Can the Standard Model CP violation near the W-bags explain the cosmological baryonic asymmetry?

TL;DR

This paper estimates the Standard Model's CP violation contribution via CKM matrix in cold electroweak baryogenesis, finding it could produce enough baryon asymmetry with a correct sign, near observed levels.

Contribution

It provides a detailed estimate of Standard Model CP violation effects in cold electroweak baryogenesis, highlighting the significance of 6th order flavor interference effects.

Findings

CP violation estimated at ~10^{-10} in the near scenario.

Baryon asymmetry close to observed levels (~10^{-10}).

Sign of the asymmetry matches cosmological observations.

Abstract

In the scenario of cold electroweak baryogenesis, oscillations of the Higgs field lead to metastable domains of unbroken phase where the Higgs field nearly vanishes. Those domains have also been identified with the $W-t-\bar{t}$ bags, a non-topological soliton made of large number ($\sim 1000$) of gauge quanta and heavy (top and anti-top) quarks. As real-time numerical studies had shown, sphalerons (topological transition events violating the baryon number) occur only inside those bags. In this work we estimate the amount of CP violation in this scenario coming from the Standard Model, via the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix, resulting in top-minus-antitop difference of the population in the bags. Since these tops/anti-tops are "recycled" by sphalerons, this population difference leads directly to the baryonic asymmetry of the Universe. We look at the effect appearing in the 4th order in weak $W$ diagrams describing interference of different quark flavor contributions. We found that there are multiple cancellations of diagrams and clearly sign-definite effect appears only in the 6th order expansion over flavor-dependent phases. We then estimate contributions to these diagrams in which weak interaction occurs (i) inside, (ii) near and (iii) far from the $W-t-\bar{t}$ b-bags, optimizing the contributions in each of them. We conclude that the second ("near") scenario is the dominant one, producing CP violation of the order of $10^{-10}$, in our crude estimates. Together with the baryon violation rate of about $10^{-2}$, previously demonstrated for this scenario, it puts the resulting asymmetry close to what is needed to explain the observed baryonic asymmetry in the Universe. Our answer also has a definite sign, which apparently seems to be the correct one.