mechanics model, which in turn can be carried out by numerical simulations using Monte Carlo methods. The field of numerical simulations of QCD is one of the main applications of high performance computing, and is perfomed in most major computational centers around the world. The demanding requirements needed in this field led also to the development of new computational architectures. The use of parallel processing is vital in these types of simulations, especially in cases that involve what is known as full QCD, where the effects of dynamic quarks are taken into account. Several packages with algorithms implemented for the study of QCD have been recently made available by research groups in this field. The focus of this work is the MILC package. Here we make a detailed description of how to use this package and a follow up of the used methods, from the Monte Carlo method applied in the Metropolis algorithm up to the development of the RHMC algorithm, recently introduced. Comparisons are made between the e_ciency of RHMC and the R algorithm, which was the most used in the past decades.

Le LHC, qui est le collisionneur proton-proton le plus puissant du monde situé au CERN (Suisse), donne une occasion unique de pouvoir tester nos connaissances des interactions fondamentales à l'échelle du TeV. Au cours de cette thèse, deux projets ont été accomplis dans ce but. Tout d'abord, la mesure de la section efficace de production d'au moins deux photons dans l'état final (pp→γγ+X) a été réalisée à l'aide des données prises avec une énergie dans le centre de masse de 8 TeV par le détecteur ATLAS, qui est l'un des détecteurs polyvalents installé autour du LHC. Les photons sont des particules intéressantes pour tester la théorie de l'interaction forte (chromodynamique quantique ou QCD) car ils sont couplés aux quarks et aux gluons sans pour autant s'hadroniser, ce qui permet de pouvoir les mesurer avec une très bonne résolution. La mesure de leur taux de production au LHC permet de tester la QCD à la fois dans le domaine perturbatif et non-perturbatif. Elle est également sensible à l'émission de particules à basse énergie dans l'état initial, qui est un phénomène délicat à décrire d'un point de vue théorique à cause des divergences molles et collinéaires découlant de la QCD. Les incertitudes expérimentales ont été divisées par un facteur 2 ou plus comparé aux mesures réalisées précédemment au LHC ou au Tevatron (Fermilab, États-Unis) et la très bonne statistique des données d'ATLAS à 8 TeV a permis une augmentation significative à la fois de la résolution et de la portée de la mesure. En général, un bon accord est observé avec les prédictions théoriques. Le second projet réalisé au cours de la thèse est consacré à l'évaluation du potentiel de découverte relié à la mesure de la diffusion γγ au LHC (γγ→γγ). La diffusion γγ est un processus singulier car prédit uniquement via des fluctuations quantiques qui n'a jamais été observé directement. Il implique un terme de couplage à quatre photons, qui montre une sensibilité significative à une large gamme de modèles d'extension du modèle standard à haute énergie, tels que ceux prédisant l'existence de dimensions supplémentaires de l'espace pour résoudre le problème de hiérarchie. En tirant profit du flux important de photons venant des protons au LHC, je montre qu'il est possible de découvrir des couplages anomaux à quatre photons avec une sensibilité permettant de rivaliser avec certaines recherches directes. Enfin, j'ai eu l'occasion de tester la nouvelle puce SAMPIC qui vise à réaliser des mesures de temps de vol avec une précision de l'ordre de quelques picosecondes grâce à un échantillonnage rapide des signaux de détecteur. Les performances de SAMPIC ont été testées à partir de signaux gaussiens produits par un générateur et par des détecteurs soumis à des impulsions infrarouges. Dans ces conditions idéales, SAMPIC permet de réaliser des mesures de temps de vol avec une résolution de l'ordre de 4 (40) ps pour les signaux générés (de détecteurs). / The LHC, which is the most powerful proton-proton collider in the world located at CERN (Switzerland), brings unprecedented opportunities to test our knowledge of the fundamental interactions at the TeV scale. In this work, two main projects have been achieved for this purpose. First, the production cross section measurement of at least two photons in the final state (pp→γγ+X) is performed with data taken at a center-of-mass energy of 8 TeV by the ATLAS detector, which is one of the multipurpose detector installed around the LHC ring. Photons are interesting probes to test the theory of strong interactions (Quantum chromodynamics or QCD) since they couple significantly to quarks and gluons but do not hadronize and thus still allow to perform high resolution measurements. The measurement of their production rate at the LHC allows to test QCD in both the perturbative and the non-perturbative domain. It is also sensitive to the emission of soft particles in the initial-state, which is tricky to handle on the theory side due to the collinear and soft divergences arising in QCD. Experimental uncertainties have been reduced by a factor 2 or more with respect to the measurements performed previously at the LHC or at the Tevatron (Fermilab, USA) and the high statistics of the ATLAS data sample at 8 TeV allows to increase significantly both the reach and the resolution of the measurement. In general, a good agreement is observed with theoretical predictions. The second project achieved in this work is dedicated to the evaluation of the light-by-light scattering potential (LbyL, γγ→γγ) for new physics searches. LbyL is an intriguing process arising from quantum fluctuations only that has never been observed directly. It involves four-photon couplings, which are shown to be highly sensitive to a broad range of new physics models at high energy such as the ones predicting the existence of extra spatial dimensions to solve the hierarchy problem currently affecting the standard model of particle physics. By taking benefit of the photon flux from the protons at the LHC, I show that one may discover anomalous four photon couplings with a sensitivity allowing to compete with several direct new physics searches. Finally, I had the opportunity to test the new SAMPIC chip which aims to perform time-of-flight measurements with a few picoseconds precision from fast samplings of detector signals. SAMPIC timing capabilities have been tested using Gaussian signals generated by a signal generator or by silicon detectors pulsed with an infrared laser. Under these ideal conditions, the SAMPIC chip has proven to be capable of timing resolutions down to 4 (40) ps with synthesized (silicon detector) signals.

