Medium corrections to the CP-violating parameter in leptogenesis

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 Standard Model (supplemented by three right-handed neutrinos) which include quantum statistical terms and medium corrected expressions for the CP-violating parameter.Comment: 13 pages, 9 figure

Systematic approach to leptogenesis in nonequilibrium QFT: self-energy contribution to the CP-violating parameter

In the baryogenesis via leptogenesis scenario the self-energy contribution to the CP-violating parameter plays a very important role. Here, we calculate it in a simple toy model of leptogenesis using the Schwinger-Keldysh/Kadanoff-Baym formalism as starting point. We show that the formalism is free of the double-counting problem typical for the canonical Boltzmann approach. Within the toy model, medium effects increase the CP-violating parameter. In contrast to results obtained earlier in the framework of thermal field theory, the medium corrections are linear in the particle number densities. In the resonant regime quantum corrections lead to modified expressions for the CP-violating parameter and for the decay width. Most notably, in the maximal resonant regime the Boltzmann picture breaks down and an analysis in the full Kadanoff-Baym formalism is required.Comment: 28 pages, 14 figure

Systematic approach to leptogenesis in nonequilibrium QFT: vertex contribution to the CP-violating parameter

The generation of a baryon asymmetry via leptogenesis is usually studied by means of classical kinetic equations whose applicability to processes in the hot and expanding early universe is questionable. The approximations implied by the state-of-the-art description can be tested in a first-principle approach based on nonequilibrium field theory techniques. Here, we apply the Schwinger-Keldysh/Kadanoff-Baym formalism to a simple toy model of leptogenesis. We find that, within the toy model, medium effects increase the vertex contribution to the CP-violating parameter. At high temperatures it is a few times larger than in vacuum and asymptotically reaches the vacuum value as the temperature decreases. Contrary to the results obtained earlier in the framework of thermal field theory, the corrections are only linear in the particle number densities. An important feature of the Kadanoff-Baym formalism is that it is free of the double-counting problem, i.e. no need for real intermediate state subtraction arises. In particular, this means that the structure of the equations automatically ensures that the asymmetry vanishes in equilibrium. These results give a first glimpse into a number of new and interesting effects that can be studied in the framework of nonequilibrium field theory.Comment: 27 pages, 21 figure

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff-Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff-Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results.Comment: 47 pages, 5 figure

Systematic approach to thermal leptogenesis

In this work we study thermal leptogenesis using nonequilibrium quantum field theory. Starting from fundamental equations for correlators of the quantum fields we describe the steps necessary to obtain quantum-kinetic equations for quasiparticles. These can easily be compared to conventional results and overcome conceptional problems inherent in the canonical approach. Beyond CP-violating decays we include also those scattering processes which are tightly related to the decays in a consistent approximation of fourth order in the Yukawa couplings. It is demonstrated explicitly how the S-matrix elements for the scattering processes in the conventional approach are related to two- and three-loop contributions to the effective action. We derive effective decay and scattering amplitudes taking medium corrections and thermal masses into account. In this context we also investigate CP-violating Higgs decay within the same formalism. From the kinetic equations we derive rate equations for the lepton asymmetry improved in that they include quantum-statistical effects and medium corrections to the quasiparticle properties