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$3$--Dimensional Approach to Hot Electroweak Matter for $M_{Higgs} \leq 70$ GeV

M. Guertler, E. -M. Ilgenfritz, J. Kripfganz, H. Perlt, A. Schiller

TL;DR

This work nonperturbatively analyzes the electroweak phase transition using a dimensionally reduced 3D SU(2)-Higgs lattice model at $M_H ≈ 70$ GeV, comparing to $M_H ≈ 35$ GeV. It locates the phase transition via Binder cumulants and an equal-weight histogram method, extracting $T_c$, latent heat, surface tension, and the infinite-volume critical coupling, confirming a first-order transition that weakens with increasing $M_H$. The study also probes the strongly coupled symmetric phase, measuring a nonzero string tension and a static force, and contrasts results with pure SU(2) and perturbative expectations. Overall, it validates the 3D dimensional reduction approach for finite-temperature electroweak dynamics and provides quantitative nonperturbative inputs relevant to early-universe baryogenesis scenarios.

Abstract

We study the electroweak phase transition by lattice simulations of an effective 3-dimensional theory, for a Higgs mass of about $70$ GeV. Exploiting a variant of the equal weight criterion of phase equilibrium, we obtain transition temperature, latent heat and surface tension and compare with $M_H \approx 35$ GeV. For the symmetric phase, bound state masses and the static force are determined and compared with results for pure $SU(2)$ theory.

$3$--Dimensional Approach to Hot Electroweak Matter for $M_{Higgs} \leq 70$ GeV

TL;DR

This work nonperturbatively analyzes the electroweak phase transition using a dimensionally reduced 3D SU(2)-Higgs lattice model at GeV, comparing to GeV. It locates the phase transition via Binder cumulants and an equal-weight histogram method, extracting , latent heat, surface tension, and the infinite-volume critical coupling, confirming a first-order transition that weakens with increasing . The study also probes the strongly coupled symmetric phase, measuring a nonzero string tension and a static force, and contrasts results with pure SU(2) and perturbative expectations. Overall, it validates the 3D dimensional reduction approach for finite-temperature electroweak dynamics and provides quantitative nonperturbative inputs relevant to early-universe baryogenesis scenarios.

Abstract

We study the electroweak phase transition by lattice simulations of an effective 3-dimensional theory, for a Higgs mass of about GeV. Exploiting a variant of the equal weight criterion of phase equilibrium, we obtain transition temperature, latent heat and surface tension and compare with GeV. For the symmetric phase, bound state masses and the static force are determined and compared with results for pure theory.

Paper Structure

This paper contains 5 sections, 7 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. Localization of the phase transition
  4. Strength of the phase transition
  5. The strongly coupled symmetric phase

Figures (4)

  • Figure 1: Binder cumulants $B_{\rho^2}^L$ for $L=30$, $48$ and $64$ at $M_H \approx 70$ GeV
  • Figure 2: Histograms $P_m$ and $P_{int}$ at $\beta_{Hc}$ for $L=64$ at $M_H \approx 70$ GeV
  • Figure 3: Static force $F$ vs. distance $R$ for $M_H \approx 35$ GeV and $M_H \approx 70$ GeV
  • Figure 4: Correlation lengths in Higgs and $W$ channel near the transition for $M_H \approx 70$ GeV