Quantum Chromodynamics (QCD) is the fundamental theory that governs

hadronic physics. However, due to its non-perturbative nature at low-energy/long

distances, QCD calculations are difficult. The only method for performing these

calculations is through lattice QCD. These computationally intensive calculations

approximate continuum physics with a discretized lattice in order 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.

Developing analytic formulae describing the systematic errors due to the

discrete lattice spacings is the main focus of this work.

To account for these systematic effects in terms of hadronic interactions, effective

field theory proves to be useful. Effective field theory (EFT) provides a

formalism for categorizing low-energy effects of a high-energy fundamental theory

as long as there is a significant separation in scales. An example of this is in chiral

perturbation theory (χPT ), where the low-energy effects of QCD are contained in a

mesonic theory whose applicability is a result of a pion mass smaller than the chiral

breaking scale. In a similar way, lattice χPT accounts for the low-energy effects of

lattice QCD, where a small lattice spacing acts the same way as the quark mass.

In this work, the basics of this process are outlined, and multiple original calculations

are presented: effective field theory for anisotropic lattices, I=2 ππ scattering

for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of

effective field theory and 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.