Nous étudions des fluctuations qui sont omniprésentes dans des collisions entre particules aux hautes énergies. Ces fluctuations peuvent être de nature classique ou quantique et nous allons considérer ces deux cas. D'abord, nous étudions les fluctuations quantiques qui sont présentes dans des collisions entre protons. Celles-ci sont calculables en théorie quantique des champs, et nous allons nous concentrer sur une certaine classe de diagrammes dans ce cadre. Dans un second temps nous allons étudier des fluctuations qui sont présentes dans des collisions entre particules plus lourdes que le proton. Celles-ci sont décrites par les lois quantiques de la nature qui donnent les positions des nucléons dans le noyau, ou bien des fluctuations classiques, d'origine thermique, qui affectent l'évolution hydrodynamique du milieu produit dans une collision. Les fluctuations dans des collisions entre protons peuvent être calculées analytiquement jusqu'à un certain ordre en théorie quantique des champs. Nous allons nous concentrer sur des diagrammes à une boucle, d'une topologie donnée. Ces diagrammes aux boucles donnent des intégrales, qui typiquement sont difficiles à calculer. Nous allons démontrer comment des outils des mathématiques modernes peuvent être utilisés pour faciliter leur évaluation. En particulier, nous allons étudier des relations entre des coupures d'un diagramme, la discontinuité à travers d'un branchement et le coproduit. Nous allons démontrer comment l'intégrale originale peut être reconstruit à partir de l'information contenue dans le coproduit. Nous nous attendons à ce que ces méthodes seront utiles pour le calcul des diagrammes avec des topologies plus difficiles et ainsi aident au calcul des nouvelles amplitudes de diffusion. A la fin, nous étudions les deux types de fluctuations qui ont lieu dans des collisions entre ions lourds. Celles-ci sont liées soit à l'état initial de la matière, soit à l'état intermédiaire produit dans une telle collision. Les fluctuations de l'état initial ont été mesurées expérimentalement, et on voit qu'elles donnent lieu à des non-Gaussianités dans le spectre final de particules. Nous allons démontrer comment ces non-Gaussianités peuvent être comprises comme des positions et des énergies d'interaction aléatoires des 'sources' dans les noyaux entrant en collision. En plus, nous étudions le bruit hydrodynamique dans le milieu produit juste après une collision. Le comportement de ce milieu est celui d'un fluide à basse viscosité. / We study fluctuations that are omnipresent in high-energy particle collisions. These fluctuations can be either of either classical or quantum origin and we will study both. Firstly, we consider the type of quantum fluctuations that arise in proton-proton collisions. These are computable perturbatively in quantum field theory and we will focus on a specific class of diagrams in this set-up. Secondly, we will consider the fluctuations that are present in collisions between nuclei that can be heavier than protons. These are the quantum laws of nature that describe the positions of nucleons within a nucleus, but also the hydrodynamic fluctuations of classical, thermal origin that affect the evolution of the medium produced in heavy-ion collisions. The fluctuations arising in proton-proton collisions can be computed analytically up to a certain order in perturbative quantum field theory. We will focus on one-loop diagrams of a fixed topology. Loop diagrams give rise to integrals that typically are hard to evaluate. We show how modern mathematical methods can be used to ease their computation. We will study the relations among unitarity cuts of a diagram, the discontinuity across the corresponding branch cut and the coproduct. We show how the original integral corresponding to a given diagram can be reconstructed from the information contained in the coproduct. We expect that these methods can be applied to solve more complicated topologies and help in the computation of new amplitudes in the future. Finally, we study the two types of fluctuations arising in heavy-ion collisions. These are related either to the initial state or the intermediate state of matter produced in such collisions. The initial state fluctuations are experimentally observed to give rise to non-Gaussianities in the final-state spectra. We show how these non-Gaussianities can be explained by the random position and interaction energy of `sources' in the colliding nuclei. Furthermore, we investigate the effect of hydrodynamical noise in the evolution of the medium produced just after a collision. This medium behaves like a fluid with a very low viscosity, and so the corresponding evolution is hydrodynamical.

