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The Large Hadron Collider (LHC) and the four major experiments set up along its 27 kilometers of circumference (ATLAS, CMS, ALICE and LHCb), have recently started to explore the high–energy frontier at √s = 8 TeV, and will move to even higher energy in just about 2 years. The aim of physics searches at LHC experiments was to complete the picture of the Standard Model (SM) of elementary particles with the discovery of the Higgs boson and to look for specific signatures of models extending the current understanding of particle interactions, at zero and non–zero temperature. In 2012, the official discovery of the Higgs boson, the only missing particle of the StandardModel, was announced by ATLAS and CMS. Other important results include the measurement of rare decay modes in heavy quarks systems, and indications of CP violation in charm decays by LHCb. Signatures of beyond the Standard Model (BSM) physics are currently being looked for in the experimental data, and this often requires the knowledge of quantities that can be computed only with non–perturbative methods. This thesis focuses on some possible extensions of the SM and the analysis of interesting physical observables, like masses or decay rates, calculated using non– perturbative lattice methods. The approach followed for the main part of this work is to model BSM theories as effective field theories defined on a lattice. This lattice approach has a twofold advantage: it allows us to explore non– renormalizable gauge theories by imposing an explicit gauge–invariant cutoff and it allows us to go beyond perturbative results in the study of strongly interacting systems. Some of the issues of the SM that we will try to address include, for example, the hierarchy problem and the origin of dynamical electroweak symmetry breaking (DEWSB). We investigate non–perturbatively the possibility that the lightness of the mass for an elementary scalar field in a four–dimensional quantum field theory might be due to a higher–dimensional gauge symmetry principle. This idea fits in the Gauge–Higgs unification approach to the hierarchy problem and the results we present extend what is known from perturbative expectations. Extra dimensional models are also often used to approach DEWSB. Another approach to DEWSB implies a new strongly interacting gauge sector that extends the SM at high energies and it is usually referred to as Technicolor. The phenomenological consequences of Technicolor can only be studied by non– perturbative methods at low energy since the theory is strongly coupled at large distances. We perform a comprehensive lattice study of fermionic and gluonic scalar bound states in one of the candidate theories for Technicolor BSM physics. We relate our findings to the nature of the newly discovered Higgs boson. New physics is also commonly believed to be hidden in the flavour sector of the SM. In this sector, lattice calculations of non–perturbative input parameters are needed in order to make precise predictions and extract signals of possible new physics. In particular, heavy quark physics on the lattice is still in development and it is important to understand the relevant discretisation errors. We describe a preliminary study of the mixing parameter of heavy–light mesons oscillations in a partially–quenched scenario, using staggered dynamical fermions and domain wall valence fermions.

It is expected that the number of flavors in a gauge theory plays an important role in model building for physics beyond the standard model. We study the phase structure of the 12 flavor case through lattice simulations using a Rational Hybrid Monte Carlo (RHMC) algorithm for different masses, betas, and volumes, to investigate the question of conformality for this number of flavors. In particular, we analyze the Fisher's zeroes, in the vicinity of the endpoint of a line of first order phase transitions. This is motivated by previous studies that show how the complex renormalization group (RG) flows can be understood by looking at the zeros. The pinching of the imaginary part of these zeros with respect to increasing volume provides information about a possible unconventional continuum limit. We also study the mass spectrum of a multiflavor linear sigma model with a splitting of fermion masses. The single mass linear sigma model successfully described a light sigma in accordance to recent lattice results. The extension to two masses predicts an unusual ordering of scalar masses, providing incentive for further lattice simulations with split quark mass.

Thesis (Ph.D.)--Boston University / In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ~ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S > 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S > 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB.

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.

The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.

