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.
Highlights
∼ Λ3ah cos (φ/feff ), where Λa and feff are mass scales
For consistency with the scenario where the hidden sector has supersymmetry, we show how the selection of a light EW scale can occur when the visible sector is UV completed to the Minimal Supersymmetric Model (MSSM) by superpartners with masses of order the cutoff
Provided the hidden sector is such that its energy density is transferred to the visible sector at reasonably late times, heating the universe to above the scale of big bang nucleosynthesis (BBN) this is compatible with cosmological observations
Summary
The Lagrangian contains an scalar φ, with an approximate shift symmetry. We will see later that for the most interesting points in parameter space the visible sector temperature satisfies Tvis ∼ Λa Under this assumption, the interactions of φ with the visible sector (and with the physics that generates the periodic Λa potential) occur at a rate Γvis approximately given by. The only constraints are that the visible sector is reheated to a temperature above ∼ MeV in order that BBN occurs, and below ∼ 100 GeV so that φ does not jump over the barriers and explore vacua with larger Higgs VEVS. Since this depends on the details of the hidden sector, and is independent of the properties required for the rest of the mechanism, we do not consider this further in the present work Provided all of these conditions are satisfied, eq (2.20) sets the point in field space at which φ will stop.
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