The lightness of the Standard Model (SM) neutrinos could be understood if their masses were to be generated by new physics at a high scale, through the so-called seesaw mechanism involving heavy fermion singlets. If new physics violates baryon minus lepton number by only a small amount, the heavy fermion singlets as well as the SM neutrinos split into pairs of quasi-Dirac states. At the scale of the fermion singlets, this quasi-Diracness allows to enhance CP violation in their decays and the cosmic matter-antimatter asymmetry can be successfully generated through resonant leptogenesis. At lower scale, this quasi-Diracness results in small SM neutrino mass splitting which can be probed in oscillation experiments. Remarkably, the parameter space for viable leptogenesis spans over the regime relevant for solar and atmospheric neutrino oscillations.
Dirac leptogenesis (or Dirac neutrinogenesis), in which neutrinos are purely Dirac particles, is an interesting alternative to the standard leptogenesis scenario. In its supersymmetric version, the modified form of the superpotential required for successful baryogenesis contributes new, generically non-flavor-diagonal terms to the slepton and sneutrino mass matrices. In this work, we examine how current experimental bounds on flavor-changing effects in the lepton sector (and particularly the bound on Mu -> e Gamma) constrain Dirac leptogenesis and we find that it is capable of succeeding with …
We show that a version of the nearly Minimal Supersymmetric Standard Model (nMSSM), extended only in the singlet sector to include the additional superfields of right-handed neutrinos and very heavy Dirac particles conserving $B-L$, admits a viable scenario for Dirac leptogenesis and naturally small Dirac neutrino masses. The origin of the ($B-L$)-conserving high singlet neutrino scale and the desired supersymmetry breaking terms is associated with dynamical supersymmetry breaking in the hidden sector.
Dirac leptogenesis, in which neutrinos are purely Dirac and develop small but nonzero effective masses without the aid of the see-saw mechanism, provides an interesting alternative to the standard leptogenesis picture. Here we review the theory and phenomenology of Dirac leptogenesis and show that it is a viable theory capable of simultaneously satisfying all relevant bounds from cosmology, neutrino physics, and flavor violation. In addition, we also explore several potential extensions of the model, such as the possibility of right-handed sneutrino dark matter and the potential for relating t…
We present a model of leptogenesis that preserves lepton number. The model maintains the important feature of more traditional leptogenesis scenarios: the decaying particles that provide the CP violation necessary for baryogenesis also provide the explanation for the smallness of the neutrino Yukawa couplings. This model clearly demonstrates that, contrary to conventional wisdom, neutrinos need not be Majorana in nature in order to help explain the baryon asymmetry of the universe.
We discuss how Dirac neutrinos can naturally be generated in supersymmetry and how they allow for an Affleck-Dine leptogenesis scenario, in which a left-right asymmetry is generated in the sneutrino sector, the left part of which is transferred to a baryon asymmetry via sphaleron transitions. No exotic fields need to be added to the MSSM other than the right-handed neutrino.
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…
Motivated by the fact that the Dirac phase in the PMNS matrix is the only CP-violating parameter in the leptonic sector that can be measured in neutrino oscillation experiments, we examine the possibility that it is the dominant source of CP violation for leptogenesis caused by the out-of-equilibrium decays of heavy singlet fermions. We do so within a low-scale extended type-I seesaw model, featuring two Standard Model singlet fermions per family, in which lepton number is approximately conserved such that the heavy singlet neutrinos are pseudo-Dirac. We find that this produces a predictive mo…
We explain the electron-positron excess reported by the DAMPE collaboration recently in a radiative Dirac seesaw model where a dark $U(1)_X$ gauge symmetry can (i) forbid the tree-level Yukawa couplings of three right-handed neutrinos to the standard model lepton and Higgs doublets, (ii) predict the existence of three dark fermions for the gauge anomaly cancellation, (iii) mediate a testable scattering of the lightest dark fermion off the nucleons. Our model can also accommodate a successful leptogenesis to generate the cosmic baryon asymmetry.
