The $\epsilon$-expansion and the electroweak phase transition

Abstract

Standard perturbative (or mean field theory) techniques are not adequate for studying the finite-temperature electroweak phase transition in some cases of interest to scenarios for electroweak baryogenesis. We instead study the properties of this transition using the renormalization group and the $\epsilon$-expansion. This expansion, based on dimensional continuation from 3 to $4-\epsilon$ spatial dimensions, provides a systematic approximation for computing the effects of (near)-critical fluctuations. The $\epsilon$-expansion is known to predict a first-order transition in Higgs theories, even for heavy Higgs boson masses. The validity of this conclusion in the standard model is examined in detail. A variety of physical quantities are computed at leading and next-to-leading order in $\epsilon$. For moderately light Higgs masses (below 100~GeV), the $\epsilon$-expansion suggests that the transition is more strongly first order than is predicted by the conventional analysis based on the one-loop (ring-improved) effective potential. Nevertheless, the rate of baryon non-conservation after the transition is found to be {\em larger\/} than that given by the one-loop effective potential calculation. Detailed next-to-leading order calculations of some sample quantities suggests that the $\eps$-expansion is reasonably well behaved for Higgs masses below 100--200 GeV. We also compare the $\eps$-expansion with large-$N$ results (where $N$ is the number of scalar fields) and find that the $\eps$-expansion is less well behaved in this limit.

71 pages w. 16 figs., UW/PT-93-24. (Latex, Revtex, epsf)

References in corpus (16)

• Progress in Electroweak Baryogenesis
• The Effective Potential and First-Order Phase Transitions: Beyond Leading Order
• Towards the Theory of Cosmological Phase Transitions
• The Standard Model Effective Potential at Two Loops
• Baryon Asymmetry of the Universe in the Minimal Standard Model
• A Lattice Monte Carlo Study of the Hot Electroweak Phase Transition
• Comments on the Electroweak Phase Transition
• Quantum Fluctuations around the Electroweak Sphaleron
• Some Two-Loop Corrections to the Finite Temperature Effective Potential in the Electroweak Theory
• On the Possibility of Second-Order Phase Transitions in Spontaneously Broken Gauge Theories
• Resummation Methods at Finite Temperature: The Tadpole Way
• Critical Behavior in the Electroweak Phase Transition
• Quantum Corrections to the Electroweak Sphaleron Transition
• Finite Temperature Scalar Potential from a 1/N Expansion
• First Order Phase Transition in a Two Higgs-doublet Model with $M_h>M_W$
• On the High $T$ Phase Transition in the Gauged $SU(2)$ Higgs Model

Cited by in corpus (43)

• Cosmic strings
• Is There a Hot Electroweak Phase Transition at $m_H\gsim m_W$?
• The Electroweak Phase Transition: A Non-Perturbative Analysis
• Electroweak Baryogenesis
• Electroweak Baryon Number Non-Conservation in the Early Universe and in High Energy Collisions
• Nonperturbative renormalization group approach to frustrated magnets
• Simulating the Electroweak Phase Transition in the SU(2) Higgs Model
• Phase Structure and Phase Transition of the SU(2) Higgs Model in Three Dimensions
• Finite Temperature Effective Potential to Order $g^4,\la^2$ and the Electroweak Phase Transition
• Phase Diagram of Superconductors from Non-Perturbative Flow Equations
• A holographic model for QCD in the Veneziano limit at finite temperature and density
• Exact relation of lattice and continuum parameters in three-dimensional SU(2)+Higgs theories
• Gravitational wave and collider implications of electroweak baryogenesis aided by non-standard cosmology
• A Hierarchy of Effective Field Theories of Hot Electroweak Matter
• Dynamics of Weak First Order Phase Transitions
• The Electroweak Phase Transition through the Renormalization Group
• Application of Renormalization Group Techniques to a Homogeneous Bose Gas at Finite Temperature
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• High Temperature Phase Transition in Two-Scalar Theories
• Effective Scalar Field Theory for the Electroweak Phase Transition
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Charge cross-over at the U(1)-Higgs phase transition
• Critical Line for H-Superfluidity in Strange Quark Matter?
• Domain walls and perturbation theory in high temperature gauge theory: SU(2) in 2+1 dimensions
• Enabling Electroweak Baryogenesis through Dark Matter
• Melting the Diquark Condensate in Two-Color QCD: A Renormalization Group Analysis
• Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials
• REDUCTION OF THE N-COMPONENT SCALAR MODEL AT TWO LOOP LEVEL
• Dynamics near the critical point: the hot renormalization group in quantum field theory
• Fluctuations and Bubble Dynamics in First-Order Phase Transitions
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Phase Transition In $SU(N)\times U(1)$ Gauge Theory With Many Fundamental Bosons
• The 3d Effective Field Theory for Finite Temperature Scalar Electrodynamics
• A strongly first order electroweak phase transition from strong symmetry-breaking interactions
• $\eps$ expansion analysis of very weak first-order transitions in the cubic anisotropy model: Part I
• The tricritical point of finite-temperature phase transitions in large N(Higgs) gauge theories
• Comparison of Renormalization-Group and Lattice Studies of the Electroweak Phase Transition
• Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU($N_c$) gauge Higgs models
• Auxiliary fields approach to shift-symmetric theories: the ${\phi }^4$ derivative theory and the crumpled-to-flat transition of membranes at two-loop order
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• An analytic study of the tricritical line in the U(Nf)xU(Nf) sigma model
• Fluctuation Induced Critical Behavior at Non-Zero Temperature and Chemical Potential
• Effective Potential Improvements, $\epsilon$-expansions, and the Electroweak Phase Transition