Dissertations / Theses on the topic 'Gluons and lattices'

This thesis presents gauge fixed gluonic observable and neutral Kaon mixing matrix element measurements using nf=2+1 Domain Wall Fermion (DWF) configurations. These were generated with the Iwasaki gauge action by the RBC and UKQCD collaborations. Results from the first measurement of the QCD strong coupling with these ensembles using the triple gluon vertex are shown. We find that while a very accurate measurement of the coupling is possible using this technique, the systematic error from the perturbative matching at current lattice scales is large. We also discuss the utilisation of this method as a probe for possible Technicolor theories. The calculation of the QCD strong coupling constant from the triple gluon vertex required an implementation of a fast code to fix lattice gauge configurations. I provide details on my implementation of a parallel and optimised Fourier-accelerated algorithm for both Landau and Coulomb gauge fixing. I include the first calculation of the highly accurate W0-scale using these ensembles, allowing for percent-level scale setting. I show results from a wide variety of smearing methods and present the first gluonic measurement of different smearing radii. This thesis also details the first nf=2+1 measurement of the BSM neutral Kaon mixing renormalised matrix elements from lattice simulations with almost exact chiral symmetry in the valence sector and the sea.

Die im infraroten Impulsbereich der Quantenchromodynamik (QCD) berechneten Gluon- und Ghost-Propagatoren spielen eine große Rolle für das sogenannte Confinement der Quarks und Gluonen. Sie sind Gegenstand intensiver Foschungen dank nicht-perturbativer Methoden basierend auf Dyson-Schwinger- (DS) und funktionalen Renormierungsgruppen-Gleichungen (FRG). Darüber hinaus sollte es deren Verhalten bei endlichen Temperaturen erlauben, den chiralen und Deconfinement-Phasenübergang bzw. das Crossover in der QCD besser aufzuklären. Unser Zugang beruht auf der gitter-diskretisierten QCD (LQCD), die es als ab-initio-Methode gestattet, verschiedenste störungstheoretisch nicht zugängliche QCD-Observablen der hadronischen Welt zu berechnen. Wir untersuchen das Temperaturverhalten der Gluon- und Ghost-Propagatoren in der Landau-Eichung für die reine Gluodynamik und die volle QCD. Für den Gluon-Propagator berechnen wir deren longitudinale (DL) sowie transversale (DT) Komponenten. Ziel ist es, Datensätze in Form von Fit-Formeln zu liefern, welche als Input für die DS- (oder FRG-) Gleichungen verwendet werden können. Wir beschäftigen uns mit der vollen (Nf=2) LQCD unter Verwendung der sogenannten twisted mass Fermiondiskretisierung. Von der tmfT-Kollaboration wurden uns dafür Eichfeldkonfigurationen für Temperaturen im Crossover-Bereich sowie jeweils für drei fixierte Pion-Massenwerte im Intervall [300, 500] MeV bereitgestellt. Schließlich berechnen wir innerhalb der reinen SU(3) Eichtheorie (bei T=0) den Landau Gluon-Propagator unter Verwendung verschiedener Eichfixierungskriterien. Unser Ziel ist es, den Einfluss von Eich-Kopien mit minimalen (nicht-trivialen) Eigenwerten des Faddeev-Popov-Operators zu verstehen. Eine solche Studie soll klären, wie Gribov-Kopien das Verhalten der Gluon- und Ghost-Propagatoren im infraroten Bereich prinzipiell beeinflussen.
Gluon and ghost propagators in quantum chromodynamics (QCD) computed in the infrared momentum region play an important role to understand quark and gluon confinement. They are the subject of intensive research thanks to non-perturbative methods based on Dyson-Schwinger (DS) and functional renormalization group (FRG) equations. Moreover, their temperature behavior might also help to explore the chiral and deconfinement phase transition or crossover within QCD at non-zero temperature. Our prime tool is the lattice discretized QCD (LQCD) providing a unique ab-initio non-perturbative approach to deal with the computation of various observables of the hadronic world. We investigate the temperature dependence of Landau gauge gluon and ghost propagators in pure gluodynamics and in full QCD. Regarding the gluon propagator, we compute its longitudinal DL as well its transversal DT components. The aim is to provide a data set in terms of fitting formulae which can be used as input for DS (or FRG) equations. We deal with full (Nf=2) LQCD with the twisted mass fermion discretization. We employ gauge field configurations provided by the tmfT collaboration for temperatures in the crossover region and for three fixed pion mass values in the range [300,500] MeV. Finally, within SU(3) pure gauge theory (at T=0) we compute the Landau gauge gluon propagator according to different gauge fixing criteria. Our goal is to understand the influence of gauge copies with minimal (non-trivial) eigenvalues of the Faddeev-Popov operator.

