The electric dipole moment of the electron is studied in detail in an extended mirror fermion model with the following unique features of (a) right-handed neutrinos are non-sterile and have masses at the electroweak scale, and (b) a horizontal symmetry of the tetrahedral group is used in the lepton and scalar sectors. We study the constraint on the parameter space of the model imposed by the latest ACME experimental limit on electron electric dipole moment. Other low energy experimental observables such as the anomalous magnetic dipole moment of the muon, charged lepton flavor violating processes like muon decays into electron plus photon and muon-to-electron conversion in titanium, gold and lead are also considered in our analysis for comparison. In addition to the well-known CP violating Dirac and Majorana phases in the neutrino mixing matrix, the dependence of additional phases of the new Yukawa couplings in the model is studied in detail for all these low energy observables.
We study a scenario where sterile neutrino (either warm or cold) dark matter (DM) is produced through (nonresonant) oscillations among right-handed neutrinos (RHNs) and can constitute the whole DM in the Universe, in contrast to the conventional sterile neutrino production through its mixing with the left-handed neutrinos. The lightest RHN can be sterile neutrino DM whose mixing with left-handed neutrinos is sufficiently small while heavier RHNs can have non-negligible mixings with left-handed neutrinos to explain the neutrino masses by the seesaw mechanism. We also demonstrate that, in our sc…
We propose new searches that exploit the unique signatures of decaying sterile neutrinos with masses below $M_W$ at the LHC, where they can be produced in rare decays of Standard Model gauge bosons. We show that for few-GeV-scale sterile neutrinos, the LHC experiments can probe mixing angles at the level of $10^{-4}-10^{-3}$ through powerful searches that look for prompt leptons in association with displaced lepton jets. For higher-mass sterile neutrinos, ${\it i.e.}$, $M_N \gtrsim 15$ GeV, Run II can explore similarly small mixing angles in prompt multilepton final states. This represents an …
Kurie-plot experiments allow for neutrino-mass measurements based on kinematics in an almost model-independent manner. A future tritium-based KATRIN-like experiment can be sensitive to light sterile neutrinos with masses below 18 keV, which are among the prime candidates for warm dark matter. Here we consider such keV neutrinos in left--right symmetric extensions, i.e. coupled to right-handed currents, which allow for an enhanced contribution to beta decay even for small active--sterile mixing, without violating astrophysical X-ray constraints. The modified spectral shape is in principle disti…
We show that existing laboratory experiments have the potential to unveil the origin of matter by probing leptogenesis in the type-I seesaw model with three right-handed neutrinos and Majorana masses in the GeV range. The baryon asymmetry is generated by CP-violating flavour oscillations during the production of the right-handed neutrinos. In contrast to the case with only two right-handed neutrinos, no degeneracy in the Majorana masses is required. The right-handed neutrinos can be found in meson decays at BELLE II and LHCb.
The extension of the minimal standard model by three right-handed sterile neutrinos with masses smaller than the electroweak scale (nuMSM) is discussed in a Q_6 flavor symmetry framework. The lightness of the keV sterile neutrino and the near mass degeneracy of two heavier sterile neutrinos are naturally explained by exploiting group properties of Q_6. A normal hierarchical mass spectrum and an approximately mu-tau symmetric mass matrix are predicted for three active neutrinos. Nonzero theta_{13} can be obtained together with a deviation of theta_{23} from the maximality, where both mixing ang…
The KATRIN experiment aims to determine the absolute neutrino mass by measuring the endpoint region of the tritium $β$ spectrum. As a large-scale experiment with a sharp energy resolution, high source luminosity and low background it may also be capable of testing certain theories of neutrino interactions beyond the standard model (SM). An example of a non-SM interaction are right-handed currents mediated by right-handed W bosons in the left-right symmetric model (LRSM). In this extension of the SM, an additional SU(2)$_\mathrm R$ symmetry in the high-energy limit is introduced, which naturall…
