In this thesis, we study the Fisher's zeros in lattice gauge theory. The analysis of singularities in the complex coupling plane is an important tool to understand the critical phenomena of statistical models. The Fisher's zero structure characterizes the scaling properties of the underlying models and has a strong influence on the complex renormalization group transformation flows in the region away from both the strong and weak coupling regimes. By reconstructing the density of states, we try to develop a systematical method to investigate these singularities and we apply the method to SU(2) and U(1) lattice gauge models with a Wilson action in the fundamental representation. We first take the perturbative approach. By using the saddle point approximation, we construct the series expansions of the density of states in both of the strong and weak regimes from the strong and weak coupling expansions of the free energy density. We analyze the SU(2) and U(1) models. The expansions in the strong and weak regimes for the two models indicate both possess finite radii of convergence, suggesting the existence of complex singularities. We then perform the numerical calculations. We use Monte Carlo simulations to construct the numerical density of states of the SU(2) and U(1) models. We also discuss the convergence of the Ferrenberg-Swendsen's method which we use for the SU(2) model and propose a practical method to find the initial values that improve the convergence of the iterations. The strong and weak series expansions are in good agreement with the numerical results in their respective limits. The numerical calculations also enable the discussion of the finite volume effects which are important to the weak expansion. We calculate the Fisher's zeros of the SU(2) and U(1) models at various volumes using the numerical entropy density functions. We compare different methods of locating the zeros. By the assumption of validity of the saddle point approximation, we find that the roots of the second derivative of the entropy density function have an interesting relation with the actual zeros and may possibly reveal the scaling property of the zeros. Using the analytic approximation of the numerical density of states, we are able to locate the Fisher's zeros of the SU(2) and U(1) models. The zeros of the SU(2) stabilize at a distance from the real axis, which is compatible with the scenario that a crossover instead of a phase transition is expected in the infinite volume limit. In contrast, with the precise determination of the locations of Fisher's zeros for the U(1) model at smaller lattice sizes L=4, 6 and 8, we show that the imaginary parts of the zeros decrease with a power law of L-3.07 and pinch the real axis at β= 1.01134, which agrees with results using other methods. Preliminary results at larger volumes indicate a first-order transition in the infinite volume limit.

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.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-15T12:16:24Z No. of bitstreams: 1 arquivototal.pdf: 5169144 bytes, checksum: 66d534e3f0c0c59bf5d35a45290fa390 (MD5) / Made available in DSpace on 2016-03-15T12:16:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 5169144 bytes, checksum: 66d534e3f0c0c59bf5d35a45290fa390 (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we propose an experimental setup for the study of Landau quantization and associated effects in a two-dimensional ultracold atomic gas. Gauge fields can emerge in the equation of motion for the optically addressed ultracold atoms. To this end, spatially dependent dark states are necessary for the internal states of the atoms. A tripod level scheme yields two degenerate dark states which can leads to either an Abelian U(1) U(1) gauge field or a non-Abelian SU(2) gauge field. Using a suitable laser configuration, we obtain a uniform U(1) U(1) magnetic field which causes the atoms organize themselves in Landau levels. The strength of the effective magnetic field depends on the relative intensity of the lasers beams at the atomic cloud. We estimate the degeneracy of the energy levels for an atomic gas formed by atoms of 87Rb. In addition, we establish the experimental conditions to reach the lowest Landau level regime. In the zero-temperature limit, we realize the emergence of magnetic oscillations in the atomic energy and its derivative as function of the inverse of the effective magnetic field (de Haas van Alphen effect). The period of the de Haas van Alphen oscillation allow us to determine area of the Fermi circle for the atomic gas via an Onsager-like relation. We also show that detuning the a laser from the two-photon resonance we generate a parabolic scalar potential that laterally confines the atoms. As a consequence, the Landau levels degeneracy is removed, since the energy spectrum depends explicitly on the transverse atomic momentum. We show that the Landau levels presents a reminiscent degeneracy when the boundaries conditions are considered. The residual degeneracy occurs when different energy levels overlap. We map the residual degeneracy points as a function of the effective magnetic field. Finally, we present an experimental scheme for observing the spin Hall effect for ultracold atoms in a tripod configuration. / Nesta tese, propomos um arranjo experimental para o estudo da quantização de Landau e efeitos associados em um gás atômico ultrafrio bidimensional. Campos de calibre podem surgir na equação de movimento para átomos ultrafrios oticamente vestidos. Para que isto ocorra, estados escuros espacialmente dependentes são necessários a partir dos estados internos dos átomos. Átomos numa configuração de níveis de energia do tipo tripod produzem dois estados escuros degenerados, que podem levar a campos de calibre Abelianos U(1) U(1) ou não-Abelianos SU(2). Utilizando uma configuração adequada de lasers, mostramos que é possível se produzir um campo magnético sintético uniforme U(1) U(1) que atua nos átomos neutros fazendo-os se organizarem em níveis de Landau. A intensidade do campo efetivo depende da intensidade relativa dos feixes de luz na nuvem atômica. Estimamos a degenerescência dos níveis de energia para um gás atômico formado por átomos de 87Rb e estabelecemos as condições experimentais para que seja atingido o regime em que todos os átomos populam unicamente o nível de Landau menos energético. Considerando o limite de temperatura nula, verificamos o surgimento de oscilações magnéticas na energia e em sua derivada como uma função do inverso do campo magnético efetivo (efeito de Haas van Alphen). O período da oscilação magnética nos permite determinar a área do círculo de Fermi para o gás atômico através de uma expressão similar a de Onsager para sistemas eletrônicos. Mostramos também que dessintonizando um dos lasers em relação à ressonância de dois fótons geramos um potencial escalar parabólico que faz com os átomos sejam lateralmente confinados. Isto resulta na remoção da degenerescência dos níveis de Landau, uma vez que a energia depende explicitamente do momento atômico transverso. Demonstramos que, aplicando condições periódicas de contorno ao sistema, temos o surgimento de uma degenerescência residual. A degenerescência remanescente ocorre quando diferentes níveis de energia se superpõem. Mapeamos os pontos de degenerescência como uma função do campo magnético efetivo. Por fim, apresentamos um esquema experimental para a observação do efeito spin Hall para átomos ultrafrios em uma configuração tripod.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23698号 / 理博第4788号 / 新制||理||1685(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 福間 將文, 准教授 吉岡 興一, 教授 萩野 浩一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