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.

Diese Arbeit untersucht im Rahmen der Gittereichtheorie verschiedene Aspekte der QCD in der Landau-Eichung, insbesondere solche, die mit den Gluon- und Geist-Propagatoren bei kleinen Impulsen zusammenhängen. Die Eichgruppe ist SU(3). Wir analysieren den Einfluss unterschiedlicher systematischer Effekte. Wir zeigen, dass der Formfaktor des Geist-Propagators bei kleinen Impulsen systematisch von der Wahl der Eichkopien (Gribov-Kopien) abhängt. Hingegen können wir einen solchen Einfluss auf den Gluon-Propagator nicht feststellen. Ebenfalls wird die Verteilung der kleinsten Eigenwerte des Faddeev-Popov-Operators durch die Wahl der Eichkopien beeinflusst. Wir zeigen außerdem, dass der Einfluss dynamischer Wilson-Fermionen auf den Geist-Propagator für die untersuchten Impulse vernachlässigbar ist. Für den Gluon-Propagator können wir jedoch einen deutlichen Einfluss für große und mittlere Impulse feststellen. Zusätzlich wurden beide Propagatoren auf asymmetrischen Gittern gemessen und mit den Daten von symmetrischen Gittern verglichen. Wir vergleichen unsere Ergebnisse mit denen aus Studien von Dyson-Schwinger-Gleichungen für den Gluon- und Geist-Propagator. Wir zeigen, dass das in dieser Arbeit gefundene Niedrigimpulsverhalten im Einklang mit verschiedenen Kriterien für Confinement (Einschluss von Farbladungen) ist. Wir berechnen die laufende Kopplung, die sich als eine renormierungsgruppeninvariante Kombination der Gluon- und Geist-Formfaktoren ergibt. Unsere Ergebnisse zeigen, dass im Bereich kleiner Impulse die laufende Kopplung kleiner wird und so vermutlich kein endlicher Infrarot-Fixpunkt im Grenzfall Impuls Null angestrebt wird. Wir präsentieren außerdem eine erste nichtstörungstheoretische Berechnung der Renormierungskonstante des SU(3) Ghost-Gluon-Vertex. Wir berichten über Untersuchungen zu spektralen Eigenschaften des Faddeev-Popov-Operators. Dazu haben wir eine Reihe der kleinsten Eigenwerte und Eigenvektoren dieses Operators berechnet.
Within the framework of lattice QCD we investigate different aspects of QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is SU(3). Different systematic effects on the gluon and ghost propagators are studied. We demonstrate the ghost dressing function to systematically depend on the choice of Gribov copies at low momentum, while the influence on the gluon dressing function is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies. We show that the influence of dynamical Wilson fermions on the ghost propagator is negligible at the momenta available to us. On the contrary, fermions affect the gluon propagator at large and intermediate momenta. In addition, we analyze data for both propagators obtained on asymmetric lattices and compare these results with data obtained on symmetric lattices. We compare our data with results from studies of Dyson-Schwinger equations for the gluon and ghost propagators. We demonstrate that the infrared behavior of both propagators, as found in this thesis, is consistent with different criteria for confinement. However, the running coupling constant, given as a renormalization-group-invariant combination of the gluon and ghost dressing functions, does not expose a finite infrared fixed point. Rather the data are in favor of an infrared vanishing coupling constant. We also report on a first nonperturbative computation of the SU(3) ghost-gluon-vertex renormalization constant. We present results of an investigation of the spectral properties of the Faddeev-Popov operator. For this we have calculated the low-lying eigenvalues and eigenmodes of the Faddeev-Popov operator.

Quantum Chromo Dynamics (QCD) is a relativistic field theory of a non-abelian gauge field coupled to several flavors of fermions. Two dimensional (one space and one time) QCD serves as an interesting toy model that shares several features with the four dimensional physically relevant theory. The main aim of the research is to study two dimensional QCD using the lattice regularization. Two dimensional QCD without any fermion content is solved analytically using lattice regularization. Explicit expressions for the expectation values of Wilson loops and the correlation of two Polyakov loops oriented in two different directions are obtained. Physics of the QCD vacuum is explained using these results. The Hamiltonian formalism of lattice QCD with fermion content serves as an approach to study quark excitations out of the vacuum. The formalism is first developed and techniques to numerically evaluate the spectrum of physical particles, namely, meson and baryons are described. The Hybrid Monte Carlo technique was used to numerically extract the lowest meson and baryon masses as a function of the quark masses. It is shown that neither the lowest meson mass nor the lowest baryon mass goes to zero as the quark mass is taken to zero. This numerically establishes the presence of a mass gap in two dimensional QCD.