We consider resonant Dirac leptogenesis in a geometry with three five-dimensional throats in the flat limit. The baryon asymmetry in the universe is generated by resonant decays of heavy Kaluza-Klein scalars that are copies of the standard model Higgs. Discrete exchange symmetries between the throats are responsible for establishing two key features of the model. First, they ensure a near degeneracy of the scalar masses and thus a resonant decay of the scalars. This allows for Dirac leptogenesis at low energies close to the TeV scale. Second, the discrete symmetries connect the observed baryon…
A TeV-scale Higgs doublet can acquire a tiny vacuum expectation value via its small mixing with the standard model Higgs doublet. Ones then can realize a testable Dirac neutrino mass generation through the sizable Yukawa couplings among this new Higgs doublet, several right-handed neutrinos and the standard model lepton doublets. We show the small mixing between the two Higgs doublets can come from certain interactions for generating the cosmic baryon asymmetry.
We study leptogenesis in two seesaw models where maximal atmospheric neutrino mixing and $U_{e3} = 0$ result from symmetries. Salient features of those models are the existence of three Higgs doublets and a twofold degeneracy of the neutrino Dirac mass matrix. We find that in those models both leptogenesis and neutrinoless double beta decay depend on the same unique Majorana phase. Leptogenesis can produce a baryon asymmetry of the universe of the right size provided the mass of the heavy neutrino whose decays generate the lepton asymmetry is in the range $10^{11}$--$10^{12} \mathrm{GeV}$. Mor…
Dirac neutrinos with lepton-number-violating interactions can give rise to a new leptogenesis mechanism. In its simplest renormalizable realization, based on a gauged B-L symmetry spontaneously broken by four units, the decay of a new scalar creates an asymmetry in the right-handed neutrinos. A neutrinophilic two-Higgs-doublet model converts this asymmetry to the baryons, provides a natural explanation of the small neutrino masses, and can lead to an effective number of relativistic degrees of freedom of N(eff) = 3.29 due to the entropy-suppressed contribution of the right-handed neutrinos.
The running of neutrino parameters in see-saw models and its implications for leptogenesis and for testing predictions of mass models with future precision experiments are discussed using analytical approximations as well as numerical results.
This work addresses the viability of \textit {Dirac phase leptogenesis}, in a scenario where the light Majorana neutrinos acquire masses by the inverse seesaw (ISS) mechanism. We show that, a successful leptogenesis in the ISS, driven (only) by the Dirac CP phase can be achieved with the involvement of an unorthodox form of the rotational matrix $R = e^{i{\bf A}} \,\,\,(e^{\bf A})$ in the Casas-Ibarra parametrisation. This particular structure of $R$ turns out to be an artefact in explaining the observed baryon asymmetry of the Universe in a pure ISS scenario. We detail here the confined regio…
Models with composite singlet neutrinos can give small Majorana or Dirac masses to the active neutrinos. The mechanism is based on the fact that conserved chiral symmetries give massless neutrinos at the renormalizable level. Thus, they acquire very small masses due to non-renormalizable terms. We investigate such models in two aspects. First, we find UV completions for them and then we investigate the possibility of giving leptogenesis. We find that these models offer new possibilities for leptogenesis. Models with Majorana masses can exhibit standard leptogenesis. Models with Dirac masses ca…
We discuss the conditions for a non-vanishing Dirac phase δand mixing angle θ_{13}, sources of CP violation in neutrino oscillations, to be uniquely responsible for the observed matter-antimatter asymmetry of the universe through leptogenesis. We show that this scenario, that we call δ-leptogenesis, is viable when the degenerate limit (DL) for the heavy right-handed (RH) neutrino spectrum is considered. We derive an interesting joint condition on \sinθ_{13} and the absolute neutrino mass scale that can be tested in future neutrino oscillation experiments. In the limit of hierarchical heavy RH …
Baryon and lepton numbers of the Universe in leptogenesis with Dirac neutrino and leptogenesis with Majorana neutrino scenarios are considered. It is shown that despite quite different features of Dirac and Majorana fermions both scenarios yield the same relation among the initial lepton and the final baryon asymmetries. Moreover right-handed neutrinos in the leptogenesis with Dirac neutrino scenario have very little impact on the effective number of relativistic degrees of freedom, constrained by BBN. Thus the two scenarios are similar from the cosmological point of view. It is also pointed o…
We describe a "neutrinogenesis" mechanism whereby, in the presence of right-handed neutrinos with sufficiently small pure Dirac masses, (B+L)-violating sphaleron processes create the baryon asymmetry of the Universe, even when B=L=0 initially. It is shown that the resulting neutrino mass constraints are easily fulfilled by the neutrino masses suggested by current experiments. We present a simple toy model which uses this mechanism to produce the observed baryon asymmetry of the Universe. (PostScript Errors corrected in latest Version).
