Orientador: Adriano Antonio Natale / Banca: Gastão Krein / Banca: Eduardo Fraga / Banca: Letícia Palhares / Banca: Marcelo Guimarães / Resumo: A presente tese é baseada em parte do trabalho realizado durante o Doutorado e diz respeito aos dois domínios da Cromodinâmica Quântica (QCD) a temperatura zero: o regime confinado, a baixas energias, e o assintoticamente livre, a altas energias. Com o objetivo de cumprir uma ponte entre estes domínios e inspirado em sugestões de aprimoramentos da série perturbativa, este trabalho investiga uma proposta para uma expansão perturbativa aprimorada, a ser um método aplicável tanto à fenomenologia da QCD quanto a estudos de seu regime não-perturbativo. A proposta consiste numa expansão em loops efetivos - um híıbrido entre equações de Schwinger-Dyson e expansão em loops usual, fazendo uso de ferramentas desta porém vestindo certas quantidades como forma de considerar seu comportamento completo dentro de loops. A tese descreve os principais avanços nesse sentido, na aplicação a funções de correlação - em particular os propagadores do gluon e do ghost, como um passo preliminar a futuras aplicações. Após lidar com questões de transversalidade do propagador do gluon e renormalizabilidade no método, a expansão em loops efetivos na sua presente forma contém gluons (dinamicamente) massivos e uma carga efetiva, além da possiblidade de uma vestimenta para o vértice de três gluons. Nesta formulação, foram obtidos resultados qualitativos razoáveis para o comportamento não-perturbativo completo dos propagadores do ghost e do gluon, e comparação com a rede é analisada. Perspectivas de curto e de mais longo prazo são discutidas / Abstract: This thesis is based on part of the work done during the Ph.D., and it concerns the two distinguished domains of Quantum Chromodynamics (QCD) at zero temperature: the low-energy, confined domain, and the high-energy, asymptotically free one. Aiming to bridge the gap between them, and inspired by suggested improvements of the QCD perturbative series, this work investigates a proposal for an improved perturbative expansion, as a method to be applicable to QCD phenomenology, as well as to nonperturbative studies. The proposal consists in an effective-loop expansion - a hybrid between Schwinger- Dyson equations and usual loop expansions, making use of the latter's framework, yet dressing certain quantities in order to account for their complete behavior inside loops. The thesis describes the main efforts on this matter, in its application to correlation functions - the gluon and ghost propagators, in particular, as a preliminary step preceding further applications. After dealing with issues as transversality of the gluon self-energy and renormalizability within the method, the present form of the effective-loop expansion contains dynamically massive gluons and an effective running charge, besides the possible dressing of the three-gluon vertex. Within this formulation, reasonable qualitative results were obtained for achieving the complete, nonperturbative behavior of the ghost and gluon propagators, and comparison with lattice is analyzed. Readily achievable and longer term prospects are also discussed / Doutor

Bibliography: p. 377-382.

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

The interactions of heavy quarks within the Quark Gluon Plasma (QGP) are interpreted utilizing an elastic, thermodynamic, 2-body T-matrix in order to calculate drag coefficients of heavy-quark systems derived from a Fokker-Planck equation. A spacelike momentum constraint is employed and produces an effective, color dependent potential with the addition of relativistic factors motivated by the appropriate Feynman diagrams. Hard Thermal Loop (HTL) corrections are interpreted in the context of a finite temperature quark-gluon system, allowing a non-perturbative determination of the gluon's contribution to the drag coefficient. An enhancement of the relaxation rate of ~2 is observed at low momenta, leading to an enhancement of the overall relaxation rate of 20%, while the high-p limit approaches a perturbative level. The importance of a nonperturbative treatment of the QGP to reproduce the dynamical drag coefficient is illustrated.

Thesis (Ph. D.)--University of Canterbury, 2007. / Typescript (photocopy). Includes bibliographical references (p. 127-135). Also available via the World Wide Web.

Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2002? / Bibliography: p. 377-382.