We present comprehensive analysis of the light and strange disconnected-sea quarks contribution to the nucleon electric and magnetic form factors. The lattice QCD estimates of strange quark magnetic moment GsM (0) = −0.064(14)(09) μN and the mean squared charge radius ⟨r2s⟩E = −0.0043(16)(14) fm2 are more precise than any existing experimental measurements and other lattice calculations. The lattice QCD calculation includes ensembles across several lattice volumes and lattice spacings with one of the ensembles at the physical pion mass. We have performed a simultaneous chiral, infinite volume, and continuum extrapolation in a global fit to calculate results in the continuum limit. We find that the combined light-sea and strange quarks contribution to the nucleon magnetic moment is−0.022(11)(09) μN and to the nucleon mean square charge radius is −0.019(05)(05) fm2. The most important outcome of this lattice QCD calculation is that while the combined light-sea and strange quarks contribution to the nucleon magnetic moment is small at about 1%, a negative 2.5(9)% contribution to the proton charge radius and a relatively larger positive 16.3(6.1)% contribution to the neutron charge radius come from the sea quarks in the nucleon. For the first time, by performing global fits, we also give predictions of the light-sea and strange quarks contributions to the nucleon electric and magnetic form factors at the physical point and in the continuum and infinite volume limits in the momentum transfer range of 0 ≤ Q2 ≤ 0.5 GeV2.

Diese Arbeit beschäftigt sich mit der Berechnung von für die Struktur des Nukleons relevanten Observablen, die experimentell durch inklusive und semi-inklusive Streuexperimente bestimmt werden können. Es werden zwei Pilotstudien erörtert, welche die Spin- und Impulsstruktur des Nukleons mithilfe von Gitter-QCD untersuchen. Hierfür wird der Twisted-Mass-Formalismus mit dynamischen Fermionen verwendet, um sicherzustellen, dass die untersuchten Größen einen verbesserten Kontinuumslimes aufweisen. Der erste Teil dieser Arbeit untersucht die Umsetzbarkeit einer Rechnung, die sich mit dem durchschnittlichen Impulsanteil der Gluonen im Nukleon auseinandersetzt. Diese Größe wurde bisher kaum im Rahmen der Gitter-QCD behandelt. In diesem Zusammenhang werden zwei verschiedene Gittermethoden untersucht: das Feynman-Hellman-Theorem, sowie die direkte Berechnung der relevanten Formfaktoren. Mithilfe der zweiten Methode und mehreren Iterationen des Schmierens der Eichlinks ist es möglich, statistisch aussagekräftige Resultate zu erhalten. Die zweite Studie beschäftigt sich mit der direkten Berechnung der vollständigen Impuls- und Spinverteilung von Quarks und Antiquarks im Nukleon. Hierfür wird untersucht, ob eine kürzlich publizierte Methode praktikabel ist, nach der eine räumliche Quasiverteilung zu berechnen und aus dieser die physikalische Verteilung abzuleiten ist. In diesem Zusammenhang wird der Einfluß des Schmierens der Eichlinks und unterschiedlicher Impulsboosts des Nukleons erprobt. Die anschließend berechneten Isovektor-Quarkverteilungen (unpolarisiert und polarisiert) weisen eine gute qualitative Übereinstimmung mit Verteilungen auf, die mithilfe von phänomenologischen Analysen bestimmt wurden. Zentrale Erkenntnis dieser Arbeit ist der Nachweis, dass es auf dem Gitter prinzipiell möglich ist, beide Observablen zu berechnen. Trotzdem muss noch erheblich mehr Arbeit aufgewendet werden, um verlässliche Resultate für diese Größen zu erhalten.
This thesis deals with the theoretical computation of nucleon structure observables as they can be experimentally obtained from inclusive and semi-inclusive scattering experiments. I present two exploratory studies on spin and momentum structure observables of the nucleon in the framework of lattice QCD. Throughout this work, I use the twisted mass formalism with dynamical fermions at maximal twist, which ensures an improved continuum limit scaling for the relevant quantities. In the first part, I investigate the feasibility of a lattice calculation of the gluons’ average momentum fraction in the nucleon, a quantity that is rarely studied in lattice QCD. For this purpose, I study two different methods, namely the Feynman-Hellman theorem and the direct computation of the relevant form factor. Applying the latter method and combining it with several steps of stout gauge link smearing, I obtain a statistically significant results for the gluon content. The second study is concerned with the direct computation of the full momentum and spin distribution of quarks and antiquarks within the nucleon. I investigate the feasibility of a recently published approach proposing the computation of a purely spatial quasi-distribution that can be related to the physical distribution. I test the influence of gauge link smearing and different nucleon momentum boosts on the lattice data. Ultimately, I obtain iso-vector quark distributions for the unpolarized and polarize case that featuring a decent qualitative agreement to quark distributions acquired from phenomenological fits. As a key result of this work, I demonstrate that the demanding calculation of gluon content and the novel approach of computing quark distributions directly within lattice QCD are feasible in principle, although significantly more effort has to be invested into obtaining accurate results with reliable uncertainties.

