We consider a minimal condition that predicts the 1-3 lepton mixing angle $θ_{13} \simeq θ_{\rm C}/\sqrt{2}$ with $θ_{\rm C}$ the Cabibbo angle, and give the improved prediction of $θ_{13}$. In the case of normal mass ordering, the theoretical value of $θ_{13}$ is predicted as $θ_{13}=8.6^\circ$, which is in good agreement with the current global best fit. In the case of inverted mass ordering, the theoretical value is predicted as $θ_{13}=9.7^\circ$, which is far from the current global best fit. We also study the leptonic CP violation. We show that any values of the leptonic Dirac CP phase $δ_{\rm CP}$ can be obtained by fine tuning. Without fine tuning, $|\sinδ_{\rm CP}|$ should be very small, typically of ${\cal O}(λ^2)$ where $λ\equiv \sinθ_{\rm C}$. Furthermore, a model-independent measure of CP violation is proposed, which is applicable to any flavor models.
In a novel parametrization of neutrino mixing and in the approximation of $τ$-lepton dominance, we show that the one-loop renormalization-group equations (RGEs) of Dirac neutrinos are different from those of Majorana neutrinos even if two Majorana CP-violating phases vanish. As the latter can keep vanishing from the electroweak scale to the typical seesaw scale, it makes sense to distinguish between the RGE running effects of neutrino mixing parameters in Dirac and Majorana cases. The differences are found to be quite large in the minimal supersymmetric standard model with sizable $\tanβ$, pro…
The magic textures are successful candidates of the correct texture for the Majorana neutrinos. In this study, we show that some types of magic texture for Majorana neutrinos approximately immanent in the flavor mass matrix for Dirac neutrinos. In addition, it turned out that the normal mass ordering of the Dirac neutrino masses is slightly preferable to the inverted mass ordering in the context of the magic textures.
The tiny neutrino masses can be explained naturally by extending the standard model with right-handed Majorana neutrinos in low-scale seesaw mechanism, and the CP violation effect induced by Majorana phase is interesting and worth studying at colliders. In this paper, we investigate the prospects for measuring CP violation in top quark pair production and rare decay via Majorana neutrinos at the LHC. The CP asymmetry stems from the significant interference of contributions from two different Majorana neutrinos and can be appreciable when the two neutrino masses are nearly-degenerate. It is fou…
The phenomenology of flavor mixing of heavy Majorana neutrinos is studied. The physical degrees of freedom, which propagate like free particles until they decay in the presence of flavor mixing, are identified by diagonalizing the resummed propagator. It is shown that they should be interpreted as quasiparticles which lose Majorana nature.
The analysis of the total and geometric phases generated by the neutrino oscillation shows that these phases for Majorana neutrinos are depending on the representation of the mixing matrix and they are different from those of Dirac neutrinos.
We clarify that one cannot distinguish between Majorana and Dirac neutrinos in the limit of vanishing neutrino mass. In particular we show, that the forward-backward asymmetry in the reaction e^+ e^- -> ννis the same for ν_M and ν_D, in contrast to recent claims made in the literature.
We generalize the geometrical description of CP violation in the Standard Model in terms of a unitarity triangle. For three left-handed Majorana neutrinos CP violation in the lepton sector is determined by three unitarity triangles. With three additional right-handed neutrinos 15 quadrangles are required to characterize CP violation. We show the relation of the unitarity polygons with physical observables.
Cross sections involving massive Dirac or Majorana neutrinos usually differ only by terms which are suppressed by the smallness of the neutrino mass. The process $e^+e^-\toνν$, however, is an example in which the two differential cross sections are quite distinct even in the limit $m_ν\to 0$ as long as $m_ν\not=0$. I discuss the cause of this phenomenon and comment on strategies to identify processes with quite different Majorana and Dirac neutrino signals.
We explain why it is so hard to determine whether neutrinos are Majorana or Dirac particles as long as the only neutrinos we study are ultra-relativistic. We then show how non-relativistic neutrinos could help, and focus on the angular distributions in the decays of an as-yet-to-be-discovered heavy neutrino $N$. We find that these angular distributions could very well tell us whether neutrinos are Majorana or Dirac particles.
