What's new with the electroweak phase transition?

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.Comment: LATTICE98(electroweak), 6 pages. List of references update

A Strong Electroweak Phase Transition up to m_H ~ 105 GeV

Non-perturbative lattice simulations have shown that there is no electroweak phase transition in the Standard Model for the allowed Higgs masses, m_H \gsim 75 GeV. In the Minimal Supersymmetric Standard Model, in contrast, it has been proposed that the transition should exist and even be strong enough for baryogenesis up to m_H ~ 105 GeV, provided that the lightest stop mass is in the range 100...160 GeV. However, this prediction is based on perturbation theory, and suffers from a noticeable gauge parameter and renormalization scale dependence. We have performed large-scale lattice Monte Carlo simulations of the MSSM electroweak phase transition. Extrapolating the results to the infinite volume and continuum limits, we find that the transition is in fact stronger than indicated by 2-loop perturbation theory. This guarantees that the perturbative Higgs mass bound m_H ~ 105 GeV is a conservative one, allows slightly larger stop masses (up to ~ 165 GeV), and provides a strong motivation for further studies of MSSM electroweak baryogenesis.Comment: 4 pages, 3 figure

First order thermal phase transition with 126 GeV Higgs mass

We study the strength of the electroweak phase transition in models with two light Higgs doublets and a light SU(3)_c triplet by means of lattice simulations in a dimensionally reduced effective theory. In the parameter region considered the transition on the lattice is significantly stronger than indicated by a 2-loop perturbative analysis. Within some ultraviolet uncertainties, the finding applies to MSSM with a Higgs mass m_h approximately 126 GeV and shows that the parameter region useful for electroweak baryogenesis is enlarged. In particular (even though only dedicated analyses can quantify the issue), the tension between LHC constraints after the 7 TeV and 8 TeV runs and frameworks where the electroweak phase transition is driven by light stops, seems to be relaxed.Comment: Presented at 31st International Symposium on Lattice Field Theory - LATTICE 201

3D Physics and the Electroweak Phase Transition: Perturbation Theory

We develop a method for the construction of the effective potential at high temperatures based on the effective field theory approach and renormalization group. It allows one to sum up the leading logarithms in all orders of perturbation theory. The method reproduces the known one-loop and two-loop results in a very simple and economic way and clarifies the issue of the convergence of the perturbation theory. We also discuss the assumptions being made for the determination of the critical temperature of the electroweak phase transition, and analyse different perturbative uncertainties in its determination. These results are then used for the non-perturbative lattice Monte Carlo simulations of the EW phase transition in forthcoming paper.Comment: 44 pages, preprint CERN-TH.6973/9

The Phase Diagram of Three-Dimensional SU(3) + Adjoint Higgs Theory

We study the phase diagram of the three-dimensional SU(3)+adjoint Higgs theory with lattice Monte Carlo simulations. A critical line consisting of a first order line, a tricritical point and a second order line, divides the phase diagram into two parts distinguished by =0 and /=0. The location and the type of the critical line are determined by measuring the condensates and , and the masses of scalar and vector excitations. Although in principle there can be different types of broken phases, corresponding perturbatively to unbroken SU(2)xU(1) or U(1)xU(1) symmetries, we find that dynamically only the broken phase with SU(2)xU(1)-like properties is realized. The relation of the phase diagram to 4d finite temperature QCD is discussed.Comment: 21 pages, 8 figure

O(2) symmetry breaking vs. vortex loop percolation

We study with lattice Monte Carlo simulations the relation of global O(2) symmetry breaking in three dimensions to the properties of a geometrically defined vortex loop network. We find that different definitions of constructing a network lead to different results even in the thermodynamic limit, and that with typical definitions the percolation transition does not coincide with the thermodynamic phase transition. These results show that geometrically defined percolation observables need not display universal properties related to the critical behaviour of the system, and do not in general survive in the field theory limit.Comment: 14 pages; references added, version to appear in Phys.Lett.

Non-perturbative plaquette in 3d pure SU(3)

We present a determination of the elementary plaquette and, after the subsequent ultraviolet subtractions, of the finite part of the gluon condensate, in lattice regularization in three-dimensional pure SU(3) gauge theory. Through a change of regularization scheme to MSbar and a matching back to full four-dimensional QCD, this result determines the first non-perturbative contribution in the weak-coupling expansion of hot QCD pressure.Comment: 6 pages, 4 figures, talk presented at Lattice 2005 (Non-zero temperature and density

High-T QCD and dimensional reduction: measuring the Debye mass

We study the high-temperature phase of SU(2) and SU(3) QCD using lattice simulations of an effective 3-dimensional SU(N) + adjoint Higgs -theory, obtained through dimensional reduction. We investigate the phase diagram of the 3D theory, and find that the high-T QCD phase corresponds to the metastable symmetric phase of the 3D theory. We measure the Debye screening mass m_D with gauge invariant operators; in particular we determine the O(g^2) and O(g^3) corrections to m_D. The corrections are seen to be large, modifying the standard power-counting hierarchy in high temperature QCD.Comment: 3 pages, Latex, 3 figures. Presented by K. Rummukainen at Lattice '9

Three-dimensional physics and the pressure of hot QCD

We update Monte Carlo simulations of the three-dimensional SU(3) + adjoint Higgs theory, by extrapolating carefully to the infinite volume and continuum limits, in order to estimate the contribution of the infrared modes to the pressure of hot QCD. The sum of infrared contributions beyond the known 4-loop order turns out to be a smooth function, of a reasonable magnitude and specific sign. Unfortunately, adding this function to the known 4-loop terms does not improve the match to four-dimensional lattice data, in spite of the fact that other quantities, such as correlation lengths, spatial string tension, or quark number susceptibilities, work well within the same setup. We outline possible ways to reduce the mismatch.Comment: 14 page

The Electroweak Phase Transition in a Magnetic Field

We study the finite temperature electroweak phase transition in an external hypercharge U(1) magnetic field H_Y, using lattice Monte Carlo simulations. For sufficiently small fields, H_Y/T^2 < 0.3, the magnetic field makes the first order transition stronger, but it still turns into a crossover for Higgs masses m_H ~ 80 GeV. For larger fields, we observe a mixed phase analogous to a type I superconductor, where a single macroscopic tube of the symmetric phase, parallel to H_Y, penetrates through the broken phase. For the magnetic fields and Higgs masses studied, we did not see indications of the expected Ambjorn-Olesen phase, which should be similar to a type II superconductor.Comment: 20 pages, 7 figures. Discussion on lattice results extended. To appear in Nucl.Phys.