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.
It is firmly believed that a signal of neutrinoless double beta decay can unquestionably confirm the Majorana nature of neutrinos. However we notice that a Majorana neutrino mass induced after some neutrinoless double beta decay processes can be accidentally cancelled by another Majorana neutrino mass induced before any neutrinoless double beta decay processes. This realistic cancellation can simultaneously allow an observable neutrinoless double beta decay and a vanishing Majorana neutrino mass. In consequence a future discovery of neutrinoless double beta decay cannot fully rule out the poss…
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…
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.
Usually it is supposed that Majorana neutrino produced in the superposition state $χ_L = ν_L + (ν_L)^c$ and then follows the neutrinoless double beta decay. But since weak interactions are chiral invariant then the neutrino at production has definite helicity (i.e., $ν_L$ and $(ν_L)^c$ neutrinos are separately produced and then neutrino is not in the superposition state). This helicity cannot change after production without any external interactions. Thus we see that for unsuitable helicity the neutrinoless double $β$ decay is not possible even if neutrino is a Majorana particle. Also transiti…
Existing data on neutrino-electron scattering do not imply that neutrinos are not Majorana particles. The question of whether neutrinos are of Majorana or of Dirac character remains completely open.
The most plausible see-saw explanation of the smallness of the neutrino masses is based on the assumption that total lepton number is violated at a large scale and neutrinos with definite masses are Majorana particles. In this review we consider in details difference between Dirac and Majorana neutrino mixing and possibilities of revealing Majorana nature of neutrinos with definite masses.
It is shown that we cannot put Majorana neutrinos in the standard Dirac theory without violation of the gauge invariance. Experiments on $ν_l \to l (l = e, μ, τ)$ transitions do not confirm this supposition. It means that on neutrino oscillation experiments, the Majorana neutrino oscillations cannot be observed.
The heavy singlet Majorana neutrinos are introduced to generate the neutrino mass in the so-called phenomenological type-I seesaw mechanism. The phenomena induced by the heavy Majorana neutrinos are important to search for new physics. In this paper, we explore the heavy Majorana neutrino production and decay at future $e^{-}p$ colliders. The corresponding cross sections via $W$ and photon fusion are predicted for different collider energies. Combined with the results of the heavy Majorana neutrino production via single $W$ exchange, this work can provide helpful information to search for heav…
We assume that neutrinoless double beta decay is caused by the exchange of three light Majorana neutrinos. Under this assumption, we obtain, by the method of perturbation, the equation representing the isocontour of effective Majorana mass which is the function of two CP-violating Majorana phases. The equation representing the isocontour (constraint equation between two Majorana phases) is expressed analytically by six parameters: two lepton mixing angles, two kinds of neutrino mass squared differences, lightest neutrino mass scale, and the effective Majorana mass. We discuss how the constrain…
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 texture zero mass matrices for the leptons and the seesaw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses.
We evaluate the predictive power of the neutrino mass matrices arising from seesaw mechanism with heavy Majorana mass matrices subject to texture zero and satisfy a cyclic permutation invariant form to the solar neutrino mixing phenomena. From eight possible patterns of heavy Majorana neutrino mass matrix, we found that there is no heavy Majorana neutrino mass matrix to be invariant in form under a cyclic permutation. But, by imposing an additional assumption that at least one of the 2x2 sub-matrices of heavy Majorana neutrino mass matrix inverse having zero determinant, we found that only two…
Assuming equal tree-level Majorana masses for the standard-model neutrinos, either from the canonical seesaw mechanism or from a heavy scalar triplet, I discuss how their radiative splitting may be relevant to neutrinoless double beta decay and neutrino oscillations.
(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…
By combining the inputs from the neutrinoless double beta decay and the fits of cosmological models of dark matter with solar and atmospheric neutrino data, we obtain constraints on two of the mixing angles of Majorana neutrinos, which become stronger when coupled with the reactor neutrino data. These constraints are strong enough to rule out Majorana neutrinos if the small angle solution of solar neutrino puzzle is borne out.
We present a massive Majorana neutrino model and see how it is constrained from the solar and atmospheric neutrino deficit experiments. This model incorporates the seesaw mechanism and Peccei-Quinn symmetry. Its consequence to the neutrinoless double beta decay is also discussed.