The helicity of a Dirac neutrino with mass $m$ evolves under the influence of a $B$-field because it has a magnetic dipole moment proportional to $m$. Moreover, it was recently shown that a polarized or anisotropic medium engenders the same effect for both Dirac and Majorana neutrinos. Because a $B$-field polarizes a background medium, it instigates helicity oscillations even for Majorana neutrinos unless the medium is symmetric between matter and antimatter. Motivated by these observations, we review the impact of a $B$-field and of an anisotropic or polarized medium on helicity oscillations …
We analyze the scenario of baryogenesis through leptogenesis induced by the out-of-equilibrium decays of heavy Majorana neutrinos and pay special attention to CP violation. Extending a recently proposed resummation formalism for two-fermion mixing to decay amplitudes, we calculate the resonant phenomenon of CP violation due to the mixing of two nearly degenerate heavy Majorana neutrinos. Solving numerically the relevant Boltzmann equations, we find that the isosinglet Majorana mass may range from 1 TeV up to the grand unification scale, depending on the mechanism of CP violation and/or the fla…
While gluinos and neutralinos are Majorana fermions in the MSSM, they can be Dirac fermion fields in extended supersymmetry models. The difference between the two cases manifests itself in production and decay processes at colliders. In this contribution, results are presented for how the Majorana or Dirac nature of gluinos and neutralinos can be extracted from di-lepton signals at the LHC.
The consequences of CP and CPT invariance for production and subsequent decay of Dirac and Majorana fermions in polarized fermion--antifermion annihilation are analytically studied. We derive general symmetry relations for the production spin density matrix and for the three--particle decay matrices and obtain constraints for the polarization and the spin--spin correlations of Dirac and Majorana fermions. We prove that only for Majorana fermions the energy and opening angle distribution factorizes exactly into contributions from production and decay if CP is conserved.
We study the conditions under which the Majorana phase of the two flavor neutrino mixing matrix appears in the oscillation probabilities and causes $CP$ violation. We find that the Majorana phase remains in the neutrino evolution equation if the neutrino decay eigenstates are not aligned with the mass eigenstates. We show that, in general, two kinds of $CP$ violation are possible: one due to the Majorana phase and the other due to the phase of the off-diagonal element of the neutrino decay matrix. We find that the $CP$ violating terms in the oscillation probabilities are also sensitive to neut…
The tree level diagonalization of a neutrino mass matrix with both Majorana and Dirac masses is discussed in a general context. Flavor changing neutral currents in such models are inevitable. Rephasing invariant quantities characterizing CP violation in FCNC Fermion-Higgs interactions are identified. At the one loop level, the mass eigenstates become an impure Majorana type. The possibility of a significant change in the mass spectrum for the left-handed neutrinos is explored, with an example of two species of neutrinos. Neutrino oscillations with impure Majorana neutrinos are also discussed.
Are neutrinos with definite masses Majorana or Dirac particles? This is one of the most fundamental problem of the modern neutrino physics. The solution of this problem could be crucial for understanding of the origin of small neutrino masses. We will review here basic arguments in favor of the Majorana nature of massive neutrinos. The phenomenological theory of $0νββ$-decay is briefly discussed and recent experimental data and sensitivity of future experiments are presented.
Dirac and Majorana neutrinos can be distinguished in relativistic neutrino oscillations if new right-handed interactions exist, due to their different propagation in matter. We review how these new interactions affect neutrino oscillation experiments and discuss the size of this eventually observable effect for different oscillation channels, baselines and neutrino energies.
After developing a general criterion for deciding which neutrino mass models belong to the category of inverse seesaw models, we apply it to obtain the Dirac analogue of the canonical Majorana inverse seesaw model. We then generalize the inverse seesaw model and obtain a class of inverse seesaw mechanisms both for Majorana and Dirac neutrinos. We further show that many of the models have double or multiple suppressions coming from tiny symmetry breaking "$μ$-terms". These models can be tested both in colliders and with the observation of lepton flavour violating processes.
