We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T=0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ~< 1) the final lepton asymmetry can change up to a factor four with respect to previous estimates.
We study the evolution of a cosmological baryon asymmetry produced via leptogenesis by means of the full classical Boltzmann equations, without the assumption of kinetic equilibrium and including all quantum statistical factors. Beginning with the full mode equations we derive the usual equations of motion for the right-handed neutrino number density and integrated lepton asymmetry, and show explicitly the impact of each assumption on these quantities. For the first time, we investigate also the effects of scattering of the right-handed neutrino with the top quark to leading order in the Yukaw…
We study the role played in leptogenesis by the equilibration of lepton flavors, as could be induced in supersymmetric models by off diagonal soft breaking masses for the scalar lepton doublets $\tilde m_{αβ}$, or more generically by new sources of lepton flavor violation. We show that if $\tilde m_{αβ}\gsim 1 $GeV and leptogenesis occurs below $\sim 100 $TeV, dynamical flavor effects are irrelevant and leptogenesis is correctly described by a one-flavor Boltzmann equation. We also discuss spectator effects in low scale leptogenesis by taking into account various chemical equilibrium condition…
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 r…
We investigate hard-thermal-loop (HTL) corrections to the final lepton asymmetry in leptogenesis. To this end we solve the Boltzmann equations with HTL-corrected rates and CP asymmetries, which we calculated in paper I of this series. We pay special attention to the influence of the two leptonic quasiparticles that arise at non-zero temperature. We include only decays and inverse decays and allow for the lepton modes to be either decoupled from each other, or to be in chemical equilibrium by some strong interaction, simulating the interaction with gauge bosons. In two additional cases, we appr…
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interaction…
We study a model for leptogenesis in which the total CP asymmetries in the decays and scatterings involving the SU(2) singlet seesaw neutrinos $N_α$ vanish ($ε_{N_α}=0$). Leptogenesis is possible due to non-vanishing CP violating lepton flavor asymmetries, realizing a situation in which the baryon asymmetry is due exclusively to flavor effects. We study the production of a net lepton asymmetry by solving the Boltzmann equations specific to this model, and we show that successful leptogenesis can be obtained at a scale as low as the TeV. We also discuss constraints on the model parameter space …
We consider variations of the standard leptogenesis picture arising from the presence of an additional scale related to the breaking of a $U(1)_X$ abelian flavor symmetry. We show that quite generically the presence of an additional energy scale might introduce new qualitative and quantitative changes on leptogenesis. Especially interesting is the possibility of having succesful TeV leptogenesis with a vanishing total CP violating asymmetry. By solving the corresponding Boltzmann equations it is shown that these kind of scenarios encounters no difficulties in generating the Cosmic baryon asymm…
We discuss the effective theory appropriate for studying soft leptogenesis at temperatures T>10^7 GeV. In this regime, the main source of the B-L asymmetry is the CP asymmetry of a new anomalous R-charge that couple to generalized anomalous electroweak processes. Baryogenesis thus occurs mainly through R-genesis, and with an efficiency that can be up to two orders of magnitude larger than in usual estimates. Contrary to common belief, a sizeable baryon asymmetry is generated also when thermal corrections to the CP asymmetries in sneutrino decays are neglected which, in soft leptogenesis, imply…
We consider a mirror world scenario, in which light Dirac neutrinos are generated from a seesaw mechanism and leptogenesis occurs at high scale without violating lepton number. After leptogenesis, the conservation laws of the theory imply the visible baryon-minus-lepton asymmetry to be equal to the mirror baryon-minus-lepton asymmetry. We extend previous work by presenting a detailed study of this Dirac leptogenesis mechanism by constructing the full set of Boltzmann Equations for both cases of unflavored and flavored regimes. We show that $Z_2$ breaking and lepton/mirror lepton flavor effects…
