Finite T Electroweak Phase Transition on the Lattice

TL;DR

This work surveys nonperturbative lattice studies of the finite-$T$ electroweak phase transition in the SU(2)-Higgs sector, combining 4D lattice results with a dimensionally reduced 3D effective theory. It shows a strong first-order transition for $m_H \lesssim 80$ GeV that weakens and ends at larger $m_H$, with precise determinations of $T_c$, latent heat $L$, and interface tension $\sigma$, and it analyzes the sphaleron rate across phases. The 3D effective theory agrees well with 4D simulations, validating the DR approach and enabling exploration of broader theories, though the sphaleron-rate results near $T_c$ disagree with simple analytic expectations, posing a challenge for baryogenesis scenarios. Overall, the static thermodynamics are largely settled, constraining Standard Model baryogenesis and guiding nonperturbative assessments of early-universe baryon-number dynamics.

Abstract

This talk reviews recent lattice results on the high $T$ electroweak phase transition. A remarkably accurate picture emerges: a) the transition is of first order for $m_H \lsim 80$GeV and vanishes for larger $m_H$; b) transition temperature, latent heat and interface tension are known, as well as c) the properties of the broken and symmetric phases. New developments in the sphaleron rate calculations are discussed.

Figures (9)

• Figure 1: $\chi(T)$ for $m_H^*=60$ and 120 GeV around the maximum klrs_heavy (Note the different $y$-axes!).
• Figure 2: $\chi_{\rm max}$ for different $m_H^*$ as a function of $V$. The continuous lines are mean field fits, the dashed line corresponds to the mean field critical exponent.
• Figure 3: Top: the $V\rightarrow\infty$ extrapolation of the pseudocritical coupling $\beta_{H,c}$. Bottom: the continuum limit ($1/\beta_G=0$) extrapolation of $T_c$ (open symbols). Also shown here is the metastability range (filled symbols) klrs_nonpert.
• Figure 4: $T_c/T_c^{\rm pert}$ from 4D desy_34 and 3D klrs_nonpert simulations. The open symbols show the extrapolation to the continuum limit (only $m^*_H=60$ for 3D) and have been shifted horizontally for clarity.
• Figure 5: The interface tension (top) and latent heat (bottom) from 4D and 3D simulations.