The seesaw theory, the leading theory for particle interactions, provides a viable mechanism for generating the matter-antimatter asymmetry of the universe. Testing the leptogenesis mechanism directly requires measurement of the d=6 operator of the low-energy effective Lagrangian, in addition to the more familiar d=5 operator which generates Majorana masses for the light neutrinos when the electroweak symmetry is spontaneously broken. This important experimental challenge awaits the next generation of particle physicists.
We propose a minimal extension of the standard model with U(1)_{B-L} \times Z_{2} symmetry. In this model by assuming that the neutrinos are Dirac (i.e. $B-L$ is an exact symmetry), we found a simultaneous solution for non zero neutrino masses and dark matter content of the universe. The observed baryon asymmetry of the universe is also explained using Dirac Leptogenesis, which is assisted by a dark sector, gauged under a U(1)_D symmetry. The latter symmetry of the dark sector is broken at a TeV scale and thereby giving mass to a neutral gauge boson Z_D. The standard model Z-boson mixes with t…
We propose a model where sterile neutrinos are introduced to make light neutrinos to be pseudo-Dirac particles. It is shown how tiny mass splitting necessary for realizing pseudo-Dirac neutrinos can be achieved. Within the model, we show how leptogenesis can be successfully generated. Motivated by the recent observation of very high energy neutrino events at IceCube, we study a possibility to observe the effects of the pseudo-Dirac property of neutrinos by performing astronomical-scale baseline experiments to uncover the oscillation effects of very tiny mass splitting. Using the result of glob…
I present here a concise summary of the preprint arXiv:0707.3024, written in collaboration with A. Anisimov and P. Di Bari. There we discuss leptogenesis when {\em CP} violation stems exlusively from the Dirac phase in the PMNS mixing matrix. Under this assumption it turns out that the situation is very constrained when a hierarchical heavy right-handed (RH) neutrino spectrum is considered: the allowed regions are small and the final asymmetry depends on the initial conditions. On the other hand, for a quasi-degenerate spectrum of RH neutrinos, the {\em CP} asymmetry can be enhanced and the si…
A triangular ansatz for the seesaw mechanism and baryogenesis via leptogenesis is explored. In a basis where both the charged lepton and the Majorana mass matrix are diagonal, the Dirac mass matrix can generally be written as the product of a unitary times a triangular matrix. We assume the unitary matrix to be the identity and then an upper triangular Dirac matrix. Constraints from bilarge lepton mixing and leptogenesis are studied.