O comportamento infra-vermelho dos propagadores de glúons e de ghosts é de fundamental importância para o entendimento do limite de baixas energias da cromodinâmica quântica (QCD), especialmente no que diz respeito ao problema do confinamento de quarks e de glúons. O objetivo desta tese é implementar um novo método para o estudo do propagador de glúons no calibre covariante linear para a QCD na rede. Em particular, analisamos em detalhe a nova implementação proposta e estudamos os algoritmos para fixação numérica deste calibre. Note que a fixação numérica da condição de calibre de Feynman apresenta vários problemas não encontrados nos casos de Landau e de Coulomb, o que impossibilitou por longo tempo o seu estudo adequado. De fato, a definição considerada inicialmente, por Giusti et. al., é de difícil implementação numérica e introduz condições espúrias na fixação de calibre. Como consequência, os únicos estudos efetuados anteriormente referem-se aos propagadores de glúons e de quarks em redes relativamente pequenas, não permitindo uma análise cuidadosa do limite infra-vemelho da QCD neste calibre. A obtenção de novas soluções para a implementação do calibre de Feynman na rede é portanto de grande importância para viabilizar estudos numéricos mais sistemáticos dos propagadores e dos vértices neste calibre e, em geral, no calibre covariante linear.
The infrared behavior of gluon and ghost propagators is of fundamental importance for the understanding of the low-energy limit of quantum chromodynamics (QCD), especially with respect to the problem of the confinement of quarks and gluons. The goal of this thesis is to implement a new method to study the gluon propagator in the linear covariant gauge in lattice QCD. In particular, we analyze in detail the newly proposed implementation and study the algorithms for numerically fixing this gauge. Note that the numerical fixing of the Feynman gauge condition poses several problems that are not present in the Landau and Coulomb cases, which prevented it from being properly studied for a long time. In fact, the definition considered initially, by Giusti et. al., is of difficult numerical implementation and introduces spurious conditions into the gauge fixing. As a consequence, the only studies carried out previously involved gluon and quark propagators on relatively small lattices, hindering a careful analysis of the infrared limit of QCD in this gauge. Obtaining new solutions for the implementation of the Feynman gauge on the lattice is therefore of great importance to enable more systematic numerical studies of propagators and vertices in this gauge and, in general, in the linear covariant gauge.

