Higgs mechanism and renormalization group flow: are they compatible?

TL;DR

This paper examines whether the geometric structure of the Higgs mechanism remains consistent under renormalization group flow, finding that it generally does not in minimal subtraction schemes, but physical consistency is preserved.

Contribution

It demonstrates that the geometric structure of the Higgs mechanism is not maintained under RG flow in minimal subtraction schemes, while proving the stability of physical consistency.

Findings

Higgs geometric structure not preserved under RG flow in minimal subtraction

Physical consistency remains stable under RG flow

Results derived for the U(1)-Higgs model at 1-loop order

Abstract

Usually the Lagrangian of a model for massive vector bosons is derived in a geometric way by the Higgs mechanism. We investigate whether this geometric structure is maintained under the renormalization group (RG) flow. Using the framework of Epstein-Glaser renormalization, we find that the answer is 'no', if the renormalization mass scale(s) are chosen in a way corresponding to the minimal subtraction scheme. This result is derived for the $U(1)$-Higgs model to 1-loop order. On the other hand we give a model-independent proof that physical consistency, which is a weak form of BRST-invariance of the time-ordered products, is stable under the RG-flow.