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In this thesis we present two different research projects in theoretical high energy physics. The first part deals with inflationary dynamics of the early universe and its observable consequences in measurements of the cosmic microwave background radiation. Here we investigate how inhomogeneous initial conditions for single field inflation with an initial fast-roll stage can alter the standard inflationary predictions for the power spectrum of the cosmic microwave background at largest scales. In the second part of the thesis we calculate long distance spin effects in gravitational scattering processes. Both classical and quantum corrections arise at the one loop level and are shown to have universal structures with forms and coefficients independent of the spins of the scattered particles. We also include calculations of electromagnetic and of mixed electromagnetic-gravitational scattering.

This thesis reports on two experiments conducted by the HAPPEx (Hall A Proton Parity Experiment) collaboration at the Thomas Jefferson National Accelerator Facility. For both, the weak neutral current interaction (WNC, mediated by the Z0 boson) is used to probe novel properties of hadronic targets. The WNC interaction amplitude is extracted by measuring the parity-violating asymmetry in the elastic scattering of longitudinally polarized electrons off unpolarized target hadrons. HAPPEx-III, conducted in the Fall of 2009, used a liquid hydrogen target at a momentum transfer of Q2 = 0.62 GeV2. The measured asymmetry was used to set new constraints on the contribution of strange quark form factors ([special characters omitted]) to the nucleon electromagnetic form factors. A value of APV = −23.803 ± 0.778 (stat) ± 0.359 (syst) ppm resulted in [special characters omitted] = 0.003 ± 0.010 (stat) ± 0.004 (syst) ± 0.009 (FF). PREx, conducted in the Spring of 2010, used a polarized electron beam on a 208Pb target at a momentum transfer of Q 2 = 0.009 GeV2. This parity-violating asymmetry can be used to obtain a clean measurement of the root-mean-square radius of the neutrons in the 208Pb nucleus. The Z 0 boson couples mainly to neutrons; the neutron weak charge is much larger than that of the proton. The value of this asymmetry is at the sub-ppm level and has a projected experimental fractional precision of 3%. We will describe the accelerator setup used to set controls on helicity-correlated beam asymmetries and the analysis methods for finding the raw asymmetry for HAPPEx-III. We will also discuss in some detail the preparations to meet the experimental challenges associated with measuring such a small asymmetry with the degree of precision required for PREx.

Charge symmetry in the nucleon parton distributions assumes the distribution of quarks in the proton are related to those in the neutron. Indirect experimental evidence constrains Charge Symmetry Violation (CSV) to be less than 9%. In Quantum Chromo-Dynamics (QCD), charge symmetry is broken by the mass difference between the up and down quarks. CSV in the valence region can be extracted from precision measurements of the cross section ratio of charged pion production in semi-inclusive deep inelastic scattering (SIDIS) from deuterium. Such measurements were proposed and carried in experiment E12-09-002 at Jefferson Lab. The experiment was conducted in Hall C from fall 2018 to spring 2019 using the upgraded 10.6 GeV incident electron beam. In this SIDIS experiment, charged pions are detected in coincidence with scattered electrons covering the four-momentum transfer of the virtual photon Q^2 from 4 to 5.5 GeV^2, the Bjorken variable x for 0.35-0.65, and the fraction of energy transfer carried by the outgoing pion z from 0.4-0.7. / Physics

We explore the mechanics of inflation within simplified extra-dimensional models involving an inflaton interacting with a Einstein-Maxwell system in two extra dimensions. The models are complicated enough to include a stabilization mechanism for the extra-dimensional radius, but simple enough to solve the full six-dimensional field equations. After performing a consistent truncation, which guarantees our six-dimensional equations are equivalently satisfied by the four dimensional equations of motion, we explore (numerically and analytically) the power-law solutions evident in our initial parameter search. After a comprehensive search for potential power-law scaling solutions in both six and four dimensions, we find two that give rise to interesting inflationary dynamics. They both can generically exist outside of the usual four dimensional effective theory, and yet, we still trust them since our truncation is consistent. One of these is a dynamical attractor whose features are relatively insensitive to initial conditions, but whose slow-roll parameters cannot be arbitrarily small; the other is not an attractor but can roll much more slowly, until eventually transitioning to another solution due to its unstable nature. We present a numerical and analytic discussion of these two solutions. Four of the appendices contain calculations in more explicit detail than are performed in the main text, while a fifth contains a representative Mathematica worksheet and the sixth contains the general results of the systematic sweep for scaling solutions. / Thesis / Master of Science (MSc) / When looking out at the night sky, we see a universe that is extremely flat and looks the same no matter what direction we stare. However, these present-day observations require the universe to have begun under very specific circumstances, which is not something that naturally occurs; think about what is necessary to hit a hole-in-one with a golf club: a very precise and specific shot is required. The theory of Cosmological Inflation—a period of rapid expansion in the early universe—is the current leading theory proposed to explain these observations. In our exploration, we aim to study inflation from a higher-dimensional perspective in which two extra spatial dimensions are added to our usual three. Ultimately, we find three classes of solutions, two of which exist outside of the regimes usually studied, that have the potential both to explain current observations, and also be useful tools in future explorations.

Two areas of nonleptonic weak interactions are examined: parity-violation in nucleon-nucleon interactions including $\Delta$ excitations, and strangeness-changing hypernuclear decay processes. In both cases we utilize SU(6)$\sb{w}$-based quark model pictures to describe the weak hadronic physics. In the first part of this dissertation we develop an effective parity-violating Hamiltonian for the weak interactions of $\Delta$'s with hadrons and mesons. We evaluate weak parity-violating $\Delta$-$\Delta$-meson and $\Delta$-nucleon-meson vertices for $\pi$, $\rho$, and $\omega$ mesons, thus extending previous work involving only nucleons and mesons. The second part of this dissertation presents the results of calculations for several observables involving the decay of hypernuclei. We examine the model dependence of these observables by considering several variations of the model and its parameters.

Dynamical Symmetry Breaking is studied as an alternative to the Standard Model. A set of dynamical equations are derived for quark and vector particle masses. When the symmetry is broken, massless pseudoscalar boundstates appear. New interactions are necessary to explain the physical mass spectrum. A number of possible models for new physics are studied, and some conditions for new interactions are obtained. Numerical result for several interesting models are presented.

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