Within the Closed Time Path (CTP) framework, we derive kinetic equations for particle distribution functions that describe leptogenesis in the presence of several lepton flavours. These flavours have different Standard-Model Yukawa couplings, which induce flavour-sensitive scattering processes and thermal dispersion relations. Kinetic equilibrium, which is rapidly established and maintained via gauge interactions, allows to simplify these equations to kinetic equations for the matrix of lepton charge densities. In performing this simplification, we notice that the rapid flavour-blind gauge interactions damp the flavour oscillations of the leptons. Leptogenesis turns out to be in the parametric regime where the flavour oscillations are overdamped and flavour decoherence is mainly induced by flavour sensitive scatterings. We solve the kinetic equations for the lepton number densities numerically and show that they interpolate between the unflavoured and the fully flavoured regimes within the intermediate parametric region, where neither of these limits is applicable.
Thermal leptogenesis, in the seesaw model, is a popular mechanism for generating the Baryon Asymmetry of the Universe. It was noticed recently, that including lepton flavour can modify significantly the results. These proceedings aim to discuss why and when flavour matters, in the thermal leptogenesis scenario for hierarchical right-handed neutrinos. No Boltzmann Equations are introduced.
For Leptogenesis based on the type-I seesaw mechanism, we present a systematic calculation of lepton-number violating and purely flavoured asymmetries within nonequilibrium Quantum Field Theory. We show that sterile neutrinos with non-degenerate masses in the GeV range can explain the baryon asymmetry of the Universe via flavoured Leptogenesis. This is possible due to the interplay of thermal and flavour effects. Our approach clarifies the relation between Leptogenesis from the oscillations of sterile neutrinos and the more commonly studied scenarios from decays and inverse decays. We explain …
We prove that taking correctly into account the lepton flavour dependence of the CP asymmetries and washout processes, it is possible to obtain successful thermal leptogenesis from the decays of the second right-handed neutrino. The asymmetries in the muon and tau-flavour channels are then not erased by the inverse decays of the lightest right-handed neutrino, N_1. In this way, we reopen the possibility of ``thermal leptogenesis'' in models with a strong hierarchy in the right-handed Majorana masses that is typically the case in models with up-quark--neutrino Yukawa unification.
A novel contribution to the leptonic CP asymmetries in type II seesaw leptogenesis scenarios is obtained for the cases in which flavor effects are relevant for the dynamics of leptogenesis. In the so-called flavoured leptogenesis regime, the interference between the tree-level amplitude of the scalar triplet decaying into two leptons and the one-loop wave-function correction with leptons in the loop, leads to a new nonvanishing CP asymmetry contribution. The latter conserves total lepton number but violates lepton flavour. Cases in which this novel contribution may be dominant in the generatio…
If the baryon asymmetry of the Universe is produced by leptogenesis, CP violation is required in the lepton sector. In the seesaw extension of the Standard Model with three hierarchical right-handed neutrinos, we show that the baryon asymmetry is insensitive to the PMNS phases: thermal leptogenesis can work for any value of the observable phases. This result was well-known when there are no flavour effects in leptogenesis; we show that it remains true when flavour effects are included.
Leptogenesis can successfully explain the matter-antimatter asymmetry via out-of-equilibrium decays of heavy Majorana neutrinos in the early Universe. In this article, we focus on non-resonant thermal leptogenesis and the possibility of lowering its scale. In order to do so, we calculate the lepton asymmetry produced from the decays of one and two heavy Majorana neutrinos using three-flavoured density matrix equations in an exhaustive exploration of the model parameter space. We find regions of the parameter space where thermal leptogenesis is viable at intermediate scales, $T\sim 10^{6}$ GeV.…
We study the impact of flavour in ``soft leptogenesis'' (leptogenesis induced by soft supersymmetry breaking terms). We address the question of how flavour effects can affect the region of parameters in which successful soft leptogenesis induced by CP violation in the right-handed sneutrino mixing is possible. We find that for decays which occur in the intermediate to strong washout regimes for all flavours, the produced total $B-L$ asymmetry can be up to a factor ${\cal O}(30)$ larger than the one predicted with flavour effects being neglected. This enhancement, permits slightly larger values…
We consider sub-TeV scale flavoured resonant leptogenesis within the minimal type-I seesaw scenario with two right-handed singlet neutrinos $N_{1,2}$ forming a pseudo-Dirac pair, concentrating on the case of masses of the pseudo-Dirac pair having values $M_{1,2} \lesssim 100$ GeV. The case when the CP violating asymmetries in the individual lepton charges $L_l$, $l=e,μ,τ$, and in the total lepton charge $L$ of the Universe are generated in $1 \leftrightarrow 2$ decay processes is investigated. We show that successful leptogenesis is possible for $M_{1,2}$ lying in the interval $M_{1,2} = (0.3 …
We revisit flavour effects in soft leptogenesis relaxing the assumption of universality for the soft supersymmetry breaking terms. We find that with respect to the case in which the heavy sneutrinos decay with equal rates and equal CP asymmetries for all lepton flavours, hierarchical flavour configurations can enhance the efficiency by more than two orders of magnitude. This translates in more than three order of magnitude with respect to the one-flavour approximation. We verify that lepton flavour equilibration effects related to off-diagonal soft slepton masses are ineffective for damping th…
We present a systematic study of leptogenesis in neutrino mass models with $μτ$-flavoured CP symmetry. In addition to the strong hierarchical $N_1$-dominated scenario ($N_1$DS) in the `two flavour regime' of leptogenesis, we show that one may choose the right-handed (RH) neutrino mass hierarchy as mild as $M_2\simeq 4.7 M_1$ for a perfectly valid hierarchical $N_1$DS. This in turn reduces the lower bound on the allowed values of $M_1$, compared to what is stated in the literature. The consideration of flavour effects due to the heavy neutrinos also translate into an upper bound on $M_1$. It is…
