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Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / The principal purpose of this thesis was to calculate certain mass differences of elementary particles in second order perturbation theory, within the framework of a gauge invariant theory of interactions. First we calculated the mass difference of the electron and the muon on the assumption that they have same bare mass and have different physical masses as a result of their interaction with a neutral vector meson field whose quantum is the phi meson. The previous attempts in this direction treated the muon and the electron unsymmetrically, which caused the ratio of the pion decay into (electron + electronic neutrino) to the pion decay into (muon + muonic neutrino) to have a value not permitted by the accuracy of the experimental results. Those calculations predicted also the value of the anomalous magnetic moment of the muon much higher than the experimental value. Our calculation, on the other hand, not only gives the mass difference of the muon and the electron in agreement with their experimental value but also does not run into any difficulty faced by the previous calculations. Secondly, generalizing the meaning of the electromagnetic interaction, we calculated the mass differences of the different members of every charge multiplet of the strongly interacting particles. Only with two adjustable parameters we have been able to predict the mass differences of the seven pairs of particles. Finally, we speculated on the origin of the masses of the phi and rho mesons. Using the coupling constants previously introduced, we calculated their masses in agreement with the experimental masses. We used the same cut-off parameter as was assumed for the electromagnetic mass splitting. / 2031-01-01

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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.

Over the course of a college mathematics degree, students are inevitably exposed to elementary physics. The derivation of the equations of motion are the classic examples of applications of derivatives and integrals. These equations of motion are easy to understand, however they can be expressed in other ways that students aren't often exposed to. Using the Lagrangian and the Hamiltonian, we can capture the same governing dynamics of Newtonian mechanics with equations that emphasize physical quantities other than position, velocity, and acceleration like Newton's equations do. Building o of these alternate interpretations of mechanics and understanding gauge transformations, we begin to understand some of the mathematical physics relating to gauge theories. In general, gauge theories are eld theories that can have gauge transformations applied to them in such a way that the meaningful physical quantities remain invariant. This paper covers the buildup to gauge theories, some of their applications, and some computational approaches to understanding them.

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.

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