Usually considered a background for experimental searches for the hypothetical neutrinoless double beta decay process, two-neutrino double beta decay nevertheless provides a complementary probe of physics beyond the Standard Model. In this paper we investigate how the presence of a sterile neutrino, coupled to the Standard Model either via a left-handed or right-handed current, affects the energy distribution and angular correlation of the outgoing electrons in two-neutrino double beta decay. We pay particular attention on the behaviour of the energy distribution at the kinematic endpoint and …
Phasing out of Darkness: From Sterile Neutrino Dark Matter to Neutrino Masses via Time-Dependent Mixing
Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；Centro de Astrofísica e Gravitação - CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学高等技术学院物理系天体物理学与引力中心）；Departamento de Física Teórica and Instituto de Física de Partículas y del Cosmos (IPARCOS-UCM), Universidad Complutense de Madrid（马德里康普顿斯大学理论物理系及粒子与宇宙物理研究所）
We investigate neutrinoless double beta ($0νββ$) decay rates in minimal left-right symmetric models in presence of relatively light right-handed neutrinos. By use of an effective field theory approach, we systematically include all contributions in the model as well as the dependence of the decay amplitude on the masses of right-handed neutrinos. In type-I and type-II seesaw scenarios, we analyze the impact of right-handed neutrinos heavier than about 10 MeV, showing that this effect can lead to a detection of $0νββ$ decay in the next-generation experiments even for the normal hierarchy and a …
The existence of right-handed neutrinos follows from theoretical consistence of the recently suggested electroweak symmetry breaking model, based on dynamical flavor gauge symmetry breaking. Only finite number of versions of the model exists. They differ by the number and the flavor structure of the right-handed neutrinos. We choose for inspection one of them, the non-minimal version with right-handed neutrinos in sextet flavor representation, and at some points we compare it with the minimal version. We show that a Majorana pairing of the sextet right-handed neutrinos is responsible for the f…
We show that a double seesaw framework for neutrino masses with $μ-τ$ exchange symmetry can lead to one of the righthanded seesaw partners of the light neutrinos being massless. This can play the role of a light sterile neutrino, giving a $3+1$ model that explains the LSND results. We get a very economical scheme, which makes it possible to predict the full $4\times 4$ neutrino mass matrix if CP is conserved. Once CP violation is included, effect of the LSND mass range sterile neutrino is to eliminate the lower bound on neutrinoless double beta decay rate which exists for the three neutrino ca…
Can, and under which conditions, the 125-\gev SM-like scalar with the signal strengths for its decays into $W^{+}W^{-}$, $ZZ$, $γγ$, $b \bar{b}$ and $τ\barτ$ being consistent with experiments be accommodated in models that go beyond the Standard Model? Is it truly what it appears to be, namely the SM Higgs boson, or could it be quite different? A minimal extension of the original electroweak-scale right-handed neutrino model, in which right-handed neutrinos naturally obtain electroweak-scale masses, shows a scalar spectrum which includes either the 125-\gev SM-like scalar or a scalar which is …
Neutrinos can have naturally small Dirac masses if the Standard Model singlet right-handed neutrinos are light composite fermions. Theories which produce light composite fermions typically generate many of them, three of which can marry the left-handed neutrinos with small Dirac masses. The rest can serve as sterile states which can mix with the Standard Model neutrinos. We present explicit models illustrating this idea.
We derive the neutrino oscillation probabilities including sterile neutrinos by using the Dirac equation. If neutrinos have both the Dirac and the Majorana mass terms, left-handed neutrino $ν_L$ and right-handed anti-neutrino $ν_R^c$ enter the same multiplet and can transfer each other. Sterile neutrinos have been introduced by hand as the fourth generation neutrino in many papers, however, we can understand sterile neutrinos naturally in the framework of three generations. We also point out that the oscillations into sterile neutrinos strongly suggest the existence of both the Dirac and the M…
In this paper, we will apply the Goldstone equivalence gauge to calculate the $1 \leftrightarrow 2$ processes of a sterile neutrino in the thermal plasma below the standard model (SM) critical temperature $T_c \approx 160 \text{ GeV}$. The sterile neutrino's mass is around the electroweak scale $50 \text{ GeV} \leq m_N \leq 200 \text{ GeV}$, and the acquired thermal averaged effective width $\barΓ_{\text{tot}}$ is continuous around the cross-over. We will also apply our results to perform a preliminary calculation of the leptogenesis.
