Coherent flavour oscillation and CP violating parameter in thermal resonant leptogenesis

Abstract

Solving the Kadanoff-Baym (KB) equations in a different method from our previous analysis, we obtain the CP violating parameter ε in the thermal resonant leptogenesis without assuming smallness of the off-diagonal Yukawa couplings. For that purpose, we first derive a kinetic equation for density matrix of RH neutrinos with almost degenerate masses M i (i = 1, 2) ∼ M . If the deviation from thermal equilibrium is small, the differential equation is reduced to a linear algebraic equation and the density matrix can be solved explicitly in terms of the time variation of (local) equilibrium distribution function. The obtained CP-violating parameter ε i is proportional to an enhancement factorwith the previous analysis. The decay width can be determined systematically by the 1PI self-energy of the RH neutrinos in the 2PI formalism.

Phenomenology of baryogenesis from lepton-doublet mixing

“…Notice that the factor (8) exhibits the well-known form characteristic for resonantly enhanced correlations with damping. It is therefore comparable with the correlations of RHNs in Resonant Leptogenesis [23,24].…”

“…[10]. An appropriate treatment of the resonant limit x → 1 reveals a similar regulating behaviour also for standard Leptogenesis [20][21][22][23][24].…”

“…For standard Leptogenesis sufficiently far away from the mass-degenerate regime, the resummed propagators can be expanded such that the leading CP-violating self-energy exhibits the familiar two-loop form in terms of tree-level propagators [30]. In the extremely mass-degenerate case, when the mass-splitting of the RHNs becomes comparable to their width, such an expansion is no longer possible and instead, solving the Kadanoff-Baym equations in terms of resummed propagators and one-loop diagrams appears to be the only presently viable technique to obtain solutions [20,[22][23][24] because the mass-splitting of the active leptons is induced by their thermal masses that are by construction of a size comparable to their thermal width, we should use the approach based on resummed propagators, as diagrammatically indicated by Fig. 1(A).…”

Lepton asymmetry from mixing and oscillations

“…On the other hand, a semi-classical treatment of mixing is possible through the inclusion of effective Yukawa couplings [15,35], which can account for the ε-and ε -type CP violation, arising respectively from self-energy and vertex effects. Recently, there has been much progress in the literature [7,8,11,[72][73][74] aiming to go beyond these semi-classical treatments and obtain 'first-principles' field-theoretic analogues of the Boltzmann equation. Often, these quantum transport equations are derived by means of the Kadanoff-Baym (KB) formalism [75,76] (for reviews, see refs.…”

“…In ref. [74], it was proposed that, in a strong-washout regime, one can obtain an approximate solution for δN at late times by neglecting the derivative of δN . This solution reads Open Access.…”