It is well known that Majorana neutrinos have a pure axial neutral current interaction while Dirac neutrinos have the standard vector-axial interaction. In spite of this crucial difference, usually Dirac neutrino processes differ from Majorana processes by a term proportional to the neutrino mass, resulting in almost unmeasurable observations of this difference. In the present work we show that once the neutrino polarization evolution is considered, there are clear differences between Dirac and Majorana scattering on electrons. The change of polarization can be achieved in astrophysical enviro…
Leptonic CP violation is one of the most important topics in neutrino physics. CP violation in the neutrino sector is strongly related to the nature of neutrinos: whether they are Dirac or Majorana particles. In \cite{Popov:2021icg} we have shown that for Majorana neutrinos arance of nonzero Majorana CP-violating phases combined with strong magnetic field during supernova core-collaple can induce new resonances in neutrino oscillations, for example in $ν_e \to \barν_τ$ channel. In this contribution we further study new resonances in Majorana neutrino oscillations, in particular energy dependen…
We investigate the interaction of fermions having both Dirac and left-handed and right-handed Majorana mass terms with vacuum domain walls. By solving the equations of motion in thin-wall approximation, we calculate the reflection and transmission coefficients for the scattering of fermions off walls.
In the framework of the left-right symmetric model the CP-parity violation has been studied in heavy Majorana neutrino decays $N\rightarrow e^{\mp} μ^{\pm} n$. The numerical estimates of CP-asymmetry for different masses of neutrino and $W_{R}^{\pm}$-boson were obtained. The possibility to detect this phenomenon at high energy colliders is mentioned.
We analize the non-cyclic geometric phase for neutrinos. We find that the geometric phase and the total phase associated to the mixing phenomenon provide a tool to distinguish between Dirac and Majorana neutrinos. Our results hold for neutrinos propagating in vacuum and through the matter. Future experiments, based on interferometry, could reveal the nature of neutrinos.
The notion of U(1) lepton number (which may only be softly broken) is applied to models of dark matter which interacts with leptons. Previous scotogenic models of Majorana or Dirac neutrino mass are shown to be derivable in this framework without additional symmetries. Only complete renormalizable theories are considered. An explicit class of models with $Z_n$ ($n \geq 5$) lepton and dark symmetry for Dirac neutrinos is derived, as well as an example of $Z_3$ dark symmetry.
The thermodynamic equations of state for Majorana and Dirac fermions are quite different even in the limit of zero mass. The corresponding equations are derived from general principles, and then applied to neutrinos. The nature of the approach to equilibrium is explored, along with the subtleties of low or zero mass neutrinos interacting via purely left-handed currents. Possible applications to cosmology, supernovae, and supersymmetry are discussed.
In the Standard Model minimally extended to include massive neutrinos, we compute the leading CP-violating zero temperature contributions to the one-loop effective action induced by integration of the leptons. Such contributions start at operators of dimension six and they are P even for Dirac neutrinos and P even or odd for Majorana neutrinos. Dimension four operators are allowed in the mixed Dirac-Majorana case. It is verified by explicit calculation that CP can be violated in two generation settings for Majorana neutrinos. Using different neutrino scenarios we give upper bounds for the coup…
It is shown that for the reason of neutrinos being left-handed and their gauge-couplings being parity-violated, linearly polarized photons acquire their circular polarization by interacting with neutrinos. Calculating the ratio of linear and circular polarizations of laser photons interacting with either Dirac or Majorana neutrino beam, we obtain this ratio for the Dirac neutrino case, which is about twice less than the ratio for the Majorana neutrino case. Based on this ratio, we discuss the possibility of using advanced laser facilities and the T2K neutrino experiment to measure the circular…
If neutrino conversions within the Sun result in partial polarization of initial solar neutrino fluxes then a new opportunity to distinguish Majorana and Dirac neutrinos by measuring the differential $ν_ee$-scattering cross section in solar neutrino detectors arises. The experiment like HELLAZ would be preferable in testing of recoil electron spectra differences initiated by Majorana and Dirac neutrinos since low energy recoil electrons ($T\geq 100 keV$) can be detected and electron energy and direction can be determined with good precision.
