International Journal of Modern Physics A

Flavor effects can have a significant impact on the final estimate of the lepton (and therefore baryon) asymmetry in scenarios of leptogenesis. It is therefore necessary to account fully for this flavor dynamics in the relevant transport equations that describe the production (and washout) of the asymmetry. Doing so can both open up and restrict viable regions of parameter space relative to the predictions of more approximate calculations. In this paper, we identify the regimes in which flavor effects can be relevant and illustrate their impact in a number of phenomenological models. These include type I and type II seesaw embeddings, and low-scale resonant scenarios. In addition, we provide an overview of the semi-classical and field-theoretic methods that have been developed to capture flavor effects in a consistent way.

We review the current status of the leptogenesis scenario originally proposed by Akhmedov, Rubakov and Smirnov (ARS). It takes place in the parametric regime where the right-handed neutrinos are at the electroweak scale or below and the CP-violating effects are induced by the coherent superposition of different right-handed mass eigenstates. Two main theoretical approaches to derive quantum kinetic equations, the Hamiltonian time evolution as well as the Closed-Time-Path technique are presented, and we discuss their relations. For scenarios with two right-handed neutrinos, we chart the viable parameter space. Both, a Bayesian analysis, that determines the most likely configurations for viable leptogenesis given different variants of flat priors, and a determination of the maximally allowed mixing between the light, mostly left-handed, and heavy, mostly right-handed, neutrino states are discussed. Rephasing invariants are shown to be a useful tool to classify and to understand various distinct contributions to ARS leptogenesis that can dominate in different parametric regimes. While these analyses are carried out for the parametric regime where initial asymmetries are generated predominantly from lepton-number conserving, but flavor violating effects, we also review the contributions from lepton-number violating operators and identify the regions of parameter space where these are relevant.

Vanilla leptogenesis within the type I seesaw framework requires the mass scale of the right-handed neutrinos to be above $10^9$ GeV. This lower bound can be avoided if at least two of the sterile states are almost mass degenerate, which leads to an enhancement of the decay asymmetry. Leptogenesis models that can be tested in current and upcoming experiments often rely on this resonant enhancement, and a systematic and consistent description is therefore necessary for phenomenological applications. In this paper, we give an overview of different methods that have been used to study the saturation of the resonant enhancement when the mass difference becomes comparable to the characteristic width of the Majorana neutrinos. In this limit, coherent flavor transitions start to play a decisive role, and off-diagonal correlations in flavor space have to be taken into account. We compare various formalisms that have been used to describe the resonant regime and discuss under which circumstances the resonant enhancement can be captured by simplified expressions for the CP asymmetry. Finally, we briefly review some of the phenomenological aspects of resonant leptogenesis.

In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter–antimatter asymmetry generated when the temperature of the hot plasma $T$ exceeds the right-handed neutrino mass scale $M$ is efficiently erased, and one can focus on the temperature window $T\ll M$. We review recent progress in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number densities, their rigorous formulation and applicability are also discussed.

The focus of this paper lies on the possible experimental tests of leptogenesis scenarios. We consider both leptogenesis generated from oscillations, as well as leptogenesis from out-of-equilibrium decays. As the Akhmedov–Rubakov–Smirnov (ARS) mechanism allows for heavy neutrinos in the GeV range, this opens up a plethora of possible experimental tests, e.g. at neutrino oscillation experiments, neutrinoless double beta decay, and direct searches for neutral heavy leptons at future facilities. In contrast, testing leptogenesis from out-of-equilibrium decays is a quite difficult task. We comment on the necessary conditions for having successful leptogenesis at the TeV-scale. We further discuss possible realizations and their model specific testability in extended seesaw models, models with extended gauge sectors, and supersymmetric leptogenesis. Not being able to test high-scale leptogenesis directly, we present a way to falsify such scenarios by focusing on their washout processes. This is discussed specifically for the left–right symmetric model and the observation of a heavy $W_R$, as well as model independently when measuring $\mathrm{\Delta }L=2$ washout processes at the LHC or neutrinoless double beta decay.

We review the current status of the data on neutrino masses and lepton mixing and the prospects for measuring the CP-violating phases in the lepton sector. The possible connection between low energy CP violation encoded in the Dirac and Majorana phases of the Pontecorvo–Maki–Nakagawa–Sakata mixing matrix and successful leptogenesis is emphasized in the context of seesaw extensions of the Standard Model with a flavor symmetry $G_f$ (and CP symmetry).