The discovery of a light scalar at the Large Hadron Collider is in basic agreement with the predictions of an elementary Higgs in the Standard Model (SM). Nonetheless, a light, fundamental scalar is difficult to accommodate in the SM because quantum corrections suggest its mass should be much higher than the scale of electroweak symmetry breaking (EWSB). A natural possibility is to replace the Higgs by a strongly coupled composite. Composite dynamics also gives a natural explanation to the origin of EWSB. Phenomenologically viable composite models of EWSB are constrained by experiment to feature approximate scale invariance. This behavior may follow from near conformal dynamics. At present, lattice gauge theory (LGT) provides the only quantitative method to study near conformal composite Higgs dynamics in a fully consistent strongly coupled relativistic quantum field theory. As a novel approach to the question of finding and studying near conformal theories, I will apply LGT to the study of a generalization of Quantum ChromoDynamics (QCD) with four chiral fermion flavors plus eight flavors of finite, tunable mass. By continuously varying the mass of the eight heavy flavors, I can tune between the four flavor chirally broken theory, which exhibits features similar to QCD, and the twelve flavor theory, which is known to have a conformal fixed point. This is the "4+8 Model" for directly studying near-conformal behavior. In this dissertation, I will review modern composite phenomenology, followed by outlining a study of the 4+8 Model over a range of heavy flavor masses. As a check of near-conformal behavior, I will measure the scale dependent coupling with the method of the Wilson Flow. After verifying the existence of controllable, approximate scale invariance, I will measure the low energy particle spectrum of the 4+8 Model. This includes a Higgs-like light composite scalar. Throughout this dissertation I will make reference to LGT measurement code I wrote and contributed to the software package FUEL.

In this thesis we are concerned with the existence of infrared fixed points and the conformal window for gauge theories with fermions. We are particularly interested in those theories that are candidates for walking technicolor. We discuss the background of technicolor and the techniques relevant to a theoretical understanding of the conformal window. Following this we extend the ideas of metric confinement and causal analyticity to theories with fermions in non-fundamental representations. We use these techniques to, respectively, provide a lower bound on the lower end of the conformal window and to provide a measure of perturbativity. As well as analytic calculations we use lattice techniques to investigate two particular candidate theories for walking technicolor - SU(2) with two adjoint fermions and with six fundamental fermions. We use Schrodinger Functional techniques to investigate the running of the theory across a wide range of scales. We measure both the running of the coupling and an estimator for the fermion mass anomalous dimension, $gamma$. We find that both theories are consistent with an infrared fixed-point. However, paying particular attention to our error estimates, we are unable to absolutely confirm their existence. This is a not unexpected result for SU(2) with two adjoint fermions but is rather surprising for SU(2) with only six fundamental fermions. In the region where we are consistent with a fixed point we find $0.05<gamma<0.56$ for $SU(2)$ with two adjoint fermions and $0.135<gamma<1.03$ for $SU(2)$ with six fundamental fermions. The measurement of $gamma$ for $SU(2)$ with two adjoint fermions is the first determination of $gamma$ for any candidate theory of walking technicolor.

Discutimos um modelo de calibre com simetria Z (N) na rede, sendo as variáveis dinâmicas definidas em faces de cubos. Mostramos a dualidade com um sistema de spins Z (N) em quatro dimensões e a autodualidade em seis dimensões para este modelo, utilizando o formalismo da matriz de transferência. Analisamos as funções de correlação invariantes por transformações de calibre, constatando os decaimentos exponenciais com o volume (para altas temperaturas e d &#8805 3) e com a área (para baixas temperaturas e d > 3). Para três dimensões, o modelo não apresenta transição de fase sendo exatamente solúvel. Estudamos também a versão U (1) do modelo e mostramos sua equivalência com uma teoria de campos clássica livre na região de baixas temperaturas / We discussus a model with a Z (N) gauge symmetry on a lattice, the dynamical variables being defined on faces of cubes. The duality with a Z (N) spin system in four dimensions and the selfduality in six dimensions is shown for this model, using the transfer matrix formalism. The gauge invariant correlation functions have been analysed and we verify their exponential decay with volume (at high temperatures and d &#8805 3) and with the área (at low temperatures and d > 3). For three dimensions, the model exhibits no phase transition, being exactly soluble. We also study a U (I) version o four model and show its equivalence with a free classical field theory in the low temperature region