Uses of Effective Field Theory in Lattice QCD

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 ...

Light and heavy-light (b) hadrons are among the most interesting and among the most challenging quantities to calculate in lattice gauge theory. One would like to avoid discretization effects from very heavy quarks and to calculate chiral extrapolations and to calculate finite volume effects from light quarks or to minimize these effects. For this one uses effective theories: Chiral Perturbation Theory and Nonrelativistic QCD or Heavy Quark Effective Theory. Lattice results a...

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. The...

A confluence of theoretical and technological developments are beginning to make possible contributions to nuclear physics from lattice QCD. Effective field theory plays a critical role in these advances. I give several examples.

These are the proceedings of the workshop on ``Effective Field Theories of QCD'' held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from November 26 to 30, 2001. The workshop concentrated on Chiral Perturbation Theory in its various settings, its relations with lattice QCD and dispersion theory and the use of effective field theories in systems with one, two or more nucleons as well as at high baryon densities. Included are a ...

In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons...

These lectures describe the use of effective field theories to extrapolate results from the parameter region where numerical simulations of lattice QCD are possible to the physical parameters (physical quark masses, infinite volume, vanishing lattice spacing, etc.). After a brief introduction and overview, I discuss three topics: 1) Chiral perturbation theory in the continuum; 2) The inclusion of discretization effects into chiral perturbation theory, focusing on the applicat...

We present a simple introduction to the techniques of effective field theory (EFT) and their application to QCD. For problems with more than one energy scale, the EFT approach is a useful alternative to more traditional model-building strategies. The most relevant such problem for this discussion is that of making contact between QCD and the hadronic phase of matter. As a simple example, an EFT calculation of the bound states of hydrogen within QED is sketched. A more signifi...

These are the proceedings of the workshop on ``Effective Field Theories in Nuclear, Particle and Atomic Physics'' held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from December 13 to 17, 2005. The workshop concentrated on Effective Field Theory in many contexts. A first part was concerned with Chiral Perturbation Theory in its various settings and explored strongly its use in relation with lattice QCD. The second part consis...

The subject of effective interactions is introduced and applications in both quantum mechanics and quantum field theory are presented. In particular the use of chiral perturbation theory as an effective low energy description of QCD is developed and it is argued that such methods rally are effective in both the meson and baryonic sectors.