A massive right-handed sterile neutrino in three-body ${\bar B}\to D^*\ell^-{\bar N}_R$ decays - a Monte Carlo simulation study
Lawrence Technological University（劳伦斯理工大学）；University of Hawaii（夏威夷大学）；University of Mississippi（密西西比大学）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）；Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3（诺曼底大学，ENSICAEN，UNICAEN，法国国家科学研究中心/法国国家核子和粒子物理研究所）
The muon-to-electron conversion in nuclei like aluminum, titanium and gold is studied in the context of a class of mirror fermion model with non-sterile right-handed neutrinos having mass at the electroweak scale. At the limit of zero momentum transfer and large mirror lepton masses, we derive a simple formula to relate the conversion rate with the on-shell radiative decay rate of muon into electron. Current experimental limits (SINDRUM II) and projected sensitivities (Mu2e, COMET and PRISM) for the muon-to-electron conversion rates in various nuclei and latest limit from MEG for the radiative…
The standard model can be interpreted as the leading order of a Low-Energy Effective Theory (LEET) invariant under a higher non linearly realized symmetry $S_{nat}\supset SU(2)_W \times U(1)_Y$ equipped with a systematic power counting. Within the minimal version of this ``not quite decoupling'' LEET, the dominant non-standard effect appears at next-to-leading order (NLO) and is a modification of the couplings of fermions to W and Z. In particular, the coupling of right-handed quarks to Z is modified and a direct coupling of right-handed quarks to W emerges. Charged right-handed lepton current…
In this work we study the current bounds from the CEνNS process and meson invisible decays on generic neutrino interactions with sterile neutrinos in effective field theories. The interactions between quarks and left-handed SM neutrinos and/or right-handed neutrinos are first described by the low-energy effective field theory (LNEFT) between the electroweak scale and the chiral symmetry breaking scale. We complete the independent operator basis for the LNEFT up to dimension-6 by including both the lepton-number-conserving (LNC) and lepton-number-violating (LNV) operators involving right-handed…
Candidates for unfication of the electroweak and strong interactions include the grand unified groups SU(5), SO(10), and the exceptional group E6. The 27-dimensional fundamental representation of E6 contains exotic fermions, including weak isosinglet quarks of charge -1/3, vector-like weak isodoublet leptons, and neutral leptons which are singlets under both left-handed and right-handed SU(2). These last are candidates for light "sterile" neutrinos, hinted at by some recent short-baseline neutrino experiments. In order to accommodate three families of quarks and charged leptons, an E6 model mu…
Some of basic problems in neutrino physics such as new energy scales, the enormous gap between neutrino masses and the lightest charged fermion mass, possible existance of sterile neutrinos in eV mass range are studied in the local gauge group $SU_{L}(4)\times U(1)$ for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that neutrino mass spectrum can be decoupled from that of the other fermions. Further normal seesaw mechanism for neutrinos, with right handed neutrino Majorana masses to be of order $M\gg M_{\text{weak}}$ as well a new eV-scale c…
We provide a comprehensive study of observable spectra from dark matter pair-annihilation or decay into sterile (right-handed) neutrinos. This occurs, for instance, in neutrino portal dark matter models, where a sterile neutrino acts as the portal between dark matter and the Standard Model sector. The subsequent decays of right-handed neutrinos produce detectable Standard Model particles, notably photons, positrons, and neutrinos. We study the phenomenology of models where the right-handed neutrino masses are below the GeV scale, as well as models where they are at, or significantly heavier th…
A model of electroweak-scale right-handed neutrino (\ewnur) model was constructed five years ago in which the right-handed neutrinos are members of mirror fermion weak doublets and where the Majorana masses of the right-handed neutrinos are found to be {\em naturally} of the order of the electroweak scale. These features facilitate their searches at the LHC through signals such as like-sign dilepton events. This model contains, in addition to the mirror quarks and leptons, extra scalars transforming as weak triplets. In this paper, we study the constraints imposed on these additional particles…
We implement a schizophrenic scenario for the active neutrinos in a model in which there are also exotic right-handed neutrinos making a model with a local U(1)_(B-L) anomaly free. Two of right-handed neutrinos carry B-L=-4 while the third one carries B-L=5.