In an $SU(3)_{c}\times SU(2)_{L}\times SU(2)_{R}\times U(1)_{B-L}$ left-right symmetric framework, we present a new leptogenesis scenario parametrized by Dirac neutrino mass matrix. Benefited from the parity symmetry motivated to solve the strong CP problem, the dimensionless couplings of the mirror fields are identified to those of the ordinary fields. In particular, the mirror Dirac neutrinos have a heavy mass matrix proportional to the light mass matrix of the ordinary Dirac neutrinos. Through the $SU(2)_R$ gauge interactions, the mirror neutrinos can decay to generate a lepton asymmetry in…
We study leptogenesis in three different realisations of the type Ib seesaw mechanism, where the effective masses of the neutrinos are obtained by the spontaneous symmetry breaking of two different Higgs doublets. In the minimal type Ib seesaw model, where two right-handed neutrinos form a Dirac mass, we show that it is impossible to produce the correct baryon asymmetry, even including a pseudo-Dirac mass splitting. In an extended type Ib seesaw model, with a third very heavy Majorana right-handed neutrino, together with the low scale Dirac pair of right-handed (RH) neutrinos and an extra sing…
We study the prediction of maximal zeros of the Dirac mass matrix on neutrino phenomenology and baryon asymmetry of the universe (BAU) within the framework of an inverse seesaw ISS $(2,3)$. We try to find the origin of the allowed two zero textures of the Dirac mass matrix from $S_{4}$ flavor symmetry. ISS $(2,3)$ model contains two pairs of quasi-Dirac particles and one sterile state in the keV scale along with three active neutrinos. The decays of the quasi-Dirac pairs create lepton asymmetry that can be converted to baryon asymmetry of the universe by the sphaleron process. Thus, BAU can be…
We propose a model for Dirac leptogenesis based on a non-anomalous $U(1)^{\prime}$ gauged family symmetry. The anomaly cancellation conditions are satisfied with no new chiral fermions other than the three right-handed neutrinos, giving rise to stringent constraints among the charges. Realistic masses and mixing angles are obtained for all fermions. The model predicts neutrinos of the Dirac type with naturally suppressed masses. Dirac leptogenesis is achieved through the decay of the flavon fields. The cascade decays of the vector-like heavy fermions in the Froggatt-Nielsen mechanism play a cr…
The leptogenesis is studied in the neutrino textures with two zeros, which reduce the number of independent phases of the CP violation. The phenomenological favored neutrino textures with two zeros are decomposed into the Dirac neutrino mass matrix and the right-handed Majorana one in the see-saw mechanism. Putting the condition to suppress the $μ\to eγ$ decay enough, the texture zeros of the Dirac neutrino mass matrix are fixed in the framework of the MSSM with right-handed neutrinos. These textures have only one CP violatig phase. The magnitude of each entry of the Dirac mass matrix is deter…
We propose the minimal, lepton-number conserving, SU(3)xSU(2)xU(1) gauge-singlet, or phantom, extension of the Standard Model. The extension is natural in the sense that all couplings are of O(1) or forbidden due to a phantom sector global U(1)_D symmetry, and basically imitates the standard Majorana see-saw mechanism. Spontaneous breaking of the U(1)_D symmetry triggers consistent electroweak gauge symmetry breaking only if it occurs at a scale compatible with small Dirac neutrino masses and baryogenesis through Dirac leptogenesis. Dirac leptogenesis proceeds through the usual out-of-equilibr…
If the masses of at least two generations of right-handed neutrinos (RHNs) are near-degenerate, the scale of leptogenesis can be as low as $\sim$ 100 GeV. In this work, we study probing such resonant leptogenesis in the $B-L$ model at the LHC and future multi-TeV muon colliders via the process $Z'\to NN\to\ell^\pm\ell^\pm+{\rm jets}$, with $Z'$ the $U(1)_{B-L}$ gauge boson and $N$ the RHN. The same-sign dilepton feature of the signal makes it almost background-free, while the event number difference between positive and negative leptons is a hint for $CP$ violation, which is a key ingredient o…
We extend the DFSZ invisible axion model to simultaneously explain small Dirac neutrino masses and cosmic matter-antimatter asymmetry. After the Peccei-Quinn and electroweak symmetry breaking, the effective Yukawa couplings of the Dirac neutrinos to the standard model Higgs scalar can be highly suppressed by the ratio of the vacuum expectation value of an iso-triplet Higgs scalar over the masses of some heavy gauge-singlet fermions, iso-doublet Higgs scalars or iso-triplet fermions. The iso-triplet fields can carry a zero or nonzero hypercharge. Through the decays of the heavy gauge-singlet fe…
