Leptogenesis with “fuzzy mass shell” for Majorana neutrinos

Abstract

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 wave functions. These considerations restrict the mass difference to be approximately equal to or smaller than the largest of the two widths: $|{M}_{i}\ensuremath{-}{M}_{j}|\ensuremath{\lesssim}\mathrm{max}{{\ensuremath{\Gamma}}_{i},{\ensuremath{\Gamma}}_{j}}.$