We analyze the power of the Tevatron dataset to exclude or discover fourth generation neutrinos. In a general framework, one can have mixed left- and right-handed neutrinos, with Dirac and Majorana neutrinos as extreme cases. We demonstrate that a single Tevatron experiment can make powerful statements across the entire mixing space, extending LEP's mass limits of 60-80 GeV up to 150-175 GeV, depending on the mixing.
The possibility of observing CP violation in the decays of Higgs particles into top-quark, W- and Z-boson pairs induced by heavy Majorana neutrinos is discussed. In the context of minimal "see-saw" models with interfamily mixings, we find that Majorana neutrinos may give rise to sizable CP-odd effects at the one-loop electroweak order. We present numerical estimates of typical CP-odd observables that might be triggered at high-energy e+e- colliders.
We analyze the possibility of $CP$ violation induced by heavy Majorana neutrinos in the decays of the Higgs particle into top-quark, $W$- and $Z$-boson pairs. In the framework of various ``see-saw" models with interfamily mixings, we find that Majorana neutrinos may give rise to sizable $CP$-odd observables at the one-loop electroweak order. Numerical estimates of these $CP$-violating effects that may be detected in high-energy colliders are presented.
We consider the matter effects on neutrinos moving in background on the basis of the corresponding quantum wave equations. Both Dirac and Majorana neutrino cases are discussed. The effects for Dirac neutrino reflection and trapping as well as neutrino-antineutrino annihilation and $ν\overlineν$ pair creation in matter at the interface between two media with different densities are considered. The spin light of neutrino in matter is also discussed.
(abridged) The physical mechanisms that make a neutrino with standard-model (SM) weak interactions a "lepton-number conservation (LNC) violating" neutrino such as the Majorana neutrino are analysed in a basis of two Majorana states that have opposite charge-parity ("charge-parity basis"). A small Majorana mass that is larger than any Dirac mass makes the neutrino not a Majorana but a "pseudo-Majorana" particle that has no definite chirality and therefore has a different phenomenology than the physical neutrino. A combination of a large Majorana and Dirac mass of nearly equal value makes the ne…
We present a scenario of neutrino masses and mixing angles. Each generation includes a sterile right handed neutrino in addition to the usual left handed one. We assume a hierarchy in their Dirac masses similar to, but much larger than the hierarchies in the quarks and charged leptons. In addition, we include a Majorana mass term for the sterile neutrinos only. These assumptions prove sufficient to accomodate scales of mass differences and mixing angles consistent with all existing neutrino oscillation data.
We compare the prospects for observing theories with Majorana or Dirac gauginos at a future 100 TeV proton-proton collider. Calculating the expected discovery and exclusion regions, we find that for heavy gluino masses the squark discovery reach is significantly reduced in Dirac gluino models relative to the Majorana case. However, if the squark and gluino masses are close the reach is similar in both scenarios. We also consider the electroweak fine tuning of theories observable at such a collider, and the impact of existing constraints from flavour and CP violating observables. Models with Ma…
We present analytic expressions corresponding to a set of one loop Feynman diagrams, built within R-parity violating (RpV) minimal supersymmetric standard model (MSSM). Diagrams involve both bilinear and trilinear RpV couplings and represent Majorana neutrino masses and magnetic moments.
The possibility of discovering heavy Majorana neutrinos and lepton number violation via the like sign dilepton signal at hadron super- colliders is investigated. The cross-sections for the production of these neutrinos singly as well as in pairs are computed both in three and four generation scenarios within the framework of the gauge group $SU(2)_L \otimes U(1)_Y$ and the dominant processes are identified. The suppression of the Standard model background by suitable kinematical cuts is also discussed.
