A interação forte a baixas energias pode ser abordada por meio de lagrangianas efetivas. Nesse contexto, o modelo de Skyrme representa uma forma de descrever bárions, que emergem como sólitons topológicos de uma lagrangiana mesônica quiral. A interação nucleon-nucleon (NN) é comumente tratada neste modelo de maneira aproximada, através do chamado Ansatz Produto (AP), cujo problema mais sério é não reproduzir a atração de alcance intermediário no canal escalar-isoescalar do potencial NN. O objetivo deste trabalho é construir um novo ansatz para o cálculo da interação NN no modelo de Skyrme. Para isso, analisamos o AP, investigando as causas deste problema fenomenológico, e concluímos que deve-se à componente azimutal de seu campo piônico. A partir disto, construímos o Ansatz Novo (AN), com o qual calculamos o novo potencial. Comparando os resultados com outros potenciais existentes, mostramos que o AN constitui uma solução plausível para o problema. / Strong interactions at low energies can be treated by means of effective lagrangians. In this context, the Skyrme model is regarded as a way to describe baryons as topological solitons from a chiral mesonic lagrangian. In the framework of this model, nucleon-nucleon (NN) interaction is usually derived in the sudden approximation, by means of the so called Product Ansatz (PA). Its most serious problem is the absence of the intermediate range attraction in the scalar-isoscalar channel of the NN potential. We construct a new ansatz to derive the NN interaction in the Skyrme model. At first, we analise the PA and investigate the causes of its phenomenological problem. We conclude it is due to the azimuthal component of its pionic field. With this result we build the New Ansatz (NA) and calculate the new potential. Comparisons of the results with other existent potentials show that NA constitutes a plausible solution to the problem.

Quantum Chromodynamics (QCD) is believed to be the theory of strong interactions. At high energies, it has been successfully applied to explain the interactions in accelerators. At these energies, the method used to do the calculations is perturbation theory. But at low energies, since the strong coupling constant becomes large, perturbation theory is no longer applicable. Hence, one needs non-perturbative approaches. Some of these approaches are based on the fundamental QCD Lagrangian, such as the QCD sum rules or lattice calculations. Some others use an effective theory approach to relate experimental observables one to the other. Chiral Perturbation Theory (ChPT) is one of these approaches. In this thesis, we make a review of chiral perturbation theory and its applications to study the mixing phenomenon between the neutral pseudoscalar mesons eta and eta-prime.

Orientador: Manoel Roberto Robilotta / Banca: José de Sá Borges Filho / Banca: Manuel M. B. Malheiro de Oliveira / Banca: Lauro Tomio / Banca: Alfredo Pio Noronha Rodrigues Galeão / Resumo: Utilizando a simetria quiral, calculamos a contribuição dominante ao potencial nucleon-nucleon (NN) devido à troca de três píons não correlacionados. Esta contribuição é isovetorial com as componentes pseudoescalar e axial. A pseudoescalar é dominante, tem um alcance de 1.0 fm e contribui no canal de píon. No mesmo contexto, estudamos a produção de um píon na interação nucleon-nucleon devida à troca de dois píons. O termo dominante do Kernel da produção é construído a partir da mesma interação básica usada no potencial NN devido à troca de três píons. Relacionamos este termo à componente central do potencial NN devido à troca de dois píons e mostramos que esta, por sua vez, é dominada pelo fator de forma escalar píon-nucleon. O Kernel obtido foi aplicado para o limiar da produção e na construção de um potencial de três nucleons. Os resultados foram generalizados para um potencial NN central qualquer e comparados ao potencial de Argonne e àquele devido à troca de um méson escalar ...ctício / Abstracts: Using the chiral symmetry, we calculated the dominant contribution to the nucleon-nucleon (NN) potential due to the exchange of three non-correlated pions (3o). This contribution is isovetor with pseudoscalar and axial components. The pseudoscalar component is dominant, it has a range of 1.0 fm and it contributes in the pion channel. In the same context, we studied the pion production in the nucleon-nucleon interaction due to the exchange of two pions (2o). The dominant term of the production Kernel is built from the same basic interaction used in the 3o-exchange NN potential. We related this term to the central component of the 2o-exchange NN potential and we showed that the latter, on its turn, is dominated by the pion-nucleon scalar form factor. The obtained Kernel was applied at the threshold and in the constructioin of a three-nucleon potential. The results were generalized foa a central NN potential of any kind and compared to the potentials of Argonne and to that due to the exchange of one ...ctitious scalar meson / Doutor

