Power Counting Regime of Chiral Effective Field Theory and Beyond

TL;DR

This paper investigates the power-counting regime of chiral effective field theory, establishing methods to identify the regime where higher-order terms are negligible, and explores the potential for an intrinsic scale to extend its applicability.

Contribution

It introduces techniques to determine the power-counting regime of chiral EFT across different renormalization schemes using nucleon mass as a benchmark.

Findings

Methods to identify the PCR where results are scheme-independent.

Evidence of a small PCR for chiral EFT.

Potential intrinsic scale for describing lattice results outside PCR.

Abstract

Chiral effective field theory complements numerical simulations of quantum chromodynamics (QCD) on a space-time lattice. It provides a model-independent formalism for connecting lattice simulation results at finite volume and a variety of quark masses to the physical world. The asymptotic nature of the chiral expansion places the focus on the first few terms of the expansion. Thus, knowledge of the power-counting regime (PCR) of chiral effective field theory, where higher-order terms of the expansion may be regarded as negligible, is as important as knowledge of the expansion itself. Through the consideration of a variety of renormalization schemes and associated parameters, techniques to identify the PCR where results are independent of the renormalization scheme are established. The nucleon mass is considered as a benchmark for illustrating this general approach. Because the PCR is small, the numerical simulation results are also examined to search for the possible presence of an intrinsic scale which may be used in a nonperturbative manner to describe lattice simulation results outside of the PCR. Positive results that improve on the current optimistic application of chiral perturbation theory beyond the PCR are reported.