We present a novel scheme where Dirac neutrinos are realized even if lepton number violating Majorana mass terms are present. The setup is the Randall-Sundrum framework with bulk right handed neutrinos. Bulk mass terms of both Majorana and Dirac type are considered. It is shown that massless zero mode solutions exist when the bulk Dirac mass term is set to zero. In this limit, it is found that the effective 4D small neutrino mass is primarily of Dirac nature with the Majorana type contributions being negligible. Interestingly, this scenario is very similar to the one known with flat extra dime…
We study the evolution of massive mixed Dirac and Majorana neutrinos in matter under the influence of a transversal magnetic field. The analysis is based on relativistic quantum mechanics. We solve exactly the evolution equation for relativistic neutrinos, find the neutrino wave functions, and calculate the transition probability for spin-flavor oscillations. We analyze the dependence of the transition probability on the external fields and compare the cases of Dirac and Majorana neutrinos. The evolution of Majorana particles in vacuum is also studied and correction terms to the standard oscil…
The effective Majorana mass which determines the rate of the neutrinoless double beta decay, |<m>|, is considered in the case of three-neutrino mixing and massive Majorana neutrinos. Assuming a rather precise determination of the parameters characterizing the neutrino oscillation solutions of the solar and atmospheric neutrino problems has been made, we discuss the information a measurement of |<m>| > (0.005 - 0.010) eV can provide on the value of the lightest neutrino mass and on the CP-violation in the lepton sector. The implications of combining a measurement of |<m>| with future measuremen…
During a large period of time, the anomalous baryon number violating interactions are in equilibrium, when the $(B+L)$ asymmetry is washed out. If there is any lepton number violation during this period, that will also erase the $(B-L)$ asymmetry. As a result, survival of the baryon asymmetry of the universe pose strong constraints on lepton number violating interactions. We review here the constraints on the left-handed Majorana neutrino masses arising from this survival requirement of the baryon asymmetry of the universe. We then briefly review models of leptogenesis, where lepton number vio…
In spite of the general belief that neutrinos are Majorana particles, their character should be revealed experimentally. We begin by discussing why it is so difficult in terrestrial experiments. If neutrinos are Majorana particles, the first signal should come from neutrinoless double $β$ decay. Still the search for such a decay of various nuclei is negative. We outline how the present knowledge of neutrino masses and mixing matrix elements combined with the bound from $(ββ)_{0ν}$ decay could help to determine their nature.
The possibility of detecting single heavy Dirac and Majorana neutrinos at LEP II is investigated for heavy neutrino masses in the range $M_N=(\sqrt s/2, \sqrt s)$. We study the process $e^+e^- \longrightarrow ν_{\ell} \ell q_i \bar q_j $ as a clear signature for heavy neutrinos. Numerical estimates for cross sections and distributions for the signal and the background are calculated and a Monte Carlo reconstruction of final state particles after hadronization is presented.
We suppose that the observed neutrino masses can be parametrised by a lepton number violating dimension-five operator, and calculate the mixing of double insertions of this operator into lepton flavour changing dimension-six operators of the standard model effective theory. This allows to predict the log-enhanced, but $m_ν^2$-suppressed lepton flavour violation that is generic to high-scale Majorana neutrino mass models. We also consider the Two Higgs Doublet Model, where the second Higgs allows the construction of three additional dimension-five operators, and evaluate the corresponding anoma…
Assuming 3-neutrino mixing and massive Majorana neutrinos, we analyze the possibility of establishing the existence of CP-violation associated with Majorana neutrinos in the lepton sector i) by measuring of the effective Majorana mass |<m>| in neutrinoless double beta-decay with a sufficient precision and ii) by measuring of, or obtaining a stringent upper limit on, the lightest neutrino mass m1. Information on m1 can be obtained in the tritium beta decay experiment KATRIN and from astrophysical and cosmological observations. Proving that the indicated CP-violation takes place requires, in par…
We propose a realization of the so-called bimodal/schizophrenic model proposed recently. We assume S4, the permutation group of four objects as flavor symmetry giving tri-bimaximal lepton mixing at leading order. In these models the second massive neutrino state is assumed quasi-Dirac and the remaining neutrinos are Majorana states. In the case of inverse mass hierarchy, the lower bound on the neutrinoless double beta decay parameter m_ee is about two times that of the usual lower bound, within the range of sensitivity of the next generation of experiments.
