Effective Field Theories and Lattice QCD

TL;DR

This paper reviews the connections between lattice QCD and effective field theories, especially chiral effective theory, highlighting how effective theories support lattice calculations and presenting recent results on low energy constants.

Contribution

It provides a comprehensive overview of how effective field theories, particularly chiral perturbation theory, enhance lattice QCD analyses and reports recent lattice results for low energy constants.

Findings

Inclusion of discretization errors into chiral effective theory.

Lattice QCD results for low energy constants of chiral theories.

Recent preliminary lattice calculations on the three-flavor chiral limit.

Abstract

I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.