The QCD Axion Stabilizes the Higgs Electroweak Vacuumby Tommy on 31/03/2017
This exposition has been extremely helpful.
The QCD Axion and Electroweak Vacuum Stability, J. McDonald (14 March 2017)
The complex field Φ containing the QCD axion has a natural portal coupling to the Higgs doublet of the form λhϕ |Φ|2 |H|2. Here we consider the possibility that λhϕ has a natural magnitude for a dimensionless coupling, λhϕ ∼ 0.1 − 1. This is possible if the total mass squared parameter of the Higgs in the vacuum, including quadratic divergent and the Φ 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 fa < 1.3 × 1010 GeV.
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