Renormalization Scheme Dependence, RG Flow and Borel Summability in $\phi^4$ Theories in $d<4$

DOI10.1103/PHYSREVD.100.045008arXiv1905.02122MaRDI QIDQ6318282

Gabriele Spada, Giacomo Sberveglieri, M. Serone

Publication date: 6 May 2019

Abstract: Renormalization group (RG) and resummation techniques have been used in $N$-component $ph{i}^4$ theories at fixed dimensions below four to determine the presence of non-trivial IR fixed points and to compute the associated critical properties. Since the coupling constant is relevant in $d<4$ 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 $$-function is trivial to all orders in perturbation theory. The presence of a non-trivial fixed point can be unambiguously established by considering a physical observable, like the mass gap, with no need of RG techniques. Focusing on the $N=1$, $d=2$ $ph{i}^4$ 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 $u$ as the scheme is varied. While the critical coupling shows a significant sensitivity on the scheme, the accuracy in $u$ is essentially constant. As by-product of our analysis, we improve the determination of $u$ obtained with RG methods by computing three more orders in perturbation theory.

This page was built for publication: Renormalization Scheme Dependence, RG Flow and Borel Summability in $\phi^4$ Theories in $d<4$

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6318282)