No presente trabalho construímos o potencial nucleon-nucleon devido à troca de dois píons dentro do contexto relativístico da teoria de perturbação quiral, formulada por Becher e Leutwyler. No estudo do espalhamento píon-nucleon, eles desenvolveram um método que exibe a regra de contagem de potências, mantendo a invariância relativística. Os autores também chamam a atenção para um problema presente na formulação de bário pesado, de que sua série quiral não converge na região de baixa energia em torno de t=4µ2, onde µ é a massa do píon. Nós mostramos que este problema é bastante relevante para o potencial nucleon-nucleon, principalmente pelo fato dessa região de energia determinar suas características assintóticas. A dinâmica da troca de dois píons na interação nucleon-nucleon é determinada pelas sub-amplitudes píon-nucleon. Partindo da sub-amplitude de Becher e Leutwyler, obtemos diagramas classificados em três famílias, de acordo com sua topologia e constantes de acoplamento envolvidas. Na definição do potencial subtraímos, da amplitude relativéstica, a iteração da troca de um píon, seguindo a prescrição de Blankenbecler e Sugar. O nosso potencial até a ordem q4 é expresso em termos de seis funções básicas, associadas a integrais de loop, calculadas relativisticamente. Ele mantém as propriedades assintóticas corretas, desde que as integrais básicas não sejam expandidas. Forçando tal expansão, com o objetivo de comparar com os resultados de Entem e Machleidt, observamos concordância na maioria dos termos. Algumas diferenças estão associadas à discrepância na relação de Goldberger-Treiman, indicadas por GT, e dois termos, a contribuições de dois loops. As demais, muito provavelmente estão relacionadas à iteração da troca de um píon. No espaço de configuração, comparamos os nossos resultados com a parte de médio alcance de duas versões do potencial de Argonne, AV14 e AV18. Observamso uma boa concordância apenas para o potencial central isoescalar, o canal mais importante para a fenomenologia. Para as demais componentes, temos discrepâncias inclusive entre as versões AV14 e Av18. Com base na classificação da dinâmica em três famílias e analisando suas contribuições para cada componente, apresentamos uma proposta de como evitar ambiguidades desse tipo na construção de potenciais fenomenológicos. / This work is devoted to the construction of a two-pion Exchange nucleon-nucleon potential in the framework of the relativist chiral perturbation theory, formulated by Becher and Leutwyler. In their study of pion-nucleon scattering they developed a method to regain the Power counting rules while keeping Lorentz invariance. These authors also Drew attention to a problem present in the heavy baryon formulation, that is chiral serie does not converge in the low-energy region around t=4µ2, where µ is the pions mass. We have shown that this problem is rather relevant to nucleon-nucleon potential, mainly due to the fact that this range of energy determines its asymptotic properties. The dynamics of the two-pion Exchange nucleon-nucleon interaction is determined by pion-nucleon sub-amplitudes. Starting from Becher and Letwylers sub-amplitude, we obtain diagrams classified in three families, according to their topology and the coupling constants involved. In the definition of the potential we substract, from the relativist amplitude, the iteration o fone-pion Exchange, following the prescription of Blankenbecler and Sugar. Our potential up to order q4 is expressed in terms of six basic functions associated to relativistic loop integrals. It keeps the correct asymptotic properties, as long as we do not expand the basic integrals. Forcing such na expansio, in order to compare it with the results from Entem and Machleidt, we observe na agreement in the majority o terms. Some differrences are associated to the Goldberg-Treiman discrepancy, indicated by GT, and two terms come from two loop calculations. The remaining ones are probably related to the prescription adopted for the iteration o fone-pion exchange. In configuration space we compare our results with the médium-range component of two versions of the Argonne potential, AV14 and AV18. We obtain agreement only for the central isoscalar potential, the most important to phenomenology. Regarding other channels, we observe discrepancies even between AV14 and AV18. Based on the classification of the dynamics in three families and analysing their contributions to each component, we propose a way to overcome such ambiguities in the construction of phenomenological potentials.

Este trabalho é resultado de uma série de estudos feitos com o objetivo de investigar a influ- ência de uma álgebra fermiônica deformada nos mecanismos de quebra e restauração da si- metria quiral no modelo de Nambu-Jona-Lasinio. Esse modelo foi escolhido pois é um modelo efetivo para a QCD que mostra com razoável facilidade uma de suas principais características, a quebra dinâmica da simetria quiral e a geração de uma massa dinâmica para os quarks. O trabalho pode ser dividido essencialmente em três partes. A primeira consiste em um estudo inicial onde a deformação foi implementada diretamente na equação de gap do modelo NJL através de um cálculo deformado do condensado. Na segunda parte, o mesmo procedimento de deformação foi aplicado na Hamiltoniana do modelo permitindo que seus efeitos se propagem nos cálculos até uma nova equação de gap. Uma extensão natural do trabalho e um estudo do modelo deformado a temperatura finita, onde a coexistência da temperatura e da deformação algébrica pode ser investigada. Esse estudo e a terceira parte do trabalho / This work is a result of a serie of studies where the aim is to investigate the influence of a de- formed fermionic algebra in the mechanisms of breaking and restoration of chiral symmetry in the Nambu-Jona-Lasinio model. This model was chosen because it is an effective model for QCD which shows with reasonable facility one of its main features, the dynamical breaking of chiral symmetry and the generation of a dynamical mass for the quarks. The work can be divided essentialy in three parts. The first consists in a initial study where the deformation was implemented directly in the gap equation of the NJL model through a defor- med calculation of the condensates. In second part, the same deformation procedure was applied in the Hamiltonian of the model allowing their effects to be propagated in the calcula- tions till a new gap equation. A natural extension of the work is a study of the deformed model at finite temperature, where the coexistence of temperature and algebric deformation can be investigated. This study is the third part of the work.

