# The QCD Axion and Electroweak Vacuum Stability

## TL;DR

This paper explores how the QCD axion, through its coupling to the Higgs, can stabilize the electroweak vacuum, leading to constraints on the axion decay constant.

## Contribution

It demonstrates that a natural portal coupling between the axion sector and the Higgs can stabilize the electroweak vacuum and derives an upper bound on the axion decay constant.

## Key findings

- Electroweak vacuum stability constrains the axion decay constant to be less than 1.3×10^{10} GeV.
- A natural portal coupling of order 0.1-1 can stabilize the Higgs potential.
- The Higgs mass parameter can be renormalized to match observations with the axion sector included.

## Abstract

The complex field $\Phi$ containing the QCD axion has a natural portal coupling to the Higgs doublet of the form $\lambda_{h \phi}|\Phi|^2 |H|^2$. Here we consider the possibility that $\lambda_{h \phi}$ has a natural magnitude for a dimensionless coupling, $\lambda_{h \phi} \sim 0.1-1$. This is possible if the total mass squared parameter of the Higgs in the vacuum, including quadratic divergent and the $\Phi$ vacuum expectation value contributions, is renormalized to reproduce the observed Higgs boson mass. It is then possible for the axion sector to stabilize the electroweak vacuum. We show the requirement of electroweak vacuum stability implies that the axion decay constant satisfies $f_{a} < 1.3 \times 10^{10}$ GeV.

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Source: https://tomesphere.com/paper/1703.04839