Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory

TL;DR

This paper reviews how Wilsonian renormalization and power counting principles can be applied to nuclear effective field theories, especially for non-perturbative phenomena like two-nucleon interactions, to improve systematic low-energy nuclear physics calculations.

Contribution

It clarifies the application of Wilsonian renormalization and power counting in non-perturbative nuclear effective field theories, extending understanding beyond perturbative methods.

Findings

Power counting can be derived within Wilsonian renormalization.

Application to two-nucleon scattering is explained.

Potential extension to many-body nuclear systems is discussed.

Abstract

Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental ---perhaps unknown or unsolvable--- high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.