2 . 1 RG consistency and low-energy phenomenology

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 boundstate 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. Copyright J. Braun et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 20-02-2019 Accepted 18-04-2019 Published 09-05-2019 Check for updates doi:10.21468/SciPostPhys.6.5.056