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What's new with the electroweak phase transition?

M. Laine, K. Rummukainen

TL;DR

The paper reviews non-perturbative lattice studies of the electroweak phase transition, showing that in the Standard Model the transition is not first-order for experimentally allowed Higgs masses, while in the MSSM a strong first-order transition may occur under specific mass hierarchies, enabling electroweak baryogenesis. It contrasts 4d lattice simulations with dimensionally reduced 3d effective theories, highlighting that dimensional reduction reliably captures infrared dynamics and agrees with full 4d results in studied regimes. The non-perturbative endpoint in the SM lies near m_H ≈ 72 GeV with Ising universality, and MSSM studies indicate possible baryogenesis-compatible regions with light right-handed stops and Higgs masses up to ~105–110 GeV. Open questions remain on CP-violation at the phase boundary and broader MSSM parameter exploration, which could be probed with extended 3d theories and targeted 4d simulations.

Abstract

We review the status of non-perturbative lattice studies of the electroweak phase transition. In the Standard Model, the complete phase diagram has been reliably determined, and the conclusion is that there is no phase transition at all for the experimentally allowed Higgs masses. In the Minimal Supersymmetric Standard Model (MSSM), in contrast, there can be a strong first order transition allowing for baryogenesis. Finally, we point out possibilities for future simulations, such as the problem of CP-violation at the MSSM electroweak phase boundary.

What's new with the electroweak phase transition?

TL;DR

The paper reviews non-perturbative lattice studies of the electroweak phase transition, showing that in the Standard Model the transition is not first-order for experimentally allowed Higgs masses, while in the MSSM a strong first-order transition may occur under specific mass hierarchies, enabling electroweak baryogenesis. It contrasts 4d lattice simulations with dimensionally reduced 3d effective theories, highlighting that dimensional reduction reliably captures infrared dynamics and agrees with full 4d results in studied regimes. The non-perturbative endpoint in the SM lies near m_H ≈ 72 GeV with Ising universality, and MSSM studies indicate possible baryogenesis-compatible regions with light right-handed stops and Higgs masses up to ~105–110 GeV. Open questions remain on CP-violation at the phase boundary and broader MSSM parameter exploration, which could be probed with extended 3d theories and targeted 4d simulations.

Abstract

We review the status of non-perturbative lattice studies of the electroweak phase transition. In the Standard Model, the complete phase diagram has been reliably determined, and the conclusion is that there is no phase transition at all for the experimentally allowed Higgs masses. In the Minimal Supersymmetric Standard Model (MSSM), in contrast, there can be a strong first order transition allowing for baryogenesis. Finally, we point out possibilities for future simulations, such as the problem of CP-violation at the MSSM electroweak phase boundary.

Paper Structure

This paper contains 9 sections, 7 equations, 2 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. PERTURBATION THEORY
  3. NON-PERTURBATIVE METHODS
  4. 4d simulations
  5. 3d simulations
  6. SIMULATION RESULTS
  7. The Standard Model
  8. MSSM
  9. FUTURE PROSPECTS

Figures (2)

  • Figure 1: The phase diagram of the Standard Model. The non-perturbative endpoint location has been studied with 3d simulations in [11--14] and with 4d simulations in [15--18]. In perturbation theory (dotted line), the transition is always of the first order.
  • Figure 2: The Higgs field expectation value in the MSSM mssmsim, compared with 2-loop perturbation theory. For $\tilde{m}_U\mathop{\hbox{$>$$\sim$}} 64...67$ GeV, there is a two-stage transition, and the values of $v_H/T$ shown represent the situation after the latter stage.