Leptogenesis with “Fuzzy Mass Shell” for Majorana Neutrinos

We study the mixing of elementary and composite particles. In quantum field theory the mixing of composite particles originates in the couplings of the constituent quarks and for neutrinos in self–energy diagrams. In the event that the incoming and outgoing neutrinos have different masses, the self–energy diagrams vanish because energy is not conserved but the finite decaying widths make the mixing possible. We can consider the neutrinos to be “fuzzy” states on their mass shell and the mixing is understood as the overlap of two wavefunctions. These considerations restrict the mass difference to be approximately equal to or smaller than the largest of the two widths: |Mi − Mj | ∼ max{Γi, Γj}. 1 Lagrangian with Majorana neutrinos. During the last few years a lot of attention was paid to the possibility of creating a baryon asymmetry through leptogenesis. The proposed schemes introduce heavy Majorana neutrinos with CP–violating couplings, where both the so–called “direct” and “indirect” contributions to leptogenesis were considered. In calculating the lepton asymmetry, the authors consider the Standard Model (SM) with the usual particle content plus three Majorana neutrinos, which are singlets under the weak SU(2)–group [1] [10]. The part of the Lagrangian with Majorana neutrinos consists of the Majorana mass term and the Yukawa interactions of these neutrinos with leptons and Higgs bosons: L = 1 2 ∑