The inclusion of heavy neutral leptons (right-handed neutrinos) to the Standard Model (SM) particle content is one of the best motivated ways to account for the observed neutrino masses and flavor mixing. The modification of the charged and neutral currents from active-sterile mixing of the neutral leptons can provide novel signatures which can be tested at the future collider experiments. In this article, we explore the discovery prospect of a very heavy right handed neutrino to probe such extensions at the future collider experiments like Large Hadron electron Collider (LHeC) and liner colli…
We study discovery prospects for long-lived sterile neutrinos at the LHC with multitrack displaced vertices, with masses below the electroweak scale. We reinterpret current displaced vertex searches making use of publicly available, parametrized selection efficiencies for modeling the detector response to displaced vertices. We focus on production of right-handed $W_{R}$ bosons and neutrinos $N$ in a left-right symmetric model, and find poor sensitivity. After proposing a different trigger strategy (considering the prompt lepton accompanying the neutrino displaced vertex) and optimized cuts in…
Light sterile neutrinos of mass about an eV with mixing $\tilde U_{ls}$ of a few percent to active neutrinos may solve some anomalies shown in experimental data related to neutrino oscillation. How to have light sterile neutrinos is one of the theoretical problems which have attracted a lot of attentions. In this article we show that such an eV scale light sterile neutrino candidate can be obtained in a seesaw model in which the right-handed neutrinos satisfy a softly-broken Friedberg-Lee (FL) symmetry. In this model a right-handed neutrino is guaranteed by the FL symmetry to be light comparin…
We present the Higgs mechanism in the context of the EW-scale $ν_R$ model in which electroweak symmetry is dynamically broken by condensates of mirror quark and right-handed neutrino through the exchange of one fundamental Higgs doublet and one fundamental Higgs triplet, respectively. The formation of these condensates is dynamically investigated by using the Schwinger-Dyson approach. The occurrence of these condensates will give rise to the rich Higgs spectrum. In addition, the VEVs of Higgs fields is also discussed in this dynamical phenomenon.
The lepton number violating interactions generated by the light Majorana neutrinos can erase the primordial baryon asymmetry of the universe during the electroweak phase transition. The Majorana masses of the left-handed neutrinos are constrained to avoid this problem. These constraints do not depend on the $(B-L)$ symmetry breaking mechanism.
The lepton flavor violating process μ \rightarrow eγ has been previously studied in a model of electroweak-scale right-handed neutrinos. We have calculated the decay amplitude in unitarity gauge [1] and Rξ gauge [2]. In this paper, we calculate the anomalous magnetic moment of μ in Rξ gauge.
It is known that a keV scale sterile neutrino is a good warm dark matter candidate. We study how this possibility could be realized in the context of gauge extensions of the standard model. The naïve expectation leads to large thermal overproduction of sterile neutrinos in this setup. However, we find that it is possible to use out-of-equilibrium decay of the other right-handed neutrinos of the model to dilute the present density of the keV sterile neutrinos and achieve the observed dark matter density. We present the universal requirements that should be satisfied by the gauge extensions of t…
Extending the Standard Model (SM) with sterile ('right-handed') neutrinos is one of the best motivated ways to account for the observed neutrino masses. We discuss the expected sensitivity of future lepton collider experiments for probing such extensions. An interesting testable scenario is given by 'symmetry protected seesaw models', which theoretically allow for sterile neutrino masses around the electroweak scale with up to order one mixings with the light (SM) neutrinos. In addition to indirect tests, e.g. via electroweak precision observables, sterile neutrinos with masses around the elec…
The possibility of constructing a model in which right-handed neutrinos have electroweak-scale masses as well as being {\em non-sterile} was espoused in Ref. 1. In this talk, I will review the ideas and results of Ref. 1 and discuss its implications for colliders such as the Tevatron, LHC and ILC.
The recent recomputation of the neutrino fluxes from nuclear reactors relaxes the tension between the LSND and MiniBooNE anomalies and disappearance data when interpreted in terms of sterile neutrino oscillations. The simplest extension of the Standard Model with such fermion singlets is the addition of right-handed sterile neutrinos with small Majorana masses. Even when introducing three right-handed neutrinos, this scenario has less free parameters than the 3+2 scenarios studied in the literature. This begs the question whether the best fit regions obtained can be reproduced by this simplest…
Electroweak scale active right-handed neutrinos such as those proposed in a recent model necessitate the enlargement of the SM Higgs sector to include Higgs triplets with doubly charged scalars. The search for and constraints on such Higgs sector has implications not only on the nature of the electroweak symmetry breaking but also on the possibility of testing the seesaw mechanism at colliders such as the LHC and the ILC.