We propose a novel way of probing high scale Dirac leptogenesis, a viable alternative to canonical leptogenesis scenario where the total lepton number is conserved, keeping light standard model (SM) neutrinos purely Dirac. The simplest possible seesaw mechanism for generating light Dirac neutrinos involve heavy singlet Dirac fermions and a singlet scalar. In addition to unbroken global lepton number, a discrete $Z_2$ symmetry is imposed to forbid direct coupling between right and left chiral parts of light Dirac neutrino. Generating light Dirac neutrino mass requires the singlet scalar to acqu…
Assuming a type-I seesaw mechanism for neutrino mass generation and invoking a baryogengesis via leptogenesis scenario, we consider a reasonable hierarchical structure for Dirac neutrino mass matrix, similar to up-type quark mass matrix. These hypotheses imply a relevant connection between high scale CP violation and low energy one. By requiring a compact heavy neutrino mass spectrum, which allows to circumvent Davidson-Ibarra limit, one can obtain an efficient leptogenesis restricting the allowed region for low energy neutrino parameters. Once the oscillating parameters are taken inside a $3σ…
The phenomenology of 3-neutrino mixing, the current status of our knowledge about the 3-neutrino mixing parameters, including the absolute neutrino mass scale, and of the Dirac and Majorana CP violation in the lepton sector, are reviewed. The problems of CP violation in neutrino oscillations and of determining the nature - Dirac or Majorana - of massive neutrinos, are discussed. The seesaw mechanism of neutrino mass generation and the related leptogenesis scenario of generation of the baryon asymmetry of the Universe, are considered. The results showing that the CP violation necessary for the …
Testing Seesaw and Leptogenesis via Gravitational Waves: Majorana versus Dirac
University of Sussex（萨塞克斯大学）；National Astronomical Observatory of Japan（日本国立天文台）；The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学）；KEK（高能加速器研究机构）；The University of Tokyo（东京大学）
We discuss neutrino masses and mixing in the context of seesaw type I models with three right-handed Majorana neutrinos and an approximately diagonal Dirac sector. This ansatz is motivated by the idea that the flavor structure in the right-handed Majorana masses is responsible for the large mixing angles, whereas the small mixing angle $θ_{13}$ originates from the Dirac Yukawa couplings in analogy to the quark sector. To obtain $θ_{13} \approx 0.15$ we study a possible $SU(5)$ grand unified theory realization with a $U(1) \times \mathbb{Z}'_2 \times \mathbb{Z}''_2 \times \mathbb{Z}'''_2$ flavo…
We address the issue of the neutrino masses and mixing in TeV scale $B-L$ extension of the Standard Model. We show that if Dirac neutrino masses are of order $10^{-4}$ Gev, then the measured neutrino masses are correctly obtained. We propose a mass relation between quarks and leptons that may account for such small Dirac neutrino masses. We analyze the leptogenesis in this type of models and provide analytical expressions for the new contributions due to the predicted extra Higgs and extra neutral gauge boson. We find that thermal leptogenesis, with a resonant enhancement due to nearly degener…
We propose a new scaling ansatz in the neutrino Dirac mass matrix to explain the low energy neutrino oscillations data, baryon number asymmetry and neutrinoless double beta decay. In this work, a full reconstruction of the neutrino Dirac mass matrix has been realized from the low energy neutrino oscillations data based on type-I seesaw mechanism. A concrete model based on $A_4$ flavor symmetry has been considered to generate such a neutrino Dirac mass matrix and imposes a relation between the two scaling factors. In this model, the right-handed Heavy Majorana neutrino masses are quasi-degenera…
A possible interplay between the two terms of the general type-II seesaw formula is exercised which leads to the generation of nonzero $θ_{13}$. The specific flavor structure of the model, guided by the $A_4 \times Z_4 \times Z_3$ symmetry and accompanied with the Standard Model singlet flavons, yields the conventional seesaw contribution to produce the tribimaximal lepton mixing which is further corrected by the presence of the $SU(2)_L$ triplet contribution to accommodate $θ_{13}$. We consider the CP symmetry to be spontaneously broken by the complex vacuum expectation value (vev) of a singl…
The Dirac nature of the gauginos (and also the Higgsinos) can be realized in $R$-symmetric supersymmetry models. In this class of models, the Dirac bino (or wino) with a small mixture of the Dirac Higgsinos is a good dark matter candidate. When the seesaw mechanism with Higgs triplet superfields is implemented to account for the neutrino masses and mixing, the leptogenesis driven by the heavy triplet decay is shown to produce not only the matter-antimatter asymmetry but also the asymmetric relic density of the Dirac gaugino dark matter. The dark matter mass turns out to be controlled by the Yu…
