SM vacuum stability and the Weyl consistency conditions: Counting to three

TL;DR

This paper explores how Weyl anomaly structures influence perturbative orderings in the Standard Model, affecting vacuum stability analysis and revealing potential unknown aspects of renormalization group equations.

Contribution

It introduces a new perturbative ordering based on Weyl anomaly structure and applies it to analyze Higgs vacuum stability within the Standard Model.

Findings

Weyl anomaly enforces different loop orders for beta functions.

Standard Model RG equations satisfy Weyl consistency conditions.

Vacuum stability results align with previous estimates despite new ordering.

Abstract

We demonstrate how a new perturbative ordering may result from the structure of the Weyl anomaly. Respecting the abelian nature of the Weyl anomaly at the lowest order enforces the use of beta functions calculated to a different loop order for different types of couplings. These consistency conditions are found to be satisfied by the renormalization group equations of the standard model, and we perform an analysis of the vacuum stability of the Higgs potential respecting the consistency conditions and compare to the previous results. Hints toward unknown structure in the standard model renormalization group equations are found, although the vacuum stability results are in agreement with previous estimates.