Wilsonian flow and mass-independent renormalization Original Research Article

Abstract We derive the Gell-Mann and Low renormalization group equation in the Wilsonian approach to renormalization of massless gΦ4 in four dimensions, as a particular case of a non-linear equation satisfied at any scale by the Wilsonian effective action. We give an exact expression for the β and γΦ functions in terms of the Wilsonian effective action at the Wilsonian renormalization scale ΛR; at the first two loops they are simply related to the gradient of the flow of the relevant couplings and have the standard values. Beyond two loops this relation is spoiled by corrections due to irrelevant couplings. We generalize this analysis to the case of massive gΦ4, introducing a mass-independent Wilsonian renormalization scheme; using the flow equation technique we prove renormalizability and we show that the limit of vanishing mass parameter exists. We derive the corresponding renormalization group equation, in which β and γΦ are the same as in the massless case; γm is also mass-independent; at one loop it is the gradient of a relevant coupling and it has the expected value.