Abstract
We show how the two physically-distinct sources of CP-asymmetry relevant to scenarios of leptogenesis: (i) resonant mixing and (ii) oscillations between different flavours can be unambiguously identified within the Kadanoff-Baym formalism. These contributions are isolated by analyzing the spectral structure of the non-equilibrium propagators without relying on the definition of particle number densities. The mixing source is associated with the usual mass shells, whereas the oscillation source is identified with a third intermediate shell. In addition, we identify terms lying on the oscillation shell that can be interpreted as the destructive interference between mixing and oscillation. We confirm that identical shell structure is obtained in both the Heisenberg- and interaction-picture realizations of the Kadanoff-Baym formalism. In so doing, we illustrate the self-consistency and complementarity of these two approaches. The interaction-picture approach in particular has the advantage that it may be used to analyze all forms of mass spectra from quasi-degenerate through to hierarchical.
Highlights
Observed baryon asymmetry through the sphaleron processes of the standard electroweak theory [14]
We show how the two physically-distinct sources of CP -asymmetry relevant to scenarios of leptogenesis: (i) resonant mixing and (ii) oscillations between different flavours can be unambiguously identified within the Kadanoff-Baym formalism
There has been much progress in the literature [7, 8, 11, 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72, 72,73,74] aiming to go beyond these semi-classical treatments and obtain ‘first-principles’ field-theoretic analogues of the Boltzmann equation. These quantum transport equations are derived by means of the Kadanoff-Baym (KB) formalism [75, 76], itself embedded in the Schwinger-Keldysh [79, 80] closed-time path formalism of non-equilibrium thermal field theory
Summary
We show that the mixing and oscillation between different flavours provide two distinct sources of lepton asymmetry, in agreement with arguments presented in refs. [9,10,11]. The translational invariance of the one-loop self-energies in the thermal bath renders the Kadanoff-Baym equations linear, i.e. a sum of two solutions is a solution Using this linearity, we obtain the following equation for the non-equilibrium part Gδk≷j ⊂ Gk≷j of the Wightman propagators induced by the external source: xδik + Mi2k Gδk≷j (x, y) = − z ΠiRk(x, z) Gδk≷j (z, y) − Kik(x, z) GkAj(z, y). [92, 96]), the leading self-energy corrections to the spectral structure of the non-equilibrium part of the propagator, the shifts of the poles in the real and imaginary directions, have been taken into account. The leading contribution to the oscillation term is proportional to the off-diagonal element of the matrix of densities δn, as one might expect, sourcing asymmetry only in the presence of flavour coherences
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