A thermodynamic model of the quark-gluon plasma using quasiparticle degrees of freedom based on the hard thermal loop self-energies is introduced. It provides a connection between an established phenomenological quasiparticle model – following from the former using a series of approximations – and QCD – from which the former is derived using the Cornwall-Jackiw-Tomboulis formalism and a special parametrization of the running coupling. Both models allow for an extrapolation of first-principle QCD results available at small chemical potentials using Monte-Carlo methods on the lattice to large net baryon densities with remarkably similar results. They are used to construct equations of state for heavy-ion collider experiments at SPS and FAIR as well as quark and neutron star interiors. A mixed-phase construction allows for a connection of the SPS equation of state to the hadron resonance gas. An extension to the weak sector is presented as well as general stability and binding arguments for compact stellar objects are developed. From the extrapolation of the most recent lattice results [Baz09, Bor10b] the existence of bound pure quark stars is not suggested. However, quark matter might exist in a hybrid phase in cores of neutron stars.

Dans cette thèse, nous nous intéressons à certains aspects concernant les phénomènes hadroniques à basse énergie sous 1 GeV, en dessous de laquelle la symétrie chirale de la Chromodynamique Quantique (QCD) est spontanément brisée. En dessous de cette échelle d'énergie, le spectre de QCD se réduit à un octet de mésons légers pseudo-scalaires (π, K and η). Mais à cause du confinement, QCD sous 1 GeV devient hautement non perturbative – il n'est donc plus possible de décrire à basse énergie la dynamique de ces mésons en termes de gluons et de quarks (ici seuls les quarks légers u, d et s sont concernés). Deux alternatives principales à cet obstacle majeur existent néanmoins: la QCD sur réseau ainsi que les Théories Effectives des Champs. La QCD sur réseau consiste à calculer de manière numériques les diverses observables hadroniques, alors que les théories effectives permettent de nouveau une approche analytique (et perturbative) adaptée à une échelle d'énergie donnée. Dans le cas de QCD à basse énergie, c'est la Théorie Chirale des Perturbations (ChiPT) qui joue le rôle de théorie effective. Cette théorie peut être construite à partir de deux saveurs de quarks légers (u et s) ou trois (u,d, et s). Il est alors possible d'utiliser certains résultats de calculs sur réseau (ainsi que certains résultats expérimentaux) afin d'extraire des valeurs numériques pour les divers paramètres libres que contient la théorie chirale. Il fut néanmoins observé que le développement en séries chirales de quelques observables hadroniques sont numériquement “malades” dans le cadre de la théorie à trois saveurs. En effet, des travaux antérieurs montrent qu'il pourrait exister une possible compétition numérique entre l'Ordre Dominant (LO) et l'Ordre Sous-Dominant (NLO): en place de la hiérarchie usuelle LO>>NLO, l'équivalence LO~NLO prévalerait. La partie principale de la thèse consiste ainsi à la description et l'utilisation d'une version alternative de ChiPT, nommée Théorie Chirale des Perturbations Ressommée (ReChiPT ). Quelques observables hadroniques de basse energie sont calculées puis étudiées dans ce cadre “ressommé”, puis nous procédons à l'ajustement de certaines données de QCD sur réseau obtenues par des simulations à 2+1 quarks dynamiques sur ces observables exprimées en ReChiPT: les constantes de désintégrations et les masses de l'octet (π, K, η), ainsi que les facteurs de forme Kl3. Nous testons ensuite la validité de notre assertion concernant la possible compétition numérique observée dans les séries chirales. Enfin, dans la dernière partie, nous discutons plusieurs aspects analytiques et numériques concernant certaines quantités topologiques liées de manière intrinsèque à la très complexe structure du vide de QCD, dans le cadre de ChiPT (ressommé), et nous confrontons de nouveau cette étude à des données réseau 2+1. / In this thesis, we focus on some aspects concerning hadronic phenomena at low energy, below 1 GeV, under which the spontaneous breaking of chiral symmetry takes place. Under this scale, the spectrum of Quantum Chromodynamics reduces to an octet of light pseudo-scalar mesons (π, K and η). But because of the confinement property, QCD under 1 GeV is highly non-perturbative, it is thus not possible to describe at low energy the dynamics of these mesons in terms of gluons and quarks (in that case the three light quarks u,d, and s). Two main