We investigate the resonant leptogenesis scenario in the minimal B-L extended standard model(SM) with the B-L symmetry breaking at the TeV scale. Through detailed analysis of the Boltzmann equations, we show how much the resultant baryon asymmetry via leptogenesis is enhanced or suppressed, depending on the model parameters, in particular, the neutrino Dirac Yukawa couplings and the TeV-scale Majorana masses of heavy degenerate neutrinos. In order to consider a realistic case, we impose a simple ansatz for the model parameters and analyze the neutrino oscillation parameters and the baryon asym…
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…
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 this work we study the contribution to leptogenesis from Delta L=1 decay and scattering processes mediated by the Higgs with quarks in the initial and final states using the formalism of non-equilibrium quantum field theory. Starting from fundamental equations for correlators of the quantum fields we derive quantum-corrected Boltzmann and rate equations for the total lepton asymmetry improved in that they include quantum-statistical effects and medium corrections to the quasiparticle properties. To compute the collision term we take into account one- and two-loop contributions to the lepton…
We perform a thermal unflavored leptogenesis analysis on minimal left-right symmetric models with discrete left-right symmetry identified as generalized parity or charge conjugation. When left-right symmetry is unbroken in the lepton Yukawa sector, the neutrino Dirac coupling matrix is completely determined by neutrino masses and mixing angles, allowing CP violation needed to generate leptogenesis totally resides in the low-energy sector. With two lepton asymmetry generation ways, both type I and mixed type I$+$II neutrino mass generation mechanisms are considered. After solving the Boltzmann …
We study the prediction for leptogenesis in two renormalizable supersymmetric $SO(10)\times A_4$ modular models in which the neutrino mass is dominantly generated by the type I seesaw mechanism. The evolution of the lepton asymmetries are described in terms of the three-flavored density matrix equations for three heavy Majorana neutrinos, where both vanishing initial condition and thermal initial condition of the right-handed neutrinos are considered. We also present an analytical approximation based on the Boltzmann equations. We find regions of parameter space compatible with the measured fe…
Thermal leptogenesis explains the observed matter-antimatter asymmetry of the universe in terms of neutrino masses, consistent with neutrino oscillation experiments. We present a full quantum mechanical calculation of the generated lepton asymmetry based on Kadanoff-Baym equations. Origin of the asymmetry is the departure from equilibrium of the statistical propagator of the heavy Majorana neutrino, together with CP violating couplings. The lepton asymmetry is calculated directly in terms of Green's functions without referring to "number densities". Compared to Boltzmann and quantum Boltzmann …
By including spectator fields into the Boltzmann equations for Leptogenesis, we show that partially equilibrated spectator interactions can have a significant impact on the freeze-out value of the asymmetry in the strong washout regime. The final asymmetry is typically increased, since partially equilibrated spectators "hide" a part of the asymmetry from washout. We study examples with leptonic and non-leptonic spectator processes, assuming thermal initial conditions, and find up to 50% enhanced asymmetries compared to the limit of fully equilibrated spectators. Together with a comprehensive o…
We derive and solve kinetic equations for leptogenesis within the Closed Time Path (CTP) formalism. It is particularly emphasised how the procedure of real intermediate state subtraction familiar from the Boltzmann approach is realised within the CTP framework; and we show how in time-independent situations, no lepton asymmetry emerges, in accordance with the CPT-theorem. The CTP approach provides new quantum statistical corrections from evaluating the loop integrals. These lead to an enhancement of the asymmetry that is originating from the Bose statistics of the Higgs particles. To quantify …
We investigate the generation of the baryon asymmetry of the Universe within a SUSY SU(5) x T' model of flavour, which gives rise to realistic masses and mixing patterns for quarks and leptons. The model employs the see-saw mechanism for generation of the light neutrino masses and the baryon asymmetry is produced via leptogenesis. We perform detailed calculations of both the CP violating lepton asymmetries, originating from the decays of the heavy Majorana neutrinos operative in the see-saw mechanism, and of the efficiency factors which account for the lepton asymmetry wash-out processes in th…
