Renormalization-Group flow for the field strength in scalar self-interacting theories

TL;DR

This paper investigates the Renormalization-Group flow of the effective potential and field strength in scalar self-interacting theories, revealing sharp peaks in field renormalization near the broken phase boundaries, supporting non-trivial vacuum effects.

Contribution

It provides a numerical analysis of coupled RG equations for V(φ) and Z(φ) in the broken phase, highlighting sharp features in Z(φ) near flatness endpoints.

Findings

Z(φ) peaks sharply near flatness region endpoints

Numerical solutions align with convexity of V(φ)

Supports non-trivial vacuum field renormalization

Abstract

We consider the Renormalization-Group coupled equations for the effective potential V(\phi) and the field strength Z(\phi) in the spontaneously broken phase as a function of the infrared cutoff momentum k. In the k \to 0 limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(\phi), indicates a sharp peaking of Z(\phi) close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.