Electroweak relaxation from finite temperature

TL;DR

The paper tackles the electroweak hierarchy problem by proposing a finite-temperature cosmological mechanism in which a shift-symmetric scalar $\phi$ coupled to the Higgs evolves as the early Universe cools. The key idea is that the temperature dependence of $\phi$'s potential—arising either from a strongly coupled hidden sector or a calculable weakly coupled one-loop thermal potential—drives $\phi$ away from zero and, through a periodic barrier, traps the Higgs in a vacuum with a small electroweak scale; this relaxation occurs without fine-tuning and can be embedded in a SUSY UV-completion of the visible sector. The authors analyze two realizations: a strong-coupling model and a weakly coupled hidden sector, deriving the required temperature hierarchies and parameter constraints (including a large anomaly coefficient $N$ and the mixing scale $f$) to ensure adiabatic evolution, appropriate Higgs triggering, and tunneling suppression. They further discuss UV completions with the visible sector realized as the MSSM at a high scale and show that a cutoff around $10\,\mathrm{TeV}$ is viable, albeit with cosmological and model-building caveats; they also outline directions for extending the framework to raise the UV scale and to explore alternative barrier structures or multi-field extensions.

Abstract

We study theories which naturally select a vacuum with parametrically small Electroweak Scale due to finite temperature effects in the early universe. In particular, there is a scalar with an approximate shift symmetry broken by a technically natural small coupling to the Higgs, and a temperature dependent potential. As the temperature of the universe drops, the scalar follows the minimum of its potential altering the Higgs mass squared parameter. The scalar also has a periodic potential with amplitude proportional to the Higgs expectation value, which traps it in a vacuum with a small Electroweak Scale. The required temperature dependence of the potential can occur through strong coupling effects in a hidden sector that are suppressed at high temperatures. Alternatively, it can be generated perturbatively from a one-loop thermal potential. In both cases, for the scalar to be displaced, a hidden sector must be reheated to temperatures significantly higher than the visible sector. However this does not violate observational constraints provided the hidden sector energy density is transferred to the visible sector without disrupting big bang nucleosynthesis. We also study how the mechanism can be implemented when the visible sector is completed to the Minimal Supersymmetric Standard Model at a high scale. Models with a UV cutoff of 10 TeV and no fields taking values over a range greater than 10^12 GeV are possible, although the scalar must have a range of order 10^8 times the effective decay constant in the periodic part of its potential.

Figures (1)

• Figure 1: The potential for $\phi$ and the location of the field, indicated by a red dot, in the different temperatures regimes. Top left:$T_{hid}> \Lambda_b$ and $T_{vis}> \Lambda_a$ when both strong coupling terms in the potential are strongly suppressed and the position of $\phi$ is set by the explicit shift symmetry breaking potential. Top right:$T_{vis} < \Lambda_a$ and $T_{hid} > \Lambda_b$ when $\Lambda_a$ becomes strong but $\phi$ is yet to be displaced. Bottom left:$T_{vis} < \Lambda_a$ and $T_{hid} \sim \Lambda_b$ so $\phi_{min}$ and $\phi$ are moving. Bottom right:$T_{vis} < \Lambda_a$ and $T_{hid} < \Lambda_b$ when $\phi$ is trapped in a local minimum of the potential with small Higgs VEV by the cosine part of the potential. In these plots $\epsilon = 10^{-8}$, $M=10^4 \,{\rm{GeV}}$, and the period of the cosine has been greatly increased from realistic parameter ranges for visibility. For phenomenologically viable values of the cosine period, $\phi$ will not stop in the first local minimum it meets, but instead travel through many until the stopping condition Eq.\ref{['eq:cond2']} is met.