Does zero temperature decide on the nature of the electroweak phase transition?

TL;DR

This paper explores how the zero-temperature vacuum energy difference influences the strength of the electroweak phase transition, providing bounds and phenomenological implications for various models.

Contribution

It establishes a strong correlation between vacuum energy difference and phase transition strength, offering numerical bounds to predict strong first-order transitions without finite temperature calculations.

Findings

Strong correlation between vacuum energy difference and phase transition strength.

Phenomenological constraints disfavor scalar sliding scenarios.

Numerical bounds for models like GNMSSM ensure strong phase transitions.

Abstract

Taking on a new perspective of the electroweak phase transition, we investigate in detail the role played by the depth of the electroweak minimum ("vacuum energy difference"). We find a strong correlation between the vacuum energy difference and the strength of the phase transition. This correlation only breaks down if a negative eigenvalue develops upon thermal corrections in the squared scalar mass matrix in the broken vacuum before the critical temperature. As a result the scalar fields slide across field space toward the symmetric vacuum, often causing a significantly weakened phase transition. Phenomenological constraints are found to strongly disfavour such sliding scalar scenarios. For several popular models, we suggest numerical bounds that guarantee a strong first order electroweak phase transition. The zero temperature phenomenology can then be studied in these parameter regions without the need for any finite temperature calculations. For almost all non-supersymmetric models with phenomenologically viable parameter points, we find a strong phase transition is guaranteed if the vacuum energy difference is greater than $-8.8\times 10^7$~\text{GeV}$^4$. For the GNMSSM, we guarantee a strong phase transition for phenomenologically viable parameter points if the vacuum energy difference is greater than $-6.9\times 10^7$~\text{GeV}$^4$. Alternatively, we capture more of the parameter space exhibiting a strong phase transition if we impose a simultaneous bound on the vacuum energy difference and the singlet mass.