A form of mixing matrix for three active and three sterile, conventional Majorana neutrinos is proposed. Its Majorana lefthanded part arises from the popular bimaximal mixing matrix for three active neutrinos that works satisfactorily in solar and atmospheric experiments if the LSND effect is ignored. One of three sterile neutrinos, effective in the Majorana righthanded and Dirac parts of the proposed mixing matrix, is responsible perturbatively for the possible LSND effect by inducing one of three extra neutrino mass states to exist actively. The corresponding form of neutrino mass matrix is …
With the help of current neutrino oscillation data, we illustrate the three-dimensional (3D) profiles of all the six distinct effective Majorana neutrino masses $|\langle m\rangle^{}_{αβ}|$ (for $α, β= e, μ, τ$) with respect to the unknown neutrino mass scale and effective Majorana CP phases. Some salient features of $|\langle m\rangle^{}_{αβ}|$ and their phenomenological implications are discussed in both the normal and inverted neutrino mass ordering cases.
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…
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.
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…
An attempt is made to generate the bimaximal mixings of the three species of neutrinos from the textures of the right-handed Majorana neutrino mass matrices. We extend our earlier work in this paper for the generation of the nearly degenerate as well as the inverted hierarchical models of the left-handed Majorana neutrino mass matrices using the non-diagonal textures of the right-handed Majorana neutrino mass matrices and the diagonal form of the Dirac neutrino mass matrices, within the frame work of the seesaw mechanism in a model independent way. Such Majorana neutrino mass models are import…
The spin flavor precession (SFP) is investigated in the three neutrino generation case assuming that the neutrinos are Majorana type. Approximate analytical formulas including all transition magnetic moments are provided for the electron neutrino survival probability and electron neutrino -> electron anti-neutrino transition probability in the SFP framework. The accuracy of the formulas is checked out for two different magnetic field profiles in the Sun.
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.
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.
In view of the recently reported evidence for a nonzero Majorana mass of the electron neutrino, together with the established phenomena of atmospheric and solar neutrino oscillations, the case of three nearly mass-degenerate Majorana neutrinos is now a distinct possibility. I show in this paper how a natural pattern of symmetry breaking in the recently proposed $A_4$ model of Majorana neutrino masses can accommodate the data on neutrino oscillations, resulting in the predictions $\sin^2 2 θ_{atm} = 1$ and $\sin^2 2 θ_{sol} = 2/3$.
We have investigated a possible connection between the Majorana phases and geometric parameters of leptonic unitarity triangle(LUT) in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz. hybrid textures, neutrino mass matrix with vanishing minors and have profound implications for geometric description of $CP$ violation. As an example, we have considered two-texture zero neutrino mass model to obtain relation between Majorana phases and LUT parameters. In particular, we find that Majorana phases depend on only one of the thr…
We apply the see-saw mechanism and an SO(10) model to neutrino masses and mixing in order to estimate the heavy Majorana masses. We discuss shortly the decay modes of heavy Majorana neutrinos and calculate their contribution to the lepton number violating processes μ\to eγ, τ\toμγand τ\to eγ.
I analyze a fourth generation lepton sector in which the lightest particle is a stable Majorana neutrino. In this scenario fourth generation neutrinos have both a Dirac and Majorana mass, resulting in two Majorana neutrino mass eigenstates. A reanalysis of LEP's lower mass bound is performed on stable Majorana neutrinos from the Z width and the lower mass bound is loosened. I also extrapolate LEP's SUSY squark search with a 2 jet plus missing missing energy final state to the production and decay of a pair of heavy Majorana neutrinos; here it is expected that significant regions of the neutrin…
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 …
There are physical Majorana phases in the lepton flavor mixing matrix when neutrinos are Majorana fermions. In the case of two degenerate neutrinos, the physical Majorana phase plays the crucial role for the stability of the maximal flavor mixing between the second and the third generations against quantum corrections. The physical Majorana phase of $π$ guarantees the maximal mixing to be stable against quantum corrections, while the Majorana phase of zero lets the maximal mixing be spoiled by quantum corrections when neutrino masses are of O(eV). The continuous change of the Majorana phase fr…
We demonstrate that Majorana neutrinos can form Cooper pairs due to long-range attractive forces and show BCS superfluidity in a class of mass varying neutrino dark energy models. We describe the condensates for Majorana neutrinos and estimate the value of the gap, critical temperature and Pippard coherence length for a simple neutrino dark energy model. In the strong coupling regime bosonic degree of freedom can become important and Bose-Einstein condensate may govern the dynamics for the mass varying neutrino models. Formation of the condensates can significantly alter the instability scenar…
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.
