Encouraged by the recent results from neutrino oscillation experiments, we perform an analytical study of SO(10)-inspired models and leptogenesis with hierarchical right-handed (RH) neutrino spectrum. Under the approximation of negligible misalignment between the neutrino Yukawa basis and the charged lepton basis, we find an analytical expression for the final asymmetry directly in terms of the low energy neutrino parameters that fully reproduces previous numerical results. This expression also shows that it is possible to identify an effective leptogenesis phase for these models. When we also impose the wash-out of a large pre-existing asymmetry N p,i B−L , the strong thermal (ST) condition, we derive analytically all those constraints on the low energy neutrino parameters that characterise the ST-SO(10)-inspired leptogenesis solution, confirming previous numerical results. In particular we show why, though neutrino masses have to be necessarily normally ordered, the solution implies an analytical lower bound on the effective neutrinoless double beta decay neutrino mass, m ee 8 meV, for N p,i B−L = 10 −3 , testable with next generation experiments. This, in combination with an upper bound on the atmospheric mixing angle, necessarily in the first octant, forces the lightest neutrino mass within a narrow range m 1 (10-30) meV (corresponding to i m i (75-125) meV). We also show why the solution could correctly predict a non-vanishing reactor neutrino mixing angle and requires the Dirac phase to be in the fourth quadrant, implying sin δ (and J CP ) negative as hinted by current global analyses. Many of the analytical results presented (expressions for the orthogonal matrix, RH neutrino mixing matrix, masses and phases) can have applications beyond leptogenesis.
Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the weak commutation condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.Contagion processes, such as the spread of diseases, information, or innovations [1][2][3][4][5], share a common theoretical framework coupling the underlying population contact structure with contagion features to provide an understanding of the resulting spectrum of emerging collective behaviors [6]. A common keystone property is the presence of a threshold behavior defining the transition between a macroscopic-level spreading regime and one characterized by a null or negligibly small contagion of individuals. Known as the epidemic threshold in the realm of infectious disease dynamics [1], the concept is analogous to the phase transition in non-equilibrium physical systems [7,8], and is also central in social contagion processes [5,[9][10][11][12][13].A vast array of theoretical results characterize the epidemic threshold [14], mainly under the limiting assumptions of quenched and annealed networks [4,[15][16][17][18], i.e., when the time scale of the network evolution is much slower or much faster, respectively, than the dynamical process. The recent availability of data on time-resolved contacts of epidemic relevance [19] has, however challenged the time scale separation, showing it may introduce important biases in the description of the epidemic spread [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] and in the characterization of the transition behavior [31,[34][35][36][37]. Departing from traditional approximations, few novel approaches are now available that derive the epidemic threshold constrained to specific contexts of generative models of temporal networks [22,32,35,[38][39][40][41] or considering generic discrete-time evolving contact patterns [42][43][44]. In particular, the recently introduced infection propagator approach [43,44] ing the probabilities of transmission of the infective agent along time-respecting paths in the network. Its spectrum allows the computation of the epidemic threshold at any given time scale and for an arbitrary discrete-time temporal network. Leveraging an original mapping of the temporal network and epidemic spread in terms of a multilayer structure, the approach is valid in the discrete representation only, similarly to previous methods [17,18,35].Meanwhile, a large interest in the study of continuously evolving temporal networks has developed, introducing novel representations [19,20,27,45] and proposing optimal discretization schemes [44,46,47] that may however...
We show that successful strong thermal leptogenesis, where the final asymmetry is independent of the initial conditions and in particular a large pre-existing asymmetry is efficiently washed-out, favours values of the lightest neutrino mass m 1 10 meV for normal ordering (NO) and m 1 3 meV for inverted ordering (IO) for models with orthogonal matrix entries respecting |Ω 2 ij | 2. We show analytically why lower values of m 1 require a higher level of fine tuning in the seesaw formula and/or in the flavoured decay parameters (in the electronic for NO, in the muonic for IO). We also show how this constraint exists thanks to the measured values of the neutrino mixing angles and could be tightened by a future determination of the Dirac phase. Our analysis also allows us to place a more stringent constraint for a specific model or class of models, such as SO(10)-inspired models, and shows that some models cannot realise strong thermal leptogenesis for any value of m 1 . A scatter plot analysis fully supports the analytical results. We also briefly discuss the interplay with absolute neutrino mass scale experiments concluding that they will be able in the coming years to either corner strong thermal leptogenesis or find positive signals pointing to a non-vanishing m 1 . Since the constraint is much stronger for NO than for IO, it is very important that new data from planned neutrino oscillation experiments will be able to solve the ambiguity.
We discuss a left-right symmetric extension of the Standard Model in which the three additional right-handed neutrinos play a central role in explaining the baryon asymmetry of the Universe, the dark matter abundance and the ultra energetic signal detected by the IceCube experiment. The energy spectrum and neutrino flux measured by IceCube are ascribed to the decays of the lightest right-handed neutrino N 1 , thus fixing its mass and lifetime, while the production of N 1 in the primordial thermal bath occurs via a freeze-in mechanism driven by the additional SU(2) R interactions. The constraints imposed by IceCube and the dark matter abundance allow nonetheless the heavier righthanded neutrinos to realize a standard type-I seesaw leptogenesis, with the B − L asymmetry dominantly produced by the next-to-lightest neutrino N 2 . Further consequences and predictions of the model are that: the N 1 production implies a specific power-law relation between the reheating temperature of the Universe and the vacuum expectation value of the SU(2) R triplet; leptogenesis imposes a lower bound on the reheating temperature of the Universe at 7 × 10 9 GeV. Additionally, the model requires a vanishing absolute neutrino mass scale m 1 0.
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