The history of research associated with the fundamental problem of the nature of massive neutrinos, which can be Dirac particles or Majorana fermions, and the related processes of neutrinoless double beta decay, $(A,Z)\rightarrow (A,Z+2) + e^- + e^-$, and two neutrino double beta decay, $(A,Z)\rightarrow (A,Z+2) + e^- + e^- + \bar{ν_e} + \bar{ν_e}$, is reviewed.
The nonzero neutrino mass can be a signal for new physics beyond the standard model. To explain the tiny neutrino mass, we can extend the standard model with right-handed Majorana neutrinos in a low-scale seesaw mechanism, while the CP violation effect can be induced due to the CP phase in the interference of heavy Majorana neutrinos. The existence of heavy Majorana neutrinos may lead to lepton number violation processes, which can be used as a probe to search for the signal of heavy Majorana neutrinos. In this paper, we focus on the CP violation effect related to two generations of heavy Majo…
It was recently claimed that the observed physical neutrinos cannot be of Majorana type because such particles lack vector interactions. Contrary to this claim we show that if the Majorana neutrino is massless it is indistinguishable from the Dirac neutrino so that observed physical neutrinos may equally well be of Majorana or Dirac type.
Majorana neutrinos naturally lead to a Lepton Number Violation (LNV). A superposition of Majorana states can mimic Dirac-type neutrinos, leading to its conservation (LNC). We demonstrate on the example of specific observables related to high and low energy processes how a strength of LNV correlates with neutrino parameters such as CP-phases, flavor mixings, mass ratios. We stress the coaction between low and high energy studies for putting phenomenological models to a quantitative test. Secondly, we conclude that in order to fully study the role of heavy neutrinos in search for New Physics (NP…
We discuss the energy scale profile of the bi-maximal mixing which is given at the GUT energy scale in the minimal SUSY model, associated with an assumption that Y_nu^dagger Y_nu is diagonal, where Y_nu is the neutrino-Yukawa coupling matrix. In this model, the Dirac mass matrix which appears in the seesaw neutrino mass matrix is determined by three neutrino masses, two relative Majorana phases and three heavy Majorana masses. All CP phases are related by two Majorana phases. We show that the requirement that the solar mixing angle moves from the maximal mixing at GUT to the observed one as th…
The radiative type-I seesaw has been already implemented to explain the lightness of Majorana neutrinos with both Majorana and Dirac heavy fermions, and the lightness of Dirac neutrinos with Dirac heavy fermions. In this work we present a minimal implementation of the radiative type-I seesaw with light Dirac neutrinos and heavy Majorana fermions. An inert doublet and a complex singlet scalar complete the dark sector which is protected by an Abelian fermiophobic gauge symmetry that also forbids tree level mass contributions for the full set of light neutrinos. A fermion vector-like extension of…
Given the most general Lorentz invariant four-fermion effective interaction possible for two neutrinos and two charged fermions, whether quarks or leptons, all possible 2-to-2 processes involving two neutrinos, whether Dirac or Majorana ones, and two charged fermions are considered. Explicit and convenient expressions are given for the associated differential cross-sections. Such a parametrization should help assess the sensitivity to physics beyond the Standard Model of neutrino beam experiments which are in the design stage at neutrino factories.
The 2$ν$-mediated force has a range of microns, well beyond the atomic scale. The effective potential is built from the t-channel absorptive part of the scattering amplitude and depends on neutrino properties on-shell. We demonstrate that neutral aggregate matter has a weak charge and calculate the matrix of six coherent charges for its interaction with definite-mass neutrinos. Near the range of the potential the neutrino pair is non-relativistic, leading to observable absolute mass and Dirac/Majorana distinction via different r-dependence and violation of the weak equivalence principle.
Enlightened by the idea of the 3 times 3 CKM angle matrix proposed recently by Harrison et al., we introduce the Dirac angle matrix Phi and the Majorana angle matrix Psi in the lepton sector for Dirac and Majorana neutrinos respectively. We show that in presence of the CP violation, the angle matrix Phi or Psi is entirely equivalent to the complex MNS matrix V itself, but has the advantage of being real, phase rephasing invariant, directly associated to the leptonic unitarity triangles (UTs) and do not depend on any particular parametrization of V. In this paper, we further analyzed how the an…