Dissertação de Mestrado em Física apresentada à Faculdade de Ciências e Tecnologia
Esta dissertação é o resultado do trabalho desenvolvido ao longo do último ano pelo autor e juntamente com os seus orientadores, Prof. Dr. Orlando Oliveira e Dr. Paulo Silva. A dissertação consiste no estudo do sector gluónico em teorias de Yang-Mills através do cálculo de funções de correlação de dois, três e quatro gluões. Para isto utilizou-se o formalismo da QCD na rede usando simulações de Monte-Carlo com a ação de Wilson na gauge de Landau.O primeiro tópico de estudo passou por analisar os desvios, relativamente ao contínuo,introduzidos pela substituição do espaço-tempo por uma rede de quatro dimensões. Para isso foram usadas representações tensoriais da rede para calcular o propagador de gluões e comparadas com a descrição tensorial do contínuo. Com esta análise foram identificadas classes de configurações cinemáticas para as quais os desvios relativamente à descriçãodo contínuo são reduzidos. Além de testar a integridade da descrição do propagador, é também possível investigar como a identidade de Slavnov-Taylor para o propagador é validada nas simulações de Monte-Carlo. Os resultados das diferentes representações tensoriais mostram que a identidade de Slavnov-Taylor é satisfeita na rede. A função de correlação de três gluões também foi calculada usando dois conjuntos de configurações na rede. O objetivo principal foi a análise do comportamento da função de correlação no infra-vermelho, nomeadamente, a existência de uma possível troca de sinal da função para baixos momentos. Esta propriedade relaciona-se com o domínio dos campos ghost para baixas escalas de momentos e que induz uma possível mudança desinal assim como uma possível divergência. Além desta hipótese, também a possibilidadeda existência de uma massa para o campo ghost que previne a divergência para baixos momentos foi estudada. Com o objetivo de melhorar a análise, foram usadas formas funcionais para modelar o vértice de três gluões e estudar as duas possibilidades no infra-vermelho. Em particular, através dos modelos, a escala para a mudança de sinal foi avaliada assim como o comportamento geral da função para baixos momentos. O último objetivo foi o cálculo do vértice de quatro gluões, que representa uma dificuldade acrescentada, nunca tendo sido avaliado na rede. A dificuldade deve-se à complexidade tensorial e às contribuições de vértices de ordem menor que surgem na computação da função de correlação completa de quatro gluões. Estas contribuições foram eliminadas através de uma escolha adequada da configuração cinemática. Além disso, as flutuações estatísticas são grandes e dificultam a análise. Os resultados demonstraram que o cálculo do vértice de quatro gluões é exequível com recursos computacionais acessíveis. No entanto, é fundamental aumentar a precisão no cálculo para obter um sinal mais definido e calcular o vértice sem propagadores externos.
This dissertation reports on the work developed in the past year by the author and in collaboration with his supervisors, Prof. Dr. Orlando Oliveira and Dr. Paulo Silva. The main topic of the thesis is the study of the gluon sector in pure Yang-Mills theories via the computation of two, three and four point Landau gauge gluon correlation functions evaluated using the lattice formalism of QCD. Monte-Carlo simulations reported herein use Wilson action for lattice QCD. The first goal was to understand and quantify the deviations, relative to the usual continuum description of lattice correlation functions, introduced by using appropriate lattice tensors. To achieve this we rely on different lattice tensor representations for the gluon propagator in four dimensions to measure the deviations of the lattice propagator from its continuum form. We also identified classes of kinematic configurations where these deviations are minimal and the continuum description of lattice tensors is improved. Other than testing how faithful our description of the propagator is, these tensor structures also allow to study how the continuum Slavnov-Taylor identity for the propagator is verified on the lattice for the pure Yang-Mills theory. We found that the Slavnov-Taylor identity is fulfilled, with good accuracy, by the lattice data for the two point function.A second goal was the lattice computation of the three gluon vertex using large ensembles of configurations. The so-called zero crossing, a property that is related with the ghost dominance at the infrared mass scales and puts restrictions on the behaviour of the three gluon vertex, was investigated. In addition, we also explore the possible existence of a ghost mass preventing the infrared divergence of the vertex. In our study of the three gluon correlation function we used functional forms to model the lattice data and explore the two different possibilities for the behaviour of the function. For the first case we provide an estimate of the mass scale associated with the zero-crossing and search for a possible sign of the divergence. On the other hand, for the second case we study the possible occurrence of a sign change and the finite value of the three gluon vertex for vanishing momentum. A last topic is the computation of the four gluon vertex. On the lattice this is a particularly difficult calculation that requires the subtraction of contributions from lower order correlation functions. A suitable choice of kinematics allows to eliminate such unwanted contributions. Furthermore, large statistical fluctuations hinder the precise computation of this object. Our investigation is a proof of concept, we show that thelattice computation of the four gluon correlation function seems to be feasible with reasonable computational resources. Nonetheless, an increase in statistics is necessary to provide a clearer and precise signal on the complete correlation function and to compute the corresponding one particle irreducible function.