Orientador: Adriano Antonio Natale / Banca: Atílio Cucchieri / Banca: Márcio José Menon / Banca: Maria Beatriz de Leone Gay Ducati / Banca: Rogério Rosenfeld / Resumo: Através da solução das equações de Schwinger-Dyson (ESD) é possível estudar diversos aspectos importantes da QCD não-perturbativa como confinamento e quebra de simetria quiral; desta forma as ESD são, obviamente, muito interessantes para estudo da fenomenologia das interações hadrônicas. Após uma breve revisão sobre equações de Schwinger-Dyson (ESD) e sobre algumas soluções da ESD do propagador do glúon disponíveis na literatura, apresentamos possíveis testes fenomenológicos para estas soluções. Observaremos que apenas uma das soluções apresentadas descreve satisfatoriamente os dados experimentais, e esta solução é compatível com uma massa dinâmica para o glúon. Finalizando, supomos que o glúon têm uma massa dinâmica e calculamos seus efeitos sobre os decaimentos de quarkônios pesados / Abstract: Through the solution of Schwinger-Dyson equations (SDE) it is possible to study important features of nonperturbative QCD such as confinement and chiral symmetry breaking; in this way SDE are, obviously, very interesting for the study of phenomenology of hadronic interactions. After a brief review on SDE and some Solutions of gluon propagator SDE available in literature, we present possible phenomenological tests for these solutions. We shall observe that only one of the solutions presented describes satisfactorily the experimental data, and such solution is compatible with a dynamical mass for the gluon. Eventually, we assume that the gluon has a dynamical mass and calculate its effects on heavy quarkonia decays / Doutor

Orientador: Adriano Antonio Natale / Banca: Juan Carlos Montero Garcia / Banca: Márcio José Menon / Resumo: Discutiremos alguns modelos fenomenológicos baseados na QCD perturbativa que tentam descreve a seção de choque total hadrônica. Falaremos sobre as principais características dos espalhamentos hadrônicos, como o crescimento da seção de choque total com a energia devido ao aumento no número de jatos, e o decrescimento da seção de choque total a baixas energias. Mostraremos a inviabilidade do tratamento perturbativo de QCD para o cálculo da seção de choque total hadrônica. Estudaremos alguns espalhamentos hadrônicos no limite de baixas energias utilizando informações não-perturbativas das propriedades do sistema, tal como o fato do gluon adquirir massa dinâmica nesta região. Averiguando propriedades e modelos que procuram descrever a seção de choque total hadrônica, obteremos idéias suficientes para propor um modelo que descreva a seção de choque total hadrônica real / Abstract: We discuss some phenomenological models based on perturbative QCD, that try to describe the total hadronic cross section. We comment on peculiarities of hadronic scattering, as the increase of cross section at high energies, as well as its decrease in low energies. Some of the problems of perturbative QCD to deal with the total cross section calculation are discussed. We discuss how non-perturbative QCD properties, as the generation of a dynamical gluon mass, can be introduced in the low energy limit of the total cross section calculation. Finally we propose a phenomenological way to modify the total hadronic cross section calculation with these non-perturbative information / Mestre

Neste texto nós discutimos o fluxo de energia em reações hadrônicas e em fotoprodução. Apresentamos um modelo de produção de partículas com o qual é fácil estudar a deposição de energia na região central e o efeito de partícula dominante. Analisamos dados de produção de partículas carregadas e charrnosas em várias energias. Discutimos o papel individual das interações soft e semi-hard. Fazemos, entre outras, a previsão de que a energia mais altas, uma fração maior da energia das colisões será depositada na região central e, como consequência, a assimetria observada na produção de charme vai diminuir. Estudamos e propomos um teste experimental para a produção de mesons pesados a partir da fragmentação de quarks leves. / We present and apply to several situations a model for particle production. With this model it is possible to understand the energy flow in hadronic reactíons, in photoproduction and also ma.ke predictions for the behaviour of some observables at higher energies. It is also possible to study the individual contributions of soft and semíhard interactions and the individual contributions coming from the central and fragmentation regions. We analyse charged and charmed particle production data at several energies. We predíct, among other things, that an increasing fraction of the reaction energy is going to be released in the central region. As a consequence the asymmetry observed in charm production will decrease. We study and propose as experimental test to heavy meson production from light quark fragmentation.

Neste texto nós discutimos o fluxo de energia em reações hadrônicas e em fotoprodução. Apresentamos um modelo de produção de partículas com o qual é fácil estudar a deposição de energia na região central e o efeito de partícula dominante. Analisamos dados de produção de partículas carregadas e charrnosas em várias energias. Discutimos o papel individual das interações soft e semi-hard. Fazemos, entre outras, a previsão de que a energia mais altas, uma fração maior da energia das colisões será depositada na região central e, como consequência, a assimetria observada na produção de charme vai diminuir. Estudamos e propomos um teste experimental para a produção de mesons pesados a partir da fragmentação de quarks leves. / We present and apply to several situations a model for particle production. With this model it is possible to understand the energy flow in hadronic reactíons, in photoproduction and also ma.ke predictions for the behaviour of some observables at higher energies. It is also possible to study the individual contributions of soft and semíhard interactions and the individual contributions coming from the central and fragmentation regions. We analyse charged and charmed particle production data at several energies. We predíct, among other things, that an increasing fraction of the reaction energy is going to be released in the central region. As a consequence the asymmetry observed in charm production will decrease. We study and propose as experimental test to heavy meson production from light quark fragmentation.