We investigate how the baryon asymmetry of our universe via leptogenesis can be achieved within the framework of the seesaw model with Fritzsch type lepton mass matrices proposed by Fukugita $et. al$. We study the cases with CP-violating phases in charged lepton Yukawa matrix, however, with and without Dirac neutrino Yukawa phases. We consider both flavor independent and flavor dependent leptogenesis, and demonstrate how they lead to different amounts of lepton asymmetries in detail. In particular, it is shown that flavor dependent leptogenesis in this model can be worked out only when the CP …
The leptogenesis is studied in the neutrino mass matrix with two zeros, which reduces the number of independent phases of the CP violation. These texture zeros are decomposed into the Dirac neutrino mass matrix and the right-handed Majorana one in the see-saw mechanism. It is found that there are six textures for the Dirac neutrino mass matrix, among which one texture with three zeros has three phases, three textures with four zeros have two phases, and two textures with five zeros have only one phase in the basis with the real right-handed Majorana mass matrix. The relation between the leptog…
Minimalistic Dirac radiative neutrino mass model based on modular symmetry is proposed. We predict maximum number of observables possible including neutrino mass splittings, neutrino mass scale, lepton mixing angles, and Dirac phases in the leptonic sector with minimum number of input parameters possible. Model is capable of accommodating multicomponent dark matter, thanks to the $\emph{R}-$parity and accidental scotogenic $\mathbb{Z}_2$ discrete symmetry. Furthermore, even-though neutrinos are Dirac in our model, matter-antimatter asymmetry of the Universe is achieved via neutrinogenesis mech…
We propose an appealing alternative scenario of leptogenesis assisted by dark sector which leads to the baryon asymmetry of the Universe satisfying all theoretical and experimental constraints. The dark sector carries a non minimal set up of singlet doublet fermionic dark matter extended with copies of a real singlet scalar field. A small Majorana mass term for the singlet dark fermion, in addition to the typical Dirac term, provides the more favourable dark matter of pseudo-Dirac type, capable of escaping the direct search. Such a construction also offers a formidable scope to radiative gener…
It is shown that the type III seesaw mechanism proposed recently can have certain advantages over the conventional (or type I) seesaw mechanism for leptogenesis. In particular a resonant enhancement of leptogenesis via heavy quasi-Dirac right-handed neutrino pairs can occur without a special flavor form or "texture" of the mass matrices being assumed. Some of the requirements for neutrino mixing and leptogenesis are effectively decoupled.
We examine the compatibility between the Neutrino Option, in which the electroweak scale is generated by PeV mass type I seesaw Majorana neutrinos, and leptogenesis. We find the Neutrino Option is consistent with resonant leptogenesis. Working within the minimal seesaw scenario with two heavy Majorana neutrinos $N_{1,2}$, which form a pseudo-Dirac pair, we explore the viable parameter space. We find that the Neutrino Option and successful leptogenesis are compatible in the cases of a neutrino mass spectrum with normal (inverted) ordering for $1.2 \times 10^6 < M \text{ (GeV)} < 8.8 \times 10^6…
We study effects of CP violation in a modified bipair neutrino mixing scheme predicting $\sin^2θ_{23}$ near both 0.4 and 0.6 currently consistent with experimentally allowed values. The source of CP violation is supplied by charged lepton mixing accompanied by a single phase, whose mixing size is assumed to be less than that of the Wolfenstein parameter for the quark mixing. Including results of leptogenesis, which is based on the minimal seesaw model, we obtain the allowed region of CP-violating Dirac and Majorana phases, which provides the observed baryon asymmetry of the universe in the cas…
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 …
The conventional seesaw-leptogenesis can simultaneously explain the suppression of neutrino masses and the generation of cosmic baryon asymmetry, but usually cannot predict an unambiguous relation between these two sectors. In this work we shall demonstrate a novel left-right symmetric scenario, motivated to solve the strong CP problem by parity symmetry, where the present baryon asymmetry is determined by three charged lepton masses and a seesaw-suppressed hermitian Dirac neutrino mass matrix up to an overall scale factor. To produce the observed baryon asymmetry, this scenario requires that …
