Can the standard modelCPviolation near theWbags explain the cosmological baryonic asymmetry?

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 $W\ensuremath{-}t\ensuremath{-}\overline{t}$ bags, a nontopological solitons made of large number ($\ensuremath{\sim}1000$) of gauge quanta and heavy (top and antitop) 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/antitops 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 $W\ensuremath{-}t\ensuremath{-}\overline{t}$ 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 ${10}^{\ensuremath{-}10}$, in our crude estimates. Together with the baryon violation rate of about ${10}^{\ensuremath{-}2}$, 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.