We present an S$_4$ flavour symmetric model within a minimal seesaw framework resulting in mass matrices that leads to TM$_1$ mixing. Minimal seesaw is realized by adding two right-handed neutrinos to the Standard Model. The model predicts Normal Hierarchy (NH) for neutrino masses. Using the constrained six-dimensional parameter space, we have evaluated the effective Majorana neutrino mass, which is the parameter of interest in neutrinoless double beta decay experiments. The possibility of explaining baryogenesis via resonant leptogenesis is also examined within the model. A non-zero, resonant…
We study the wash-out of a cosmological baryon asymmetry produced via leptogenesis by subsequent interactions. Therefore we focus on a scenario in which a lepton asymmetry is established in the out-of-equilibrium decays of the next-to-lightest right-handed neutrino. We apply the full classical Boltzmann equations without the assumption of kinetic equilibrium and including all quantum statistical factors to calculate the wash-out of the lepton asymmetry by interactions of the lightest right-handed state. We include scattering processes with top quarks in our analysis. This is of particular inte…
Cyclic symmetry in the neutrino sector with the type-I seesaw mechanism in the mass basis of charged leptons and right chiral neutrinos ($N_{iR}$, $i=e,μ,τ$) generates two fold degenerate light neutrino and three fold degenerate heavy neutrino mass spectrum. Consequently, such scheme, produces vanishing one light neutrino mass squared difference and lepton asymmetry. To circumvent such unphysical outcome, we break cyclic symmetry in the diagonal right chiral neutrino mass term by a small breaking parameter. Nonzero mass squared differences and mixing angles are generated with the help of the s…
In many phenomenologically interesting models of thermal leptogenesis the heavy neutrinos are non-relativistic when they decay and produce the baryon asymmetry of the Universe. We propose a non-relativistic approximation for the corresponding rate equations in the non-resonant case, and a systematic way for computing relativistic corrections. We determine the leading order coefficients in these equations, and the first relativistic corrections. The non-relativistic approximation works remarkably well. It appears to be consistent with results obtained using a Boltzmann equation taking into acco…
We study the impact of effective thermal masses and widths on resonant leptogenesis. We identify two distinct possibilities which we refer to as crossing and runaway regimes. In the runaway regime the mass difference grows monotonously with temperature, whereas it initially decreases in the crossing regime, such that the effective masses become equal at some temperature. Following the conventional logic the source of the asymmetry would vanish in the latter case. Using non-equilibrium quantum field theory, we analytically demonstrate that the vanishing of the difference of the effective masses…
We investigate the possibility of viable leptogenesis in an appealing $Δ(27)$ model with a universal texture zero in the (1,1) entry. The model accommodates the mass spectrum, mixing and CP phases for both quarks and leptons and allows for grand unification. Flavoured Boltzmann equations for the lepton asymmetries are solved numerically, taking into account both $N_1$ and $N_2$ right-handed neutrino decays. The $N_1$-dominated scenario is successful and the most natural option for the model, with $M_1 \in [10^9, 10^{12}]$ GeV, and $M_1/M_2 \in [0.002, 0.1]$, which constrains the parameter spac…
We derive and discuss the solution of the Boltzmann equations for leptogenesis in a phenomenologically viable SU(5) x A5 golden ratio flavour model proposed in arXiv:1410.2057 [hep-ph], arXiv:1502.00110 [hep-ph] . The model employs, in particular, the seesaw mechanism of neutrino mass generation. We find that the results on the baryon asymmetry of the Universe, obtained earlier in arXiv:1502.00110 [hep-ph] using approximate analytic expressions for the relevant CP violating asymmetry and efficiency factors, are correct, as was expected, up to 20-30 %. The phenomenological predictions for the l…
We study a class of leptogenesis models where the light neutrinos acquire their observed small masses by a symmetry-motivated construction. This class of models may naturally include three nearly degenerate heavy Majorana neutrinos that can strongly mix with one another and have mass differences comparable to their decay widths. We find that such a tri-resonant heavy neutrino system can lead to leptonic CP asymmetries which are further enhanced than those obtained in the usual bi-resonant approximation. Moreover, we solve the Boltzmann equations by paying special attention to the temperature d…
