Baryon Asymmetry of the Universe in the Standard Model

TL;DR

This work argues that the observed baryon asymmetry of the universe could arise within the minimal Standard Model if the electroweak phase transition is strongly first order. By treating quarks as thermal quasiparticles and computing CP-violating reflections from a moving Higgs domain wall in a one-dimensional, quasi-static framework, the authors show that CKM CP violation can evade the usual GIM suppression in certain kinematic regimes, yielding a baryon-number flux that sphalerons can convert into a net $n_B/s$. The analysis combines analytic limits (no mixing, thin-wall) with a detailed numerical solution of the 1D Dirac equation in a hot plasma, revealing a sensitive dependence on quark masses and mixings and predicting a sign and magnitude of the BAU that can approach observations under optimistic dynamical assumptions. The results hinge on uncertain aspects of the phase transition dynamics and on flux/sphaleron efficiencies, but they demonstrate that the MSM cannot be discounted as a viable BAU mechanism and highlight key parameters that future work must constrain.

Abstract

We study the interactions of quarks and antiquarks with the changing Higgs field during the electroweak phase transition, including quantum mechanical and some thermal effects, with the only source of CP violation being the known CKM phase. The magnitude and sign of the predicted BAU agrees with the observed value, with moderately optimistic assumptions about the dynamics of the phase transition. At present uncertainties related to the dynamics of the ew phase transition and the oversimplifications of our treatment are too great to decide whether or not this is the correct explanation for the presence of remnant matter in our universe, however the present work makes it clear that the minimal standard model cannot be discounted as a contender for explaining this phenomenon.

Figures (14)

• Figure 1: Dispersion relation for $s$-quarks in the unbroken phase, neglecting mixing. The figure is essentially identical for the broken phase, except for the neighborhood of the crossing.
• Figure 2: Dispersion relation for $b$-quarks in the unbroken phase, neglecting mixing.
• Figure 3: Dispersion relation for $b$-quarks in the broken phase, for zero CKM angles.
• Figure 4: Dispersion relation for $d$ (short-dashed), $s$ (long-dashed), and $b$ (solid) -quarks in the broken phase, focusing on the region of total reflection of the $d$ and $s$. It is the $R_n$ branch of the $b$ which is visible in this region. CKM angles have been set to zero.
• Figure 5: Dependence of $\Delta$ on $\omega$, in GeV, for the "canonical" choices of masses and mixing angles, and wall velocity $v=0$.