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High Temperature Dimensional Reduction of the MSSM and other Multi-Scalar Models

Marta Losada

TL;DR

The paper develops a three-stage dimensional reduction to produce a finite-temperature 3D effective theory for the MSSM, generalizing the approach to general two-Higgs-doublet models and the NMSSM. It provides full one-loop matching between 3D couplings and the underlying four-dimensional parameters, including temperature-dependent logarithms, Debye masses, and potential two-light-scalar scenarios. After integrating out non-static modes, heavy squarks/sleptons, and then heavy Higgs and A_o, the authors derive explicit expressions for the 3D gauge and scalar couplings (g_3^2 and bar{λ}_3) that govern the infrared dynamics, enabling non-perturbative lattice analyses of the electroweak phase transition in these multi-scalar theories. The work also discusses non-generic cases with multiple light scalars and outlines extensions to 2HDM and NMSSM, highlighting the broader applicability of dimensional reduction to finite-temperature SUSY and non-SUSY multi-scalar models.

Abstract

Using dimensional reduction we construct an effective 3D theory of the Minimal Supersymmetric Standard Model at finite temperature. The final effective theory is obtained after three successive stages of integration out of massive particles. We obtain the full 1-loop relation between the couplings of the reduced theory and the underlying 4D couplings and masses. The procedure is also applied to a general two Higgs doublet model and the Next to Minimal Supersymmetric Standard Model.

High Temperature Dimensional Reduction of the MSSM and other Multi-Scalar Models

TL;DR

The paper develops a three-stage dimensional reduction to produce a finite-temperature 3D effective theory for the MSSM, generalizing the approach to general two-Higgs-doublet models and the NMSSM. It provides full one-loop matching between 3D couplings and the underlying four-dimensional parameters, including temperature-dependent logarithms, Debye masses, and potential two-light-scalar scenarios. After integrating out non-static modes, heavy squarks/sleptons, and then heavy Higgs and A_o, the authors derive explicit expressions for the 3D gauge and scalar couplings (g_3^2 and bar{λ}_3) that govern the infrared dynamics, enabling non-perturbative lattice analyses of the electroweak phase transition in these multi-scalar theories. The work also discusses non-generic cases with multiple light scalars and outlines extensions to 2HDM and NMSSM, highlighting the broader applicability of dimensional reduction to finite-temperature SUSY and non-SUSY multi-scalar models.

Abstract

Using dimensional reduction we construct an effective 3D theory of the Minimal Supersymmetric Standard Model at finite temperature. The final effective theory is obtained after three successive stages of integration out of massive particles. We obtain the full 1-loop relation between the couplings of the reduced theory and the underlying 4D couplings and masses. The procedure is also applied to a general two Higgs doublet model and the Next to Minimal Supersymmetric Standard Model.

Paper Structure

This paper contains 20 sections, 155 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Three Dimensional Theory
  3. Effective Theory
  4. First Stage
  5. Second Stage
  6. Third Stage
  7. Non-Generic Case
  8. Other Models
  9. Conclusions
  10. MSSM in Four Dimensions
  11. Explicit Relationships between Parameters
  12. First Stage Parameters
  13. Second Stage Parameters
  14. Two Light Higgses
  15. 2HDM and NMSSM
  16. ...and 5 more sections

Figures (7)

  • Figure 1: Feynman diagrams contributing to the mass of the scalar Higgses and to wavefunction renormalization.
  • Figure 2: Diagrams contributing to the mass of the $A_{o}$ field and wavefunction renormalization of the gauge fields. We use a wavy line for both spatial and temporal components of the gauge fields.
  • Figure 3: Diagrams contributing to the mass and wavefunction renormalization of the squarks and sleptons.
  • Figure 4: Diagrams contributing to the quartic Higgs couplings.
  • Figure 5: Diagrams contributing to the gauge and quartic $A_{o}$-scalar couplings.
  • ...and 2 more figures