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Cold electroweak baryogenesis with Standard Model CP violation

Anders Tranberg, Andres Hernandez, Thomas Konstandin, Michael G. Schmidt

TL;DR

The paper investigates cold electroweak baryogenesis as a mechanism to generate the Universe’s baryon asymmetry during a tachyonic electroweak transition, using a Standard Model–derived CP-violating operator obtained by integrating out quarks as the sole CP source. Through lattice simulations of the SU(2)-Higgs system with a regulator to manage gradient-expansion breakdown, the authors demonstrate a nonzero bias in Chern-Simons and winding numbers, translating into a baryon asymmetry that, for certain parameter choices, greatly exceeds the observed value. The results highlight that SM CP violation can operate effectively in this zero-temperature, tachyonic context when nonpolynomial mass dependence is present, though the outcome is highly sensitive to the cutoff and needs further refinement. Overall, the work suggests cold electroweak baryogenesis with SM CP violation remains a plausible, testable scenario deserving deeper investigation and more precise control of the effective operator’s regime of validity.

Abstract

We study a mechanism that generates the baryon asymmetry of the Universe during a tachyonic electroweak phase transition. We utilize as sole source of CP violation an operator that was recently obtained from the Standard Model by integrating out the quarks.

Cold electroweak baryogenesis with Standard Model CP violation

TL;DR

The paper investigates cold electroweak baryogenesis as a mechanism to generate the Universe’s baryon asymmetry during a tachyonic electroweak transition, using a Standard Model–derived CP-violating operator obtained by integrating out quarks as the sole CP source. Through lattice simulations of the SU(2)-Higgs system with a regulator to manage gradient-expansion breakdown, the authors demonstrate a nonzero bias in Chern-Simons and winding numbers, translating into a baryon asymmetry that, for certain parameter choices, greatly exceeds the observed value. The results highlight that SM CP violation can operate effectively in this zero-temperature, tachyonic context when nonpolynomial mass dependence is present, though the outcome is highly sensitive to the cutoff and needs further refinement. Overall, the work suggests cold electroweak baryogenesis with SM CP violation remains a plausible, testable scenario deserving deeper investigation and more precise control of the effective operator’s regime of validity.

Abstract

We study a mechanism that generates the baryon asymmetry of the Universe during a tachyonic electroweak phase transition. We utilize as sole source of CP violation an operator that was recently obtained from the Standard Model by integrating out the quarks.

Paper Structure

This paper contains 4 sections, 19 equations, 3 figures.

Table of Contents

  1. Introduction
  2. CP violation in the Standard Model
  3. Numerical analysis
  4. Discussion and conclusions

Figures (3)

  • Figure 1: Two example configuration: The right configuration results in a difference in the Higgs winding number for CP conjugate initial conditions, while the left does not. The Higgs field (straight curve) is normalized to $v^2$. The red and blue lines denote $N_{cs}$ and $N_w$ respectively.
  • Figure 2: The final value of Higgs winding number for all $167$ pairs of configurations. Black $x$-marks correspond to $+\kappa_{CP}$, red $+$-marks to $-\kappa_{CP}$. In total $5$ pairs of configurations contribute to a net baryon asymmetry. Deviations from integer values are rather small and due to lattice discretization errors.
  • Figure 3: The average Higgs field (scaled by a factor $1/50$), Chern-Simons number and winding number as functions of time. The average value $5/334$ is superposed (dashed line) as well as the estimated error band (dotted lines).