A Correlation Between the Higgs Mass and Dark Matter

TL;DR

This paper explores how the Higgs mass influences the stability of the electroweak vacuum and proposes a correlation between the Higgs mass and dark matter abundance via the Peccei-Quinn scale, supported by current data.

Contribution

It introduces a novel link between the Higgs mass, vacuum stability, and dark matter through the Peccei-Quinn mechanism and statistical arguments.

Findings

Higgs mass determines the instability scale of the electroweak vacuum.

The Peccei-Quinn scale is statistically likely to match the instability scale.

Predicted dark matter abundance aligns with current observations.

Abstract

Depending on the value of the Higgs mass, the Standard Model acquires an unstable region at large Higgs field values due to RG running of couplings, which we evaluate at 2-loop order. For currently favored values of the Higgs mass, this renders the electroweak vacuum only meta-stable with a long lifetime. We argue on statistical grounds that the Higgs field would be highly unlikely to begin in the small field meta-stable region in the early universe, and thus some new physics should enter in the energy range of order, or lower than, the instability scale to remove the large field unstable region. We assume that Peccei-Quinn (PQ) dynamics enters to solve the strong CP problem and, for a PQ-scale in this energy range, may also remove the unstable region. We allow the PQ-scale to scan and argue, again on statistical grounds, that its value in our universe should be of order the instability scale, rather than (significantly) lower. Since the Higgs mass determines the instability scale, which is argued to set the PQ-scale, and since the PQ-scale determines the axion properties, including its dark matter abundance, we are led to a correlation between the Higgs mass and the abundance of dark matter. We find the correlation to be in good agreement with current data.