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Electroweak Baryon Number Non-Conservation in the Early Universe and in High Energy Collisions

V. A. Rubakov, M. E. Shaposhnikov

TL;DR

Rubakov and Shaposhnikov review non-perturbative electroweak baryon-number non-conservation, focusing on sphaleron transitions at finite temperature and instanton-like processes in high-energy collisions. They develop a framework based on Green's-function formalisms and probability-flux interpretations, connect high-temperature dynamics to a 3D effective theory via dimensional reduction, and discuss lattice results for the electroweak phase transition. The work highlights that while B+L violation is rapid in the unbroken phase, generating viable baryogenesis in the Minimal Standard Model is challenging due to washout after the transition, pointing to extensions with stronger first-order transitions and new CP-violating sources. Additionally, they address the status of instanton-induced processes in collider energies, arguing for persistent exponential suppression and underscoring the need for non-perturbative methods to settle the question.

Abstract

We review recent progress in the study of the anomalous baryon number non-conservation at high temperatures and in high energy collisions. Recent results on high temperature phase transitions are described, and applications to electroweak baryogenesis are considered. The current status of the problem of electroweak instanton-like processes at high energies is outlined. This paper is written on the occasion of Sakharov's 75th anniversary and will appear in the memorial volume of Uspekhi (Usp. Fiz. Nauk, volume 166, No 5, May 1996).

Electroweak Baryon Number Non-Conservation in the Early Universe and in High Energy Collisions

TL;DR

Rubakov and Shaposhnikov review non-perturbative electroweak baryon-number non-conservation, focusing on sphaleron transitions at finite temperature and instanton-like processes in high-energy collisions. They develop a framework based on Green's-function formalisms and probability-flux interpretations, connect high-temperature dynamics to a 3D effective theory via dimensional reduction, and discuss lattice results for the electroweak phase transition. The work highlights that while B+L violation is rapid in the unbroken phase, generating viable baryogenesis in the Minimal Standard Model is challenging due to washout after the transition, pointing to extensions with stronger first-order transitions and new CP-violating sources. Additionally, they address the status of instanton-induced processes in collider energies, arguing for persistent exponential suppression and underscoring the need for non-perturbative methods to settle the question.

Abstract

We review recent progress in the study of the anomalous baryon number non-conservation at high temperatures and in high energy collisions. Recent results on high temperature phase transitions are described, and applications to electroweak baryogenesis are considered. The current status of the problem of electroweak instanton-like processes at high energies is outlined. This paper is written on the occasion of Sakharov's 75th anniversary and will appear in the memorial volume of Uspekhi (Usp. Fiz. Nauk, volume 166, No 5, May 1996).

Paper Structure

This paper contains 33 sections, 258 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Basics of anomalous non-conservation of fermion quantum numbers
  3. Baryon asymmetry: preliminaries
  4. Sphaleron rate at finite temperatures
  5. Qualitative discussion
  6. The Green's function approach
  7. The relation to the "probability flux" formulae
  8. Quantum versus classical rate
  9. The sphaleron rate in the broken phase
  10. Real time numerical simulations
  11. Strong sphalerons
  12. Concluding remarks
  13. Phase transitions in gauge theories
  14. Equilibrium approximation
  15. Simple estimates
  16. ...and 18 more sections

Figures (16)

  • Figure 1: Schematic plot of the static energy as function of gauge and Higgs fields. The minima correspond to the classical vacua.
  • Figure 2: Effective potential evolution at first order phase transition.
  • Figure 3: The critical value $x_c=\lambda_3/g_3^2$ as a function of the physical Higgs mass $m_H$ and the top quark mass $m_{\rm top}$. In general, $x$ depends on the Higgs mass, the top mass and logarithmically on the temperature. From ref. K1
  • Figure 4: The schematical phase diagrams for gauge-Higgs SU(2) system.
  • Figure 5: The evolution of the distribution of $\langle R_L^2\rangle$ with $\beta_H$ (temperature). From ref. K3.
  • ...and 11 more figures