Medium corrections to theCP-violating parameter in leptogenesis

Abstract

In two recent papers, arXiv:0909.1559 and arXiv:0911.4122, it has been demonstrated that one can obtain quantum corrected Boltzmann kinetic equations for leptogenesis using a top-down approach based on the Schwinger-Keldysh/Kadanoff-Baym formalism. These "Boltzmann-like" equations are similar to the ones obtained in the conventional bottom-up approach but differ in important details. In particular there is a discrepancy between the CP-violating parameter obtained in the first-principle derivation and in the framework of thermal field theory. Here we demonstrate that the two approaches can be reconciled if causal n-point functions are used in the thermal field theory approach. The new result for the medium correction to the CP-violating parameter is qualitatively different from the conventional one. The analogy to a toy model considered earlier enables us to write down consistent quantum corrected Boltzmann equations for thermal leptogenesis in the SM+3νR which include quantum statistical terms and medium corrected expressions for the CP-violating parameter.

Improving electro-weak fits with TeV-scale sterile neutrinos

“…(15), (18) and (19) reduce to the expressions derived in [71]. The observation that the heavy neutrinos can 'screen' the tree-level contributions by generating a negative T parameter together with the explicit formulae for the S, T, U constitutes one of the main results of the present work.…”

“…Note that the PMNS matrix does not appear in (17) since the mixing becomes unphysical for massless neutrinos. The S parameter reads…”

“…However, their combinations in Eqs. (15), (18) and (19) are finite. This can be checked explicitly by using the unitarity of the full mixing matrix U as well as the relation (m L ) αβ = 3+n i=1 U αi m i U T iβ = 0, where α, β ∈ {e, µ, τ }.…”

“…Substituting the terms proportional to g µν of Π µν W W and Π µν ZZ into the definitions of the S, T, U parameters we obtain Eqs. (15), (18) and (19 …”

“…According to this scenario the lepton asymmetry which is produced by the heavy neutrinos * evgeny.akhmedov@mpi-hd.mpg.de † alexander.kartavtsev@mpp.mpg.de ‡ manfred.lindner@mpi-hd.mpg.de § lisa.michaels@mpi-hd.mpg.de ¶ juri.smirnov@mpi-hd.mpg.de is converted into the baryon asymmetry by anomalous electro-weak processes [8][9][10]. Depending on the values of the masses and couplings in (1) the generation of the asymmetry proceeds either through decays [11][12][13][14][15][16][17][18][19][20][21][22][23] or via oscillations of the heavy neutrinos [24]. The extension of the SM spectrum by sterile neutrino states may even provide a solution to the third problem, since sterile neutrinos are a perfect dark matter candidate (see e.g.…”