A interação forte a baixas energias pode ser abordada por meio de lagrangianas efetivas. Nesse contexto, o modelo de Skyrme representa uma forma de descrever bárions, que emergem como sólitons topológicos de uma lagrangiana mesônica quiral. A interação nucleon-nucleon (NN) é comumente tratada neste modelo de maneira aproximada, através do chamado Ansatz Produto (AP), cujo problema mais sério é não reproduzir a atração de alcance intermediário no canal escalar-isoescalar do potencial NN. O objetivo deste trabalho é construir um novo ansatz para o cálculo da interação NN no modelo de Skyrme. Para isso, analisamos o AP, investigando as causas deste problema fenomenológico, e concluímos que deve-se à componente azimutal de seu campo piônico. A partir disto, construímos o Ansatz Novo (AN), com o qual calculamos o novo potencial. Comparando os resultados com outros potenciais existentes, mostramos que o AN constitui uma solução plausível para o problema. / Strong interactions at low energies can be treated by means of effective lagrangians. In this context, the Skyrme model is regarded as a way to describe baryons as topological solitons from a chiral mesonic lagrangian. In the framework of this model, nucleon-nucleon (NN) interaction is usually derived in the sudden approximation, by means of the so called Product Ansatz (PA). Its most serious problem is the absence of the intermediate range attraction in the scalar-isoscalar channel of the NN potential. We construct a new ansatz to derive the NN interaction in the Skyrme model. At first, we analise the PA and investigate the causes of its phenomenological problem. We conclude it is due to the azimuthal component of its pionic field. With this result we build the New Ansatz (NA) and calculate the new potential. Comparisons of the results with other existent potentials show that NA constitutes a plausible solution to the problem.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20174号 / 理博第4259号 / 新制||理||1612(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 菅沼 秀夫, 教授 國廣 悌二, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25106号 / 理博第5013号 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 杉本 茂樹, 教授 青木 慎也, 教授 橋本 幸士 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

One of the most promising routes to create advanced materials is self-assembly. Self-assembly refers to the self-organisation of building blocks to form ordered structures. As the properties of the self-assembled materials will inherit the properties of the basic building blocks, it is then possible to engineer the properties of the materials by tailoring the properties of the building blocks. In order to create mesoscale materials, the self-assembly of molecular building blocks of different sizes and interactions is important. Mesoscopic materials can be obtained by using larger building blocks such as nano and colloidal particles. Colloidal particles are particularly attractive as building blocks because it is possible to design interparticle interactions by controlling both the chemistry of the particles' surface and the properties of the solvent in which the particles are immersed. The self-assembly of spherical colloidal particles has been widely reported in the literature. However, advances in experimental techniques to produce particles with different shapes and sizes have opened new opportunities to create more complex structures that cannot be formed using spherical particles. Indeed, the particles' shape and effective interactions between them dictate the spatial arrangement and micro-structure of the system, which can be engineered to produce functional materials for a wide range of applications. The driving forces determining the self-assembly of colloidal particles can be modified by the use of external influences such as geometrical confinement and electromagnetic forces. Geometrical confinement, for example, has been used to design quasi two-dimensional materials such as multi-layered structures of spheres, dimers, rods, spherical caps, and monolayers of platelets with various geometries and symmetries. In this dissertation, we present three computer simulations studies using Monte Carlo and Molecular Dynamics simulations determining the self-assembly of monolayer colloidal platelets with different shapes confined in two dimensions. These particles have been selected due to recent experiments in colloidal particles with similar shapes. All the particles' models are represented by planar polygons, and three different effects affecting their self-assembly have been analysed: (a) the curvature of the particles' vertices; (b) the curvature of the particles' edges; and finally (c) the addition of functional groups on the particles' surface. These studies aim to demonstrate that the subtle changes on the particle's shape can be used to engineer complex patterns for the fabrication of advanced materials. Monte Carlo simulations are performed to study the self-assembly of colloidal platelets with rounded corners with 4, 5, and 6-fold symmetries. Square platelets provide a rich phase behaviour that ranges between disorder-order and order-order phase transitions. Suprisingly, the disk-like shape of pentagons and hexagons prevents the total crystallisation of these systems, even at a high pressure state. A hysteresis gap is observed by the analysis of compression and expansion runs for the case of square platelets and the thermodynamic method known as direct coexistence method is used to be accurately determined the point of the order-order transition. Further, unexpected results are obtained by performing Molecular Dynamics simulations in systems with platelets with 3, 4, 5, and 6-fold symmetries when all the sides of each polygon are curved. Macroscopic chiral symmetry breaking is observed for platelets with 4 and 6-fold symmetries, and for the first time a rule is promoted to explain when these chiral structures can be formed driven only by packing effects. This unique rule is verified also for platelets with the same curved sides as previously when functional chains tethered to either vertices or sides. Indeed, square platelets with curved sides confined in two dimensions can form chiral structures at medium densities when flexible chains tethered to either vertices or sides. Triangular platelets with curved sides can form chiral structures only when the chains are tethered to the corners, since the chains experience an one-hand rotation to sterically protect one side. When the chains are symmetrically tethered to the sides, local chiral symmetry breaking is observed as both left-hand and right-hand sides on each vertex are sterically protected allowing the same probability for rotation either in clockwise or anticlockwise direction.

