In the context of two flavour neutrino oscillations, it is understood that the $2\times 2$ mixing matrix is parameterized by one angle and a Majorana phase. However, this phase does not impact the oscillation probabilities in vacuum or in matter with constant density. Interestingly, the Majorana phase becomes relevant when we describe neutrino oscillations along with neutrino decay. This is due to the fact that effective Hamiltonian has Hermitian and anti-Hermitian components which cannot be simultaneously diagonalized (resulting in decay eigenstates being different from the mass eigenstates). We consider the $\cal PT$ symmetric non-Hermitian Hamiltonian describing two flavour neutrino case and study the violation of Leggett-Garg Inequalities (LGI) in this context for the first time. We demonstrate that temporal correlations in the form of LGI allow us to probe whether neutrinos are Dirac or Majorana. We elucidate the role played by the mixing and decay parameters on the extent of violation of LGI. We emphasize that for optimized choice of parameters, the difference in $K_4$ ($K_3$) for Dirac and Majorana case is $\sim 15\%$ ($\sim 10\%$).
We propose a novel scheme for distinguishing between the Dirac and Majorana nature of neutrinos via interaction of a neutrino beam with microwave photons inside a cavity. We study the effective photon-photon polarization exchange induced by the photon-neutrino scattering. The quantum field theoretical studies of such effective picture are presented for both Dirac and Majorana neutrinos. Our phenomenological analyses show that the difference between Dirac and Majorana neutrinos can manifest itself in scattering rate of the photons. To enhance the effect a cavity scheme is employed. An experimen…
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.
We revisit the possibility of distinguishing between Dirac and Majorana neutrinos via neutrino-electron elastic scattering in the presence of all possible Lorentz-invariant interactions. Defining proper observables, certain regions of the parameter space can only be reached for Dirac neutrinos, but never for Majorana neutrinos, thus providing an alternative method to differentiate these two possibilities. We first derive analytically and numerically the most general conditions that would allow to distinguish Dirac from Majorana neutrinos, both in the relativistic and non-relativistic cases. Th…
Neutrinos may acquire small Dirac or Majorana masses by new low-energy physics in terms of the chiral gravitational anomaly, as proposed by Dvali and Funcke (2016). This model predicts fast neutrino decays, $ν_i\toν_j+ϕ$ and $ν_i\to\barν_j+ϕ$, where the gravi-majorons $ϕ$ are pseudoscalar Nambu-Goldstone bosons. The final-state neutrino and antineutrino distributions differ depending on the Dirac or Majorana mass of the initial state. This opens a channel for distinguishing these cases, for example in the spectrum of high-energy astrophysical neutrinos. In particular, we put bounds on the neut…
We investigate purely leptonic decays of leptons $ł^{\prime-}\to l^-\barν_lν_{l^{\prime}}$ to distinguish Dirac or Majorana neutrinos. We derive the differences of the decay width (and associated quantities) between the two neutrino hypotheses by the effect of identical particles. Evidence from experimental data makes the hypothesis of Majorana neutrinos very unlikely and our results strongly favor the hypothesis of Dirac neutrinos (in the standard three-neutrino theory). Moreover, our exploration for decay widths can be extended to the polarization angles of leptons, which will inspire new in…
Massive neutrinos can have helicity $s_{\parallel}\neq -1$. Neutrino helicity changes when the neutrino interacts with an external magnetic field and it is possible that the left-handed neutrinos born inside the Sun or a supernova could leave their sources with a different helicity. Since Dirac and Majorana neutrinos have different cross sections in the scattering on electrons for different neutrino helicities, a change in the final neutrino helicity may generate a different number of events and spectra in terrestrial detectors when astrophysical neutrinos have travelled regions with strong ma…
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 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 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 …
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.
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…
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.
We study the purely leptonic decays of $W^\pm \to e^\pm e^\pm μ^\mp ν$ and $μ^\pm μ^\pm e^\mp ν$ produced at the LHC, induced by sterile neutrinos with mass $m_N$ below $M_W$ in the intermediate state. Since the final state neutrino escapes detection, one cannot tell whether this process violates lepton number, what would indicate a Majorana character for the intermediate sterile neutrino. Our study shows that when the sterile neutrino mixings with electrons and muons are different enough, one can still discriminate between the Dirac and Majorana character of this intermediate neutrino by simp…
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…
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.
(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 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 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…
We discuss the potential to observe lepton number violation (LNV) in displaced vertex searches for heavy neutral leptons (HNLs) at future lepton colliders. Even though a direct detection of LNV is impossible for the dominant production channel because lepton number is carried away by an unobservable neutrino, there are several signatures of LNV that can be searched for. They include the angular distribution and spectrum of decay products as well as the HNL lifetime. We comment on the perspectives to observe LNV in realistic neutrino mass models and argue that the dichotomy of Dirac vs Majorana…
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 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…
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…
We analyse the possibility of distinguishing Dirac and Majorana neutrinos in future neutrino factory experiments in which neutrinos are produced in muon decay when, in addition to a vector type as in the SM, there are also scalar interactions. We check this possibility in an experiment with a near detector, where the observed neutrinos do not oscillate, and in a far detector, after the neutrino oscillations. Neglecting higher-order corrections, even neutrino observation in the near detector does not give a chance to differentiate their character. However, this possibility appears in the leadin…
Neutrino masses could originate in seesaw models testable at colliders, with light mediators and an approximate lepton number symmetry. The minimal model of this type contains two quasi-degenerate Majorana fermions forming a pseudo-Dirac pair. An important question is to what extent future colliders will have sensitivity to the splitting between the Majorana components, since this quantity signals the breaking of lepton number and is connected to the light neutrino masses. We consider the production of these neutral heavy leptons at the ILC, where their displaced decays provide a golden signal…
In this paper we analyze the neutrinoless double beta decay predictions in some scenarios with admixture of pseudo-Dirac and Majorana neutrinos in the 3 and 3+1 neutrino frameworks. We found that some of the cases can be falsifiable in near-term and future generations of neutrinoless double beta decay experiments even for the normal neutrino mass hierarchy. In the 3+1 framework we consider the sterile neutrino with a mass of the order of 1 eV. The complementarity between cosmological constraints and the future sensitivