On the Extraction of Observables from Lattice QCD and the First Lattice Calculation of Nuclear Parity Violation

The fundamental field theory for nuclear physics interactions is quantum chromodynamics (QCD). Currently the only known way to calculate observables directly from this underlying theory is to perform numerical calculations using a method known as lattice QCD. Due to limitations on currently available computer resources for these calculations they must be performed at unphysical pion masses, in small volumes, and with a finite lattice spacing. To account for the effects of these constraints, lattice QCD calculations must currently be paired with the results of effective field theory calculations to extract physical observables that can be directly compared with experiment.;This thesis discusses aspects of lattice QCD and effective field theory (EFT) calculations relevant to the extraction of several observables of interest to nuclear physics. In Chap. 2 the EFT of heavy baryon chiral perturbation theory (HBchiPT) is examined in a regime where the lattice size and pion mass are both small, known as the epsilon-regime, where the effects of pion zero momentum modes must be treated nonperturbatively. A formalism is developed to calculate nucleon observables in the regime to all orders and it is applied to the calculation the nucleon axial charge and magnetic moment. In Chap. 3 nonrelativistic perturbation theory is used in a large volume expansion to calculate the ground state energy of a system of arbitrary numbers of two species of mesons (pion and kaons) up to O (L-6). This will allow the extraction of the pion, kaon, and pion-kaon scattering lengths and three-body interactions from lattice QCD calculations. Finally, in Chap. 4 the first exploratory calculation of a nuclear parity violating quantity in QCD is performed. Due to the small size of the lattice used, this calculation has very large systematic errors. However, it provides a baseline that can be used to determine the parameters of a more realistic calculation on larger lattice sizes.