Neutrinoless double beta decay (NDBD) is the only experiment that could probe the Majorana nature of the neutrino. Here we study the theoretical implications of NDBD for models yielding tri-bimaximal lepton mixing like A4 and S4.
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.
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.
We discuss the one-loop electroweak renormalization of the leptonic mixing matrix in the case of Majorana neutrinos, and establish its relationship with the renormalization group evolution of the dimension five operator responsible for the light Majorana neutrino masses. We compare our results in the effective theory with those in the full seesaw theory.
If the neutrinos are Majorana fermions, there are at least three new, potentially observable CP-odd phases that parameterize CP-invariance violating phenomena. We currently have no information regarding any of them and know that two out of the three, the so-called Majorana phases, are very hard to access experimentally. Here, we discuss the effect of Majorana phases on charged-lepton electric dipole moments (EDM), and explicitly show that neutrino Majorana phases induce EDMs even in the absence of other sources of CP-invariance violation. We also argue that while the Majorana neutrino contribu…
Neutrinos are the only known elementary fermions that can exhibit Majorana nature. As per the "practical Dirac-Majorana confusion theorem" it is impossible to distinguish between Dirac and Majorana neutrinos via any kinematic tests when their masses are very small. However, it is also well known that Majorana neutrino and anti-neutrino present in the final state must obey the Fermi-Dirac statistics, irrespective of how small the mass of neutrino is. We propose a new method to search for Majorana neutrinos by exploiting their quantum statistical property. We analyse `effective' three-body decay…
The electric dipole moment of the electron, $d_e$, is known to vanish up to thre e-loops in the standard model with massless neutrinos. However, if neutrinos are massive Majorana particles, we obtain the result that $d_e$ induced by leptonic CKM mechanism is non-vanishing at two-loop order, and it applies to all massive Majorana neutrino models.
We study the $B_C$ meson rare decay in order to search for the Majorana neutrino signal. It is found that the the corresponding decay rate is sensitive to the Majorana neutrino mass and mixing angles. The signal of $B_C^\pm\to l_1^\pm l_2^\pm M^\mp $ induced by the Majorana neutrino within the mass region $m_π<m_n<m_B$ may be observed at LHCb.
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.
A form of mixing matrix for three active and three sterile, conventional Majorana neutrinos is proposed. Its Majorana lefthanded part arises from the popular bimaximal mixing matrix for three active neutrinos that works satisfactorily in solar and atmospheric experiments if the LSND effect is ignored. One of three sterile neutrinos, effective in the Majorana righthanded and Dirac parts of the proposed mixing matrix, is responsible for the possible LSND effect by inducing one of three extra neutrino mass states to exist actively. The corresponding form of neutrino mass matrix is derived. Also, …
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.
After introducing a master formula for the Majorana neutrino mass matrix we present a master parametrization for the Yukawa matrices automatically in agreement with neutrino oscillation data. This parametrization can be used for any model that induces Majorana neutrino masses. The application of the master parametrization is also illustrated in an example model, with special focus on its lepton flavor violating phenomenology.
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…
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.
We consider the effect of ambient matter on the Majorana phase of neutrinos. We find that this can lead to an observable signal if a neutrino oscillation experiment could be performed where the source and the detector are at appropriately different matter densities. We illustrate the situation using a beta beam neutrino source as an example and show that a 5 sigma signal for the matter modification of the Majorana phase could be possible in a 5-year run.
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.
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.
If it can be ascertained experimentally that the 3X3 Majorana neutrino mass matrix M_nu has vanishing determinants for one or more of its 2X2 submatrices, it may be interpreted as supporting evidence for the theoretically well-known canonical seesaw mechanism. I show how these two things are connected and offer a realistic M_nu with two zero subdeterminants as an example.
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…
Lepton number violation processes can be induced by the Majorana neutrino exchange, which provide evidence for the Majorana nature of neutrinos. In addition to the natural explanation of the small neutrino masses, Type-I seesaw mechanism predicts the existence of Majorana neutrinos. The aim of this work is to study the B meson rare decays $B^{+} \to K^{(*)+}μ^+μ^-$ in the standard model and its extensions, and then to investigate the same-sign decay processes $B^{+}\to K^{(*)-}μ^{+}μ^+$. The corresponding dilepton invariant mass distributions are predicted. It is found that the dilepton angula…