When calculating scattering amplitudes in gauge and gravitational theories one encounters infrared (IR) divergences associated with massless fields. These are known to be artifacts of constructing a quantum field theory starting with free fields, and the assumption that in the asymptotic limit (i.e. well before and after a scattering event) the incoming and outgoing states are non-interacting. In 1937, Bloch and Nordsieck provided a technical procedure eliminating the IR divergences in the cross-sections. However, this did not address the source of the problem: A detailed analysis reveals that, in quantum electrodynamics (QED) and in perturbative quantum gravity (PQG), the interactions cannot be ignored even in the asymptotic limit. This is due to the infinite range of the massless force-carrying bosons. By taking these asymptotic interactions into account, one can find a picture changing operator that transforms the free Fock states into asymptotically interacting Faddeev- Kulish (FK) states. These FK states are charged (massive) particles surrounded by a “cloud” of soft photons (gravitons) and will render all scattering processes infrared finite already at an S-matrix level. Recently it has been found that the FK states are closely related to asymptotic symmetries. In the case of QED the FK states are eigenstates of the large gauge transformations – U(1) transformations with a non-vanishing transformation parameter at infinity. For PQG the FK states are eigenstates of the Bondi-Metzner-Sachs (BMS) transformations – the asymptotic symmetry group of an asymptotically flat spacetime. It also appears that the FK states are related the Wilson lines in the Mandelstam quantization scheme. This would allow one to obtain the physical FK states through geometrical or symmetry arguments. We attempt to clarify this relation and present a derivation of the FK states in PQG from the gravitational Wilson line in the eikonal approximation, a result that is novel to this thesis.

La recherche de phases magnétiques exotiques de la matière qui fondent même à T=0 uniquement sous l'action des fluctuations quantiques a été long et ardu, à la fois théoriquement et expérimentalement. La percée est venue récemment avec la découverte de l'Herbertsmithite, un composé formant un réseau kagome parfait avec des moments magnétiques de spin-1/2. Des expériences pionnières, mêlant des mesures de NMR, µSR et de diffusion de neutrons, ont montré une absence totale de gel ou d'ordre des moments magnétiques de spin, fournissant ainsi une forte signature d'une phase paramgnétique quantique. Théoriquement, l'Herbertsmithite est extrêmement bien modélisé par le modèle de Heisenberg quantique antiferromagnétique pour des spins-1/2 sur le réseau kagome, problème qui n'a pas été résolu jusqu'à présent. Plusieurs méthodes approximatives numériques et analytiques ont donné différents états fondamentaux, allant des liquides de spins Z2 gappés et un liquide de spins exotique algébrique U(1) de Dirac aux liquides de spins chiraux et les cristaux à liaisons de valence. Dans cette thèse, le problème est traité dans le cadre d'une approche particule-esclave fermionique, à savoir le formalisme des fermions de Schwinger SU(2). Il est conclu qu'un liquide de spins sans gap algébrique de Dirac a l'énergie variationnelle la plus basse et peut en fait constituer un vrai état fondamental physique de liquide de spins. Une implémentation sophistiquée de méthodes numériques de pointes comme le Monte-Carlo variationnel, le Monte-Carlo fonctions de Green et l'application de pas Lanczos dans un schéma variationnel ont été utilisés. Il est montré que contrairement à la croyance habituelle, le liquide de spins de Dirac U(1) projeté en "2+1" dimensions est remarquablement robuste par rapport à une large classe de perturbations, incluant les liquides de spins topologiques Z2 et les cristaux à liaisons de valence. De plus, l'application de deux pas Lanczos sur la fonction d'onde du liquide de spins de Dirac U(1) montre que son énergie est compétitive avec celles proposées pour les liquides de spins topologiques Z2. Ce résultat, combiné avec les indications expérimentales qui pointent vers un liquide de spins sans gap pour l'Herbertsmithite, appuie l'affirmation que le vrai état fondamental de ce modèle est en fait un liquide de spins algébrique de Dirac.

This thesis presents the search for the dark sector process h -> Zd Zd -> 4l in events collected by the ATLAS detector at the Large Hadron Collider in 2015--2018. In this theorized process, the Standard Model Higgs boson (h) decays to four leptons via two intermediate Beyond-the-Standard-Model particles each called Zd. This process arises from interactions of the Standard Model with a dark sector. A dark sector consists of one or more new particles that have limited or zero interaction with the Standard Model, such as the new vector boson Zd (dark photon). It could have a rich and interesting phenomenology like the visible sector (the Standard Model) and could naturally address many outstanding problems in particle physics. For example, it could contain a particle candidate for dark matter. In particular, Higgs decays to Beyond-the-Standard-Model particles are well-motivated theoretically and are not tightly constrained; current measurements of Standard Model Higgs properties permit the fraction of such decays to be as high as approximately 30%. The results of this search do not show evidence for the existence of the h -> Zd Zd -> 4l process and are therefore interpreted in terms of upper limits on the branching ratio B(h -> Zd Zd) and the effective Higgs mixing parameter kappa^prime. / Graduate