Renormalization scheme dependence, RG flow, and Borel summability in phi^4 Theories in d<4

Renormalization group (RG) and resummation techniques have been used in N-component.4 theories at fixed dimensions below four to determine the presence of nontrivial IR fixed points and to compute the associated critical properties. Since the coupling constant is relevant in d &lt; 4 dimensions, the RG is entirely governed by renormalization scheme-dependent terms. We show that the known proofs of the Borel summability of observables depend on the renormalization scheme and apply only in "minimal" ones, equivalent in d = 2 to an operatorial normal ordering prescription, where the beta-function is trivial to all orders in perturbation theory. The presence of a nontrivial fixed point can be unambiguously established by considering a physical observable, like the mass gap, with no need of RG techniques. Focusing on the N = 1, d = 2.4 theory, we define a one-parameter family of renormalization schemes where Borel summability is guaranteed and study the accuracy on the determination of the critical exponent. as the scheme is varied. While the critical coupling shows a significant sensitivity on the scheme, the accuracy in. is essentially constant. As a by-product of our analysis, we improve the determination of. obtained with RG methods by computing three more orders in perturbation theory.