alternatives exist to circumvent this major obstacle: Lattice QCD and Effective Field Theories. Lattice QCD is concerned with the numerical computations of various hadronic observables, while Effective Field Theories correspond to analytical frameworks adapted to a particular energy scale. In the case of QCD at low energy, this role is devoted to Chiral Perturbation Theory (ChiPT). This theory can be built either from two quark flavours (u and d), or three (u,d, and s). Using the numerical results from Lattice QCD, it is possible to obtain numerical values for the unknown parameters that ChPT contains. It was however observed that the series expansions of hadronic observables stemming from ChiPT calculations do not “behave well” numerically in the three-flavour case. Indeed, previous works shown that there could exists at the numerical level a competition between the Leading and the Next-to- Leading order (LO and NLO); i.e., instead of the usually expected hierarchy LO>>NLO, one would have LO~NLO. The main part of the thesis work consists in the description and the use of a modified version of ChiPT allowing this numerical competition in the chiral series that was called “Resummed ChiPT”. Within this “Resummed” framework, we proceed to fitting data from 2+1 lattice calculations to hadronic observables computed in ChiPT: decay constants and masses of π, K and η, and Kl3 form factors, and check the consistency of our claim about the numerical competition in ChiPT expansions. In the last part, we discuss topological quantities that are intrinsically tied to the very complex structure of the QCD vacuum, in the (resummed) ChiPT framework and in the light of 2+1 lattice data, in their analytical and numerical aspects.

In dieser Arbeit wird die Berechnung der farbführenden Zweischleifen-QCD-Korrekturen für die Top-Quark-Paarproduktion mit einem zusätzlichen Jet an einem Lepton-Collider präsentiert. Das Matrixelement wird in Vektor- und Axial-Vektorströme zerlegt und die Ströme werden weiter in Dirac-Spinorstrukturen und Formfaktoren zerlegt. Die Formfaktoren werden mit Projektoren extrahiert. Die auftretenden Feynmanintegrale werden mittels IBP-Identitäten und Dimensionsverschiebungstransformationen durch eine Basis quasi-finiter Masterintegrale in 6−2ϵ Dimensionen ausgedrückt. Die Mehrheit der Feynmanintegrale gehört zu einer Doppelbox-Integralfamilie. Die Berechnung der Masterintegrale erfolgt durch numerisches Lösen von Differentialgleichungen in kinematischen Invarianten. Asymptotische Reihenentwicklungen der Masterintegrale in der Top-Quarkmasse werden verwendet, um die Anfangsbedingungen für die numerischen Lösungen der Differentialgleichungen zu bestimmen. Die führenden Terme dieser Entwicklung werden mit der Expansion-by-Regions-Methode berechnet. Höhere Reihenkoeffizienten werden durch die Anwendung einer Differentialgleichung auf einen Ansatz für die Reihenentwicklung bestimmt. Die renormierten Formfaktoren und die farbführende Zweischleifenamplitude werden an einem Referenzphasenraumpunkt zu hoher Präzision numerisch ausgewertet. Die Resultate werden mit elektroschwachen Ward-Identitäten und durch numerische Vergleiche der IR-Singularitäten mit der erwarteten Singularitätsstruktur überprüft. / In this work, the calculation of the leading-colour two-loop QCD corrections for top-quark pair production with an additional jet at a lepton collider is presented. The matrix element is decomposed into vector and axial-vector currents and the currents are further decomposed into Dirac spinor structures and form factors. The form factors are extracted with projectors. The Feynman integrals are reduced to a quasi-finite basis in 6 − 2ϵ dimensions using IBP identities and dimension-shift transformations. The majority of master integrals belong to a double-box integral family. The master integrals are computed by numerically solving systems of differential equations in the kinematic invariants. Asymptotic expansions of the master integrals in the top-quark mass variable are used to calculate initial conditions for the numerical differential equation solutions. The leading terms of the expansion are obtained with the expansion by regions and the higher orders are calculated by solving a system of equations obtained from applying the differential equation onto an ansatz of the expansion. The renormalized form factors and the leading-colour two-loop amplitude are evaluated numerically to high precision at a benchmark phase space point. The results are cross-checked with electroweak Ward identities and by numerically comparing the IR singularities with the expected singularity structure.