In this thesis I explore the physical effects of improved actions combined with improved operators in the framework of lattice QCD. All calculations are done in the quenched approximation, that is, when all of the dynamical fermion interactions have been suppressed by setting the determinant of the fermion matrix to a constant. The thesis first briefly introduces lattice QCD to familiarize the reader with the basic concepts. It then describes the common numerical procedures used. It is made up of three major sections. The first is the exploration of gauge field configurations and the study of the role of instantons in lattice QCD. In this work the Wilson gauge action and a standard 1 loop topological charge operator are used to determine the relative rates of standard cooling and smearing algorithms in pure SUc(3)-color gauge theory. I consider representative gauge field configurations on 16³ × 32 lattices at β = 5.70 and 24³ × 36 lattices at β = 6.00. I find the relative rate of variation in the action and topological charge under various algorithms may be succinctly described in terms of simple formulae ¹. The results are in accord with recent suggestions from fat-link perturbation theory. This work is then extended to O(a²)-improved gauge action and O(a²)-improved operators ². In particular, an O(a²)-improved version of APE smearing is motivated by considerations of smeared link projection and cooling. The extent to which the established benefits of improved cooling carry over to improved smearing is critically examined. I consider representative gauge field configurations generated with an O(a²)-improved gauge field action on 16³ × 32 lattices at β = 4.38 and 24³ × 36 lattices at β = 5.00 having lattice spacings of 0.165(2) fm and 0.077(1) fm respectively. While the merits of improved algorithms are clearly displayed for the coarse lattice spacing, the fine lattice results put the various algorithms on a more equal footing and allow a quantitative calibration of the smoothing rates for the various algorithms. I find that the relative rate of variation in the action may also be described in terms of simple calibration formulae for O(a²)-improvement which accurately describes the relative smoothness of the gauge field configurations at a microscopic level. In the second section the first calculation of the gluon propagator using an O(a²)- improved action with the corresponding O(a²)-improved Landau gauge fixing ³ condition is presented ⁴. The gluon propagator obtained from the improved action and improved Landau gauge condition is compared with earlier unimproved results on similar physical lattice volumes of 3.2³ × 6.4⁴ fm. It is found that there is good agreement between the improved propagator calculated on a coarse lattice with lattice spacing a = 0.35 fm and the unimproved propagator calculated on a fine lattice with spacing a = 0.10 fm. This motivated us to calculate the gluon propagator on a coarse very large-volume lattice of 5.6³ × 11.2⁴fm. The infrared behavior observed in previous studies is confirmed. The gluon propagator is enhanced at intermediate momenta and suppressed at infrared momenta. The observed infrared suppression of the Landau gauge gluon propagator is not a finite volume effect. This work is then extended to a variety of lattices with spacing ranging from a = 0.17 to a = 0.4 fm ⁵ to further explore finite volume and discretization effects. In this work a technique previously used for minimizing lattice artifacts, known as “tree-level correction”, has also been extended. It is demonstrated that by using tree-level correction, determined by the tree-level behavior of the action being considered, it is possible to obtain scaling behavior over a very wide range of momenta and lattice spacings. This makes it possible to explore the infinite volume and continuum limits of the Landau-gauge gluon propagator. As a final part of this thesis I present the first results for the quark propagator using an Overlap fermionic quark action ⁶. I compare the results with those obtained from the standard Wilson fermion. The overlap quark action is O(a)-improved compared with the Wilson fermion. This action realizes exact chiral symmetry on the lattice unlike the Wilson fermion and it demonstrates that the fastest way forward in this field is with improved lattice operators. The idea of studying improved actions in lattice gauge theory was suggested to me by A/Prof. Anthony G. Williams during the “Nonperturbative Methods in Quantum Field Theory” workshop in early February 1998. Initially it was suggested to me that a calculation of the gluon propagator using improved action on large volumes, following a study just done with standard gauge action in Ref. [62]. The point of interest was to study the effect an improved gauge field action would have on the gluon propagator. This study would then be extended to quark actions. In the meantime when generating gauge field configurations using a computer code written in Fortran 77 (provided by Dr. Derek B. Leinweber), it occurred to me that it would be good to explore the content of these gauge field configurations. In order to do realistic calculations on large lattices we needed a gauge field configuration generator that would run on our CM5 computer and so Connection Machine Fortran (CMF) became the adopted language. I started writing the computer code to generate the gauge field configuration in the SUc(2) with the help of Dr. Derek B. Leinweber, who introduced me to the basic concepts in lattice QCD. I then extended this code to the SUc(3) gauge group. This is commonly known as the standard Wilson gauge action. After investigating with some of the optimization possibilities, I moved on to code an O(a²)-improved gauge action. The code uses a masking procedure for the link update. I have generalized the masking procedure for any planar gauge field action in SUc(N), Ref. [18]. From there it was very obvious that by applying a continuous repetition of some sections of code that I written, that some bigger Wilson loops could easily be included in the action and hence highly improved actions could be easily constructed. The only difficulty was to calculate the improvement coefficients. I then moved on to study smearing algorithms. I adapted the gauge field configuration code to a cooling and a 1 × 2 and 2 × 1 improved cooling code in which we inserted higher order loop operators. This was the tool used to explore gauge field configurations and their topological structures. Once the short range quantum fluctuations are removed it is possible to see instantons. Instantons are believed to play a crucial role in the spontaneous chiral symmetry breaking mechanism. We improved the topological charge operator from the clover term to an (1 × 2 and 2 × 1) O(a²)–improved topological charge operator (see Appendices, Sections E.16 and E.17). This code was subsequently adapted by Sundance Bilson-Thompson so that he could insert higher order loops. I have also inserted my O(a²)–improved operator to construct an O(a²)–improved smearing algorithm. Using these tools I have calibrated the relative rates of cooling and smearing. Another piece of work on gauge fixing, reviewed in Chapter 8, was led by Dr. Patrick O. Bowman, Ref. [63]. There I supplied the gauge field configurations and checked some of the analytical work. For the gluon propagator work I supplied all of the lattice configurations with the exception of the 32³ × 64 used in Ref. [62]. The analysis was primarily carried out by Dr. Patrick O. Bowman and partly inspired by the one carried out in hep-lat/0106023. While this gluon propagator work is not being presented here as my own Ph. D. qualifying work, I am a co author on the subsequent papers and so I have therefore decided to include a review of this work in Chapter 9. I have also made some contribution in the construction of the Fat–link quark action (with and without the clover term) developed by James M. Zanotti. These contributions involve the code for the Reunitarization of the smeared links, Appendix E.21. Because of the code developed for the improved lattice definition of the Fµν(x) term I have also made some contribution to the Fat–link clover quark action although I will not discuss about this work in the following thesis. My main contribution for the overlap quark propagator study was in the analysis of the propagator data. The overlap propagators were generated by Dr. Jianbo Zhang and the research was also carried out in collaboration with A/Prof. Anthony G. Williams and Dr. Derek B. Leinweber. The quark propagators for the Wilson fermion were generated by a computer code parallelized by James M. Zanotti and originally written by Prof. Frank X. Lee. The anisotropic lattice code has not been used in any calculations yet although it has been tested and verified. The code was extended from the isotropic improved generator code in SUc(3). After a literature search, we decided to implement the action described in Ref. [31] for the anisotropic Wilson action and in Ref. [11, 32] for the improved anisotropic case. Apart from the work on the gauge fixing and the gluon propagator, done in collaboration with Dr. Patrick O. Bowman, and which for completeness is briefly reviewed in Chapters 8 and 9 respectively, this thesis contains no material which has been accepted for the award of any other degree or diploma in any university or other institution and to the best of knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to this copy of my thesis, when deposited in the University Library, being available for loan and photocopying. Fr´ed´eric D. R. Bonnet Date: 20th of September 2001. ____________ [Footnotes]: ¹F. D. R. Bonnet, P. Fitzhenry, D. B. Leinweber, M. R. Stanford & A. G. Williams, Phys. Rev. D 62, 094509 (2000) [hep lat/0001018]. ²F. D. R. Bonnet, D. B. Leinweber, A. G. Williams & J. M. Zanotti, Submitted to Phys. Rev. D. [hep-lat/0106023]. ³F. D. R. Bonnet, P. O. Bowman, D. B. Leinweber, D. G. Richards & A. G. Williams, Aust. J. Phys. 52, 939 (1999). ⁴F. D. R. Bonnet, P. O. Bowman, D. B. Leinweber & A. G. Williams, Infrared behavior of the gluon propagator on a large volume lattice, Phys. Rev. D 62, 051501, (2000). ⁵F. D. R. Bonnet, P. O. Bowman, D. B. Leinweber, A. G. Williams & J. M. Zanotti, Infinite volume and continuum limits of the landau gauge gluon propagator, Phys. Rev. D 64, 034501 (2001) [hep-lat/0101013]. ⁶F. D. R. Bonnet, P. O. Bowman, D. B. Leinweber, A. G. Williams & J. Zhang, Overlap Propagator in Landau Gauge, to be Submitted to Phys. Rev. D.
Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2002

