A series of experiments using a polarized beam incident on a polarized frozen spin target

(FROST) was conducted at Jefferson Lab in 2010. Results presented here were taken

during the second running period with the FROST target using the CEBAF Large Acceptance

Spectrometer (CLAS) detector at Jefferson Lab, which used transversely-polarized

protons in a butanol target and a circularly-polarized incident tagged photon beam with

energies between 0.62 and 2.93 GeV. Data are presented for the F and T polarization observables

for h meson photoproduction on the proton from W = 1.55 GeV to 1.80 GeV.

The data presented here will improve the world database and refine theoretical approaches

of nucleon structure.

In this thesis, I present the study of nucleon structure from distinct perspectives. I start by elaborating the motivations behind the endeavors and then introducing the key concept, namely the generalized parton distribution functions (GPDs), which serves as the frame- work describing hadronic particles in terms of their fundamental constituents. The second chapter is then devoted to a detailed phenomenological study of the Virtual Compton Scattering (VCS) process, where a more comprehensive parametrization is suggested. In the third chapter, the renormalization kernels that enters the QCD evolution equations at twist- 4 accuracy are computed in terms of Feynman diagrams in momentum space, which can be viewed as an extension of the work by Bukhvostov, Frolov, Lipatov, and Kuraev (BKLK). The results can be used for determining the QCD background interaction for future precision measurements.

Spin-orbit interactions are important in determining nuclear structure. They lead to a shift in the energy levels in the nuclear shell model, which could explain the sequence of magic numbers in nuclei. Also in nucleon-nucleon scattering, the large nucleon polarization observed perpendicular to the plane of scattering needs to be explained by adding the spin-orbit interactions in the potential. Their effects change the equation of state and other properties of nuclear matter. Therefore, the simulation of spin-orbit interactions is necessary in nuclear matter.

The auxiliary field diffusion Monte Carlo is an effective and accurate method for calculating the ground state and low-lying exited states in nuclei and nuclear matter. It has successfully employed the Argonne v6' two-body potential to calculate the equation of state in nuclear matter, and has been applied to light nuclei with reasonable agreement with experimental results. However, the spin-orbit interactions were not included in the previous simulations, because the isospin-dependent spin-orbit potential is difficult in the quantum Monte Carlo method. This work develops a new method using extra auxiliary fields to break up the interactions between nucleons, so that the spin-orbit interaction with isospin can be included in the Hamiltonian, and ground-state energy and other properties can be obtained.

Monte Carlo methods often used in nuclear physics, such as auxiliary field diffusion Monte Carlo and Green's function Monte Carlo, have typically relied on phenomenological local real-space potentials containing as few derivatives as possible, such as the Argonne-Urbana family of interactions, to make sampling simple and efficient. Basis set methods such as no-core shell model or coupled-cluster techniques typically use softer non-local potentials because of their more rapid convergence with basis set size. These non-local potentials are typically defined in momentum space and are often based on effective field theory. Comparisons of the results of the two types of methods are complicated by the use of different potentials. This thesis discusses progress made in using such non-local potentials in quantum Monte Carlo calculations of light nuclei. In particular, it shows methods for evaluating the real-space, imaginary-time propagators needed to perform quantum Monte Carlo calculations using non-local potentials and universality properties of these propagators, how to formulate a good trial wave function for non-local potentials, and how to perform a "one-step" Green's function Monte Carlo calculation for non-local potentials.

The theory of quantum electrodynamics predicts that beta decay of the neutron into a proton, electron, and anti-neutrino should be accompanied by a continuous spectrum of photons. A recent experiment, RDK I, reported the first detection of radiative decay photons from neutron beta decay with a branching ratio of (3.09 ± 0.32) × 10-3 in the energy range of 15 keV to 340 keV. This was achieved by prompt coincident detection of an electron and photon, in delayed coincidence with a proton. The photons were detected by using a single bar of bismuth germanate scintillating crystal coupled to an avalanche photodiode. This thesis deals with the follow-up experiment, RDK II, to measure the branching ratio at the level of approximately 1% and the energy spectrum at the level of a few percent. The most significant improvement of RDK II is the use of a photon detector with about an order of magnitude greater solid angle coverage than RDK I. In addition, the detectable energy range has been extended down to approximately 250 eV and up to the endpoint energy of 782 keV. This dissertation presents an overview of the apparatus, development of a new data analysis technique for radiative decay, and results for the ratio of electron-proton-photon coincident Repg to electron-proton coincident Rep events.

Quark matter at sufficiently high density and low temperature is expected to be a color superconductor, and may exist in the interior of neutron stars. The properties of two simplest possible color-superconducting phases, i.e., the color-flavor-locked (CFL) and two-flavor superconducting (2SC) phases, are reviewed. The effect of a magnetic field on the pairing dynamics in two-flavor color-superconducting dense quark matter is investigated. A universal form of the gap equation for an arbitrary magnetic field is derived in the weakly coupled regime of QCD at asymptotically high density, using the framework of Schwinger-Dyson equation in the improved rainbow approximation. The results for the gap in two limiting cases, weak and strong magnetic fields, are obtained and discussed. It is shown that the superconducting gap function in the weak magnetic field limit develops a directional dependence in momentum space. This property of the gap parameter is argued to be a consequence of a long-range interaction in QCD.