We derive non-equilibrium quantum transport equations for flavour-mixing fermions. We develop the formalism mostly in the context of resonant leptogenesis with two mixing Majorana fermions and one lepton flavour, but our master equations are valid more generally in homogeneous and isotropic systems. We give a hierarchy of quantum kinetic equations, valid at different approximations, that can accommodate helicity and arbitrary mass differences. In the mass-degenerate limit the equations take the familiar form of density matrix equations. We also derive the semiclassical Boltzmann limit of our e…
Majoron-driven spontaneous leptogenesis in type-II seesaw model
Korea Institute for Advanced Study（韩国高等科学研究院）；Institute for Basic Science (IBS)（基础科学研究院）；Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交大李政道研究所与物理与天文学院）
We discuss resonant leptogenesis arising from the decays of two nearly-degenerate right-handed neutrinos, identified as the inflaton and stabiliser superfields in a model of chaotic sneutrino inflation. We compare an analytical estimate of the baryon asymmetry $ η_B $ in the Boltzmann approximation to a numerical solution of the full density matrix equations, and find that the analytical result fails to capture the correct physics in certain regions of parameter space. The observed baryon asymmetry can be realised for a breaking of the mass degeneracy as small as $ \mathcal{O}(10^{-8}) $. The …
We discuss N_2-dominated leptogenesis in the presence of flavour dependent effects that have hitherto been neglected, in particular the off-diagonal entries of the flavour coupling matrix that connects the total flavour asymmetries, distributed in different particle species, to the lepton and Higgs doublet asymmetries. We derive analytical formulae for the final asymmetry including the flavour coupling at the N_2-decay stage as well as at the stage of washout by the lightest right-handed neutrino N_1. Moreover, we point out that in general part of the electron and muon asymmetries (phantom ter…
We use $S_4$ discrete group to construct a neutrino flavour model which leads to $TM_1$ mixing and is consistent with the neutrino oscillation data. Using the model's constrained parameter space, we predict the values of Dirac $CP$ phase and the light neutrino mass as $-1<\sin δ<-0.9$ and $1.7<m_1 (\text{meV})<5.5$ respectively. We thoroughly examine the usefulness of this model in explaining the observed baryon asymmetry of the Universe. Near-maximal breaking of CP symmetry (arising due to the $\text{TM}_1$ constraint) helps us in generating adequate baryon asymmetry through leptogenesis. We …
The nature of dark matter (DM) particles and the mechanism that provides their measured relic abundance are currently unknown. In this paper we investigate inert scalar and vector like fermion doublet DM candidates with a charge asymmetry in the dark sector, which is generated by the same mechanism that provides the baryon asymmetry, namely baryogenesis-via-leptogenesis induced by decays of scalar triplets. At the same time the model gives rise to neutrino masses in the ballpark of oscillation experiments via type II seesaw. We discuss possible sources of depletion of asymmetry in the DM and v…
We discuss leptogenesis in a model with heavy right-handed Majorana neutrinos propagating in a constant but otherwise generic CPT-violating axial time-like background (which could be motivated by string theory considerations). At temperatures much higher than the temperature of the electroweak phase transition we solve analytically but approximately (using Pade approximants) the corresponding Boltzmann equations, which describe lepton asymmetry generation due to the tree-level decays of the heavy neutrinos into standard model leptons. These leptons are effectively massless at such temperatures…
To calculate the baryon asymmetry in the baryogenesis via leptogenesis scenario one usually uses Boltzmann equations with transition amplitudes computed in vacuum. However, the hot and dense medium and, potentially, the expansion of the universe can affect the collision terms and hence the generated asymmetry. In this paper we derive the Boltzmann equation in the curved space-time from (first-principle) Kadanoff-Baym equations. As one expects from general considerations, the derived equations are covariant generalizations of the corresponding equations in Minkowski space-time. We find that, af…