Quantenchromodynamik mit zwei leichten Quarks wird in der Gitterregularisierung mit verbesserten Wilson Fermionen betrachtet. Die chirale Symmetrie in dieser Formulierung wird von Gitterartefakten, die linear im Gitterabstand a sind, explizit gebrochen. Daher erfordern die axialen Isospin Ströme Verbesserung (im Symanzik Sinn), sowie eine endliche Renormierung, wenn sie die Ward--Takahashi Identitäten des Kontinuums bis auf kleine Gitterkorrekturen proportional zu a^2 erfüllen sollen. Algorithmische Probleme bei großen Gitterabständen machen die numerischen Simulationen der Gittertheorie schwierig. Der Hybrid Monte Carlo Algorithmus leidet unter einem verformten Dirac Spektrum in Form unphysikalisch kleiner Eigenwerte. Es wird gezeigt, daß dies ein Gitterartefakt ist, welches schnell verschwindet, wenn der Gitterabstand verringert wird. Ein alternativer Algorithmus, der polynomische Hybrid Monte Carlo Algorithmus, zeigt erheblich bessere Eigenschaften im Umgang mit den außergewöhnlich kleinen Eigenwerten. Durch Erweiterung und Verbesserung vorher verwendeter Methoden wird die nicht-perturbative Verbesserung und Renormierung des Axialstroms durch Korrelationsfunktionen im Schrödinger Funktional implementiert. In beiden Fällen wird dies erzielt, indem man Ward Identitäten des Kontinuums bei endlichem Gitterabstand erzwingt. Zusammen stellt dies die chirale Symmetrie bis zur quadratischen Ordnung im Gitterabstand wieder her. Mit wenig zusätzlichem Aufwand wird auch der Normierungsfaktor des lokalen Vektorstroms berechnet. Die Methoden, die hier entwickelt und implementiert wurden, können leicht auch für andere Wirkungen verwendet werden, die im Schrödinger Funktional formuliert werden können. Dies umfaßt verbesserte Eichwirkungen sowie Theorien mit mehr als zwei dynamischen Quarks. / Quantum Chromodynamics with two light quark flavors is considered in the lattice regularization with improved Wilson fermions. In this formulation chiral symmetry is explicitly broken by cutoff effects linear in the lattice spacing a. As a consequence the isovector axial currents require improvement (in the Symanzik sense) as well as a finite renormalization if they are to satisfy the continuum Ward-Takahashi identities associated with the isovector chiral symmetries up to small lattice corrections of order a^2. In exploratory numerical simulations of the lattice theory algorithmic difficulties were encountered at coarse lattice spacings. There the hybrid Monte Carlo algorithm used suffers from a distorted Dirac spectrum in the form of unphysically small eigenvalues. This is shown to be a cutoff effect, which disappears rapidly as the lattice spacing is decreased. An alternative algorithm, the polynomial hybrid Monte Carlo algorithm, is found to perform significantly better in the presence of exceptionally small eigenvalues. Extending previously used methods both the improvement and the renormalization of the axial current are implemented non-perturbatively in terms of correlation functions formulated in the framework of the Schrödinger functional. In both cases this is achieved by enforcing continuum Ward identities at finite lattice spacing. Together, this restores the isovector chiral symmetry to quadratic order in the lattice spacing. With little additional effort the normalization factor of the local vector current is also obtained. The methods developed and implemented here can easily be applied to other actions formulated in the Schrödinger functional framework. This includes improved gauge actions as well as theories with more than two dynamical quark flavors.