We briefly review the main aspects of leptogenesis, describing both the unflavoured and the flavoured versions of the $N_2$-dominated scenario. A study of the success rates of both classes of models has been carried out. We comment on these results and discuss corrective effects to this simplest scenario. Focusing on the flavoured case, we consider the conditions required by strong thermal leptogenesis, where the final asymmetry is fully independent of the initial conditions. Barring strong cancellations in the seesaw formula and in the flavoured decay parameters, we show that strong thermal l…
The CP-violation necessary for the generation of the baryon asymmetry of the Universe $Y_B$ in the "flavoured" leptogenesis scenario can arise from the "low energy" PMNS neutrino mixing matrix $U$ and/or from the "high energy" part of neutrino Yukawa couplings, which can mediate CP-violating phenomena only at some high energy scale. The possible interplay between these two types of CP-violation is analysed. The type I see-saw model with three heavy right-handed Majorana neutrinos having hierarchical spectrum is considered. We show that in the case of inverted hierarchical light neutrino mass s…
We discuss the conditions to realize a scenario of strong thermal leptogenesis, where the final asymmetry is fully independent of the initial conditions, when both heavy and light flavor effects are taken into account. In particular the contribution to the final asymmetry from a residual initial pre-existing asymmetry has to be negligible. We show that in the case of a hierarchical right-handed (RH) neutrino mass spectrum, the only possible way is a N_2-dominated leptogenesis scenario with a lightest RH neutrino mass M_1 << 10^9 GeV and with a next-to-lightest RH neutrino mass 10^12 GeV >> M_2…
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 …
Although $SO(10)$ Supersymmetric (SUSY) Grand Unification Theories (GUTs) are very attractive for neutrino mass and mixing, it is often quite difficult to achieve successful leptogenesis from the lightest right-handed neutrino $N_1$ due to the strong relations between neutrino and up-type quark Yukawa couplings. We show that in a realistic model these constraints are relaxed, making $N_1$ leptogenesis viable. To illustrate this, we calculate the baryon asymmetry of the Universe $ Y_B $ from flavoured $ N_1 $ leptogenesis in a recently proposed $ Δ(27) \times SO(10) $ SUSY GUT. The flavoured Bo…
We present a systematic study on minimally perturbed neutrino mass matrices which at the leading order give rise to Tri-BiMaximal (TBM) mixing due to a residual $\mathbb{Z}_2\times \mathbb{Z}_2^{μτ}$ Klein symmetry in the neutrino mass term of the low energy effective seesaw Lagrangian. Considering only the breaking of $\mathbb{Z}_2^{μτ}$ with two relevant breaking parameters ($ε_{4,6}^\prime$), after a comprehensive numerical analysis, we show that the phenomenologically viable case in this scenario is a special case of TM1 mixing. For this class of models, from the phenomenological perspecti…
Both neutrinoless double beta decay and leptogenesis require neutrinos to be Majorana fermions. A relation between these two phenomena can be derived once the mechanism of neutrino mass generation is specified. We first derive the constraints on the Majorana phases by minimising the effective neutrino mass in neutrinoless double beta decay with respect to the smallest mass among the light neutrinos. Given these phases, we derive a lower bound on $M_{1}$ (the mass of the lightest of the heavy neutrinos) in the framework of Type-I seesaw mechanism, subject to the constraint that the CP asymmetry…
If lepton masses and mixings are explained by a flavour symmetry in seesaw model which leads to U_{e3}=0 at leading order, we find that, under reasonable assumptions, a future observation of low energy leptonic CP violation implies, barring accidental cancellations, a lepton asymmetry both in flavoured leptogenesis and in its one-flavour approximation. We explicitly implement this approach with a predictive seesaw model for Tri-Bimaximal Mixing (TBM) and show how cosmological baryon asymmetry can be directly trigged by low energy phases appearing in $U_{e3}$. Thanks to this direct correlation …
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…
Using the Closed-Time-Path approach, we perform a systematic leading order calculation of the relaxation rate of flavour correlations of left-handed Standard Model leptons. This quantity is of pivotal relevance for flavoured Leptogenesis in the Early Universe, and we find it to be 5.19*10^-3 T at T=10^7 GeV and 4.83*10^-3 T at T=10^13 GeV. These values apply to the Standard Model with a Higgs-boson mass of 125 GeV. The dependence of the numerical coefficient on the temperature T is due to the renormalisation group running. The leading linear and logarithmic dependencies of the flavour relaxati…
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…
In a novel standard model extension it has been suggested that, even in the absence of right-handed neutrinos and type-I seesaw, purely triplet leptogenesis leading to baryon asymmetry of the universe can be realised by two heavy Higgs triplets which also provide type-II seesaw ansatz for neutrino masses. In this work we discuss this model for hierarchical neutrino masses in concordance with recently determined cosmologocal bounds and oscillation data including $θ_{23}$ in the second octant and large Dirac CP phases. We also address the issues on dark matter and vacuum stability of the scalar …
We discuss how seesaw neutrino models can be graphically represented in lepton flavour space. We examine various popular models and show how this representation helps understanding their properties and connection with experimental data showing in particular how certain texture zero models are ruled out. We also introduce a new matrix, the bridging matrix, that brings from the light to the heavy neutrino mass flavour basis, showing how this is related to the orthogonal matrix and how different quantities are easily expressed through it. We then show how one can randomly generate orthogonal and …
