Renormalization group consistency and low-energy effective theories

Understand

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.