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.

Thesis (Ph. D.)--Florida State University, 2004.
Advisor: Dr. Bernd A. Berg, Florida State University, College of Arts and Sciences, Dept. of Physics. Title and description from dissertation home page (viewed June 16, 2004). Includes bibliographical references.

Dissertação de Mestrado em Física apresentada à Faculdade de Ciências e Tecnologia
Numa Teoria Quântica de Campos, a estrutura analítica das funções de correlação de 2 pontos, i.e., os propagadores, contêm diversas informações acerca das propriedades dos quanta da teoria, em particular se estes estão, ou não, confinados. No entanto, em Cromodinâmica Quântica (QCD), uma solução analítica é apenas possível num quadro perturbativo da teoria. A obtenção dos propagadores de uma forma não perturbativa pode ser feita com recurso a soluções numéricas da QCD para momentos definidos no espaço Euclidiano. Estas soluções podem ser conseguidas com base, por exemplo, em simulações de Monte Carlo na rede. Neste trabalho baseamo-nos em Aproximantes de Padé (PA) para analisar os propagadores do gluão e do campo fantasma, dessa forma obtidos na gauge de Landau, e investigamos a sua estrutura analítica.Numa primeira fase, são exploradas as vantagens do uso de PAs para reproduzir as propriedades de uma função, em especial a sua estrutura analítica. É testada a utilização de sequências de PAs nas soluções não perturbativas dos propagadores, sendo feita uma análise de resíduos como auxílio à identificação da estrutura analítica. É, também, proposta e testada uma nova técnica para aproximar um conjunto discreto de pontos a um PA, que é, por último, aplicada aos propagadores do gluão e do campo fantasma provindos de simulações na rede.Um par conjugado de polos complexos, associado à estrutura de infravermelho da teoria, é identificado no propagador do gluão, estanto de acordo com a presença de singularidades em momentos complexos em teorias nas quais se observa confinamento. Quanto ao propagador do campo fantasma, é identificado um polo em p^2=0. Em ambos os propagadores é identificada uma descontinuidade no eixo-p^2 real negativo, sendo, desta forma, recuperada a análise perturbativa a altos momentos.
In a Quantum Field Theory, the analytic structure of the 2-points correlation functions, i.e. the propagators, encloses information about the properties of the corresponding quanta, particularly if they are or not confined. However, in Quantum Chromodynamics (QCD), we can only have an analytic solution in a perturbative picture of the theory. For the non-perturbative propagators, one resorts on numerical solutions of QCD that accesses specific regions of the Euclidean momentum space, as, for example, those computed via Monte Carlo simulations in the lattice. In the present work, we rely on Padé Approximants (PA) to treat the resulting data for the gluon and ghost propagators, and investigate their analytic structures.In a first stage, the advantages of using PAs are explored when reproducing the properties of a function, focusing on its analytic structure. The use of PA sequences is tested for the perturbative solutions of the propagators, and a residue analysis is performed to help in the identification of the analytic structure. A technique used to approximate a PA to a discrete set of points is proposed and tested for some test data sets. Finally, the methodology is applied to the Landau gauge gluon and ghost propagators, obtained via lattice simulations. The results identify a conjugate pair of complex poles for the gluon propagator, that is associated with the infrared structure of the theory. This is in line with the presence of singularities for complex momenta in theories where confinement is observed. Regarding the ghost propagator, a pole at p^2=0 is identified. For both propagators, a branch cut is found on the real negative p^2-axis, which recovers the perturbative analysis at high momenta.
Outro - Fundação para a Ciências e a Tecnologia - UIDB/04564/2020

We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approaches. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium charmonium regeneration is found to be a 3-to-2 process. Its corresponding regeneration rates from different input charmquark momentum spectra are evaluated. Experimental data on J/[psi] production at CERN-SPS and BNL-RHIC are compared with our numerical results in terms of both rapidity-dependent inclusive yields and transverse momentum (pt) spectra. Within current uncertainties from (interpreting) lQCD data and from input charm-quark spectra the centrality dependence of J/[psi] production at SPS and RHIC (for both mid-and forward rapidity) is reasonably well reproduced. The J/[psi] pt data are shown to have a discriminating power for in-medium charmonium properties as inferred from different interpretations of lQCD results.

Ultra-relativisitic heavy ion collisions produce quark gluon plasma-a hot and dense soup of deconfined quarks and gluons akin to the early universe. We study two models in the context of these collisions namely, Polyakov Quark Meson Model (PQM) and Hadron Resonance Gas Model (HRGM).The PQM Model provides us with a simple and intuitive understanding of the QCD equation of state and thermodynamics at non zero temperature and baryon density while the HRGM is the principle model to analyse the hadron yields measured in these experiments across the entire range of beam energies. We study the effect of including the commonly neglected fermionic vacuum fluctuations to the (2+1) flavor PQM model. The conventional PQM model suffers from a rapid phase transition contrary to what is found through lattice simulations. Addition of the vacuum term tames the rapid transition and significantly improves the model’s agreement to lattice data. We further investigate the role of the vacuum term on the phase diagram. The smoothening effect of the vacuum term persists even at non zero . Depending on the value of the mass of the sigma meson, including the vacuum term results in either pushing the critical end point into higher values of the chemical potential or excluding the possibility of a critical end point altogether. We compute the fluctuations(correlations) of conserved charges up to sixth(fourth) order. Comparison is made with lattice data wherever available and overall good qualitative agreement is found, more so for the case of the normalised susceptibilities. The model predictions for the ratio of susceptibilities approach to that of an ideal gas of hadrons as in HRGM at low temperatures while at high temperature the values are close to that of an ideal gas of massless quarks. We examine the stability of HRGMs by extending them to take care of undiscovered resonances through the Hagedorn formula. We find that the influence of unknown resonances on thermodynamics is large but bounded. We model the decays of resonances and investigate the ratios of particle yields in heavy-ion collisions. We find that extending these models do not have much effect on hydrodynamics but the hadron yield ratios show better agreement with experiment. In principle HRGMs are internally consistent up to a temperature higher than the cross over temperature in QCD; but by examining quark number susceptibilities we find that their region of applicability seems to end even below the QCD cross over.