We consider a Mass Varying Neutrinos (MaVaNs) model in supersymmetric theory. The model includes effects of supersymmetry breaking transmitted by the gravitational interaction from the hidden sector, in which supersymmetry was broken, to the dark energy sector. Then evolutions of the neutrino mass and the equation of state parameter of the dark energy are presented in the model. It is remarked that only the mass of a sterile neutrino is variable in the case of the vanishing mixing between the left-handed and a sterile neutrino on cosmological time scale. The finite mixing makes the mass of the…
The super-weak model is a U(1) extension of the Standard Model. In addition to a mediator $Z'$, a singlet scalar field $χ$ is added to deal with the meta-stability of the SM vacuum, and right-handed neutrinos are introduced to account for the non-vanishing neutrino masses. We demonstrate that the lightest right-handed neutrino is a possible dark matter candidate with masses of $\mathcal{O}(10)~\mathrm{MeV}$ via the resonant freeze-out scenario. The dark matter production is explored and the available parameter space is discussed from the point of view of various experiments and beyond SM aspec…
It has been pointed out in ref.[1] that in the nuMSM (Standard Model extended by three right-handed neutrinos with masses smaller than the electroweak scale), there is a corner in the parameter space where CP-violating resonant oscillations among the two heaviest right-handed neutrinos continue to operate below the freeze-out temperature of sphaleron transitions, leading to a lepton asymmetry which is considerably larger than the baryon asymmetry. Consequently, the lightest right-handed (``sterile'') neutrinos, which may serve as dark matter, are generated through an efficient resonant mechani…
The Standard Model extended with right-handed neutrinos whose masses are below the electroweak scale provides a simultaneous solution for the origin of neutrino masses and of the baryon asymmetry of the Universe, that can be tested in current experiments. If three right-handed neutrinos participate to the processes, their parameter space of solutions extends to very large mixing angles, saturating the current experimental constraints. Solutions with right-handed neutrino masses at the GeV scale can be probed in the decay of $B$ mesons at the LHC. For this channel the collision of isotopes of i…
Model-building issues raised by the prospect of light sterile neutrinos are discussed in a pedagogical way. I first review the na\"ıve proposal that sterile neutrinos be identified with ``right handed neutrinos''. A critical discussion of the simple expedient of adding three gauge singlet fermions to the usual minimal standard model matter content is followed by an examination of right handed neutrinos in extended theories. I introduce the terminology of ``fully sterile'' and ``weakly sterile'' to classify varieties usually conflated under the sterile neutrino banner. After introducing the con…
We discuss a model where a mixed warm and hot keV neutrino dark matter rises naturally. We arrange active and sterile neutrinos in the same $SU(3)_L$ multiplet, with the lightest sterile neutrino being dark matter. The other two heavy sterile neutrinos, through their out-of-equilibrium decay, contribute both to the dilution of dark matter density and its population, after freeze-out. We show that this model features all ingredients to overcome the overproduction of keV neutrino dark matter, and explore the phenomenological implications for Big Bang Nucleosynthesis and the number of relativisti…
The insular nature of the Standard Model may be explained if the Higgs mass parameter is only sensitive to quantum corrections from physical states. Starting from a scale-free electroweak sector at tree-level, we postulate that quantum effects of heavy right-handed neutrinos induce a mass term for a scalar weak doublet that contains the dark matter particle. In turn, below the scale of heavy neutrinos, the dark matter sector sets the scale of the Higgs potential. We show that this framework can lead to a Higgs mass that respects physical naturalness, while also providing a viable scalar dark m…
The standard model Higgs quartic coupling vanishes at $(10^{9}-10^{13})$ GeV. We study $SU(2)_L \times SU(2)_R \times U(1)_{B-L}$ theories that incorporate the Higgs Parity mechanism, where this becomes the scale of Left-Right symmetry breaking, $v_R$. Furthermore, these theories solve the strong CP problem and predict three right-handed neutrinos. We introduce cosmologies where $SU(2)_R \times U(1)_{B-L}$ gauge interactions produce right-handed neutrinos via the freeze-out or freeze-in mechanisms. In both cases, we find the parameter space where the lightest right-handed neutrino is dark matt…
Sterile neutrinos, if they exist, are potential harbingers for physics beyond the Standard Model. They have the capacity to shed light on our flavor sector, grand unification frameworks, dark matter sector and origins of baryon anti-baryon asymmetry. There have been a few seminal studies that have broached the subject of sterile neutrinos with low, electroweak-scale masses (i.e. $Λ_{\text{\tiny{QCD}}} \ll m_{N_R} \ll m_{W^\pm}$) and investigated their reach at hadron colliders using lepton jets. These preliminary studies nevertheless assume background-free scenarios after certain selection cri…
We consider the minimal extended seesaw model which can accommodate an eV scale sterile neutrino. The scenario also includes three heavy right handed neutrinos in addition to the light sterile neutrino. In this model, the active-sterile mixing act as non-unitary parameters. If the values of these mixing angles are of $\mathcal{O}(0.1)$, the model introduces deviation of the PMNS matrix from unitarity to this order. We find that the oscillation data from various experiments imposes an upper bound on the lightest heavy neutrino mass scale as $\sim 10^{11}$ GeV in the context of this model. We st…
A recently proposed asymmetric mirror dark matter model where the mirror sector is connected with the visible one by a right handed neutrino portal, is shown to lead naturally to a 3+1 active-sterile neutrino spectrum, if the portal consists only of two right handed neutrinos. At the tree level the model has four massless neutrino states, three active and one sterile. The active neutrinos pick up tiny masses via the minimal radiative inverse seesaw mechanism at the one loop level. The loop effects also generate the large solar and atmospheric mixings, as well as the observed reactor mixing for…
Constraints on the heavy sterile neutrino mixing angles are studied in the framework of a minimal supersymmetric ${\rm SO}(10)$ model with {\it double see-saw mechanism}. A new singlet matter in addition to the right-handed neutrinos is introduced to realize the double see-saw mechanism. The minimal ${\rm SO}(10)$ model gives an unambiguous Dirac neutrino mass matrix, which enables us to predict the masses and the mixing angles in the enlarged $9 \times 9$ neutrino mass matrix. Mixing angles between the light Majorana neutrinos and the heavy sterile neutrinos are shown to be within the LEP exp…
We use the LHC Higgs data to derive updated constraints on electroweak-scale sterile neutrinos that naturally occur in many low-scale seesaw extensions of the Standard Model to explain the neutrino masses. We also analyze the signal sensitivity for a new final state involving a single charged lepton and two jets with missing energy, which arises from the decay of sterile neutrinos produced through the Higgs and $W,Z$ boson mediated processes at the LHC. Future prospects of these sterile neutrino signals in precision Higgs measurements, as well as at a future 100 TeV collider, are also discusse…
We explore scenarios where the $R(D^{(*)})$ anomalies arise from semitauonic decays to a right-handed sterile neutrino. We perform an EFT study of all five simplified models capable of generating at tree-level the lowest dimension electroweak operators that give rise to this decay. We analyze their compatibility with current $R(D^{(*)})$ data and other relevant hadronic branching ratios, and show that one simplified model is excluded by this analysis. The remainder are compatible with collider constraints on the mediator semileptonic branching ratios, provided the mediator mass is of order TeV…
We analyze leptogenesis in gauge extensions of the Standard Model with keV sterile neutrino dark matter. We find that both the observed dark matter abundance and the correct baryon asymmetry of the Universe can simultaneously emerge in these models. Both the dark matter abundance and the leptogenesis are controlled by the out of equilibrium decays of the same heavy right handed neutrino.
The usual see-saw mechanism for the generation of light neutrino masses is based on the assumption that all of the flavours of right-handed (more properly, sterile) neutrinos are heavy. If the sterile Majorana mass matrix is singular, one or more of the sterile neutrinos will have zero mass before mixing with the active (left-handed) neutrinos and be light after that mixing is introduced. In particular, a rank 1 sterile mass matrix leads naturally to two pseudo-Dirac pairs, one very light active Majorana neutrino and one heavy sterile Majorana neutrino. For any pattern of Dirac masses, there e…
