Lattice methods and effective field theory

TL;DR

This paper discusses lattice field theory techniques applied to nuclear effective field theory, focusing on pionless EFT, including code examples, uncertainty analysis, and extensions beyond pionless EFT.

Contribution

It provides a detailed lattice formulation of pionless EFT with practical code guidance and discusses systematic uncertainties and extensions to more complex EFTs.

Findings

Lattice methods effectively study nuclear EFTs.

Systematic and statistical errors are quantifiable.

Extensions beyond pionless EFT are feasible.

Abstract

Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply these techniques to nuclear Effective Field Theory (EFT), a non-relativistic theory for nuclei involving the nucleons as the basic degrees of freedom. The lattice formulation of [1,2] for so-called pionless EFT is discussed in detail, with portions of code included to aid the reader in code development. Systematic and statistical uncertainties of these methods are discussed at length, and extensions beyond pionless EFT are introduced in the final Section.