Electroweak relaxation from finite temperature

TL;DR

This paper proposes a mechanism where finite temperature effects in the early universe naturally select a small Electroweak Scale via a scalar field with temperature-dependent potential, compatible with high-scale supersymmetry.

Contribution

It introduces a novel finite temperature-based approach for dynamically setting the Electroweak Scale using a scalar with a temperature-dependent potential and explores its realization within supersymmetric models.

Findings

Scalar follows potential minimum as universe cools, trapping in a small Electroweak vacuum.

Hidden sector reheating can be high without conflicting with nucleosynthesis.

Models achieve a UV cutoff of 10 TeV with large scalar field ranges.

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.