Possible Role of the WZ-Top-Quark Bags in Baryogenesis

The heaviest members of the SM -- the gauge bosons $W,Z$ and the top quarks and antiquarks -- may form collective bag-like excitations of the Higgs vacuum provided their number is large enough, both at zero and finite temperatures. Since Higgs vacuum expectation value (VEV) is significantly modified inside them, they are called "bags". In this work we argue that creation of such objects can explain certain numerical studies of cosmological baryogenesis. Using as an example a hybrid model, combining inflationary preheating with cold electroweak transition, we identify "spots of unbroken phase" found in numerical studies of this scenario with such $W-Z$ bags. We argue that the baryon number violation should happen predominantly inside these objects, and show that the rates calculated in numerical simulations can be analytically explained using finite-size pure gauge sphaleron solutions, developed previously in the QCD context by Carter, Ostrovsky and Shuryak (COS). Furthermore, we point out significant presence of the top quarks/antiquarks in these bag (which were not included in those numerical studies). Although the basic sphaleron exponent remains unchanged by the top's presence, we find that tops help to stabilize them for a longer time. Another enhancement of the transition rate comes from the "recycling" of the tops in the topological transition. Inclusion of the fermions (tops) enhances the sphaleron rate by up to 2 orders of magnitude. We finally discuss the magnitude of the CP violation needed to explain the observed baryonic asymmetry of the Universe, and give arguments that the difference in the top-antitop population in the bag of the right magnitude can arise both from CP asymmetries in the top decays and in top propagation into the bags, due to Farrar-Shaposhnikov effect.