Topics in Lattice QCD and Effective Field Theory

Effective field theories provide a formalism for categorizing low-energy effects of a high-energy fundamental theory in terms of the low-energy degrees of freedom. This process has been well established in mapping the fundamental theory of QCD in terms of the hadronic degrees of freedom, which allows for quantitative connections and predictions between hardronic observables. A more direct approach to performing the non-perturbative QCD calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. However, the fundamental theory of interest here is lattice QCD, as opposed to the usual continuum QCD. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 $\pi\pi$ scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a usage of effective field theories and the employment of an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.