Renormalization group consistency and low-energy effective theories

TL;DR

This paper discusses the importance of renormalization group consistency in low-energy effective theories of QCD, highlighting how cutoff effects and regularization schemes influence their predictive power, especially in finite and dense systems.

Contribution

It provides a framework for analyzing cutoff effects and regularization-scheme dependences in low-energy effective theories of QCD, emphasizing the role of renormalization group consistency.

Findings

Violations of RG consistency significantly impact model predictions.

Regularization scheme dependence affects the reliability of low-energy QCD models.

Ensuring RG consistency improves the predictive power of effective theories.

Abstract

Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are consistent quantum field theories by themselves and can be embedded in QCD, but typically have a physical ultraviolet cutoff that restricts their range of validity. Here, we provide a discussion of the concept of renormalization group consistency, aiming at an analysis of cutoff effects and regularization-scheme dependences in general studies of low-energy effective theories. For illustration, our findings are applied to low-energy effective models of QCD in different approximations including the mean-field approximation. More specifically, we consider hot and dense as well as finite systems and demonstrate that violations of renormalization group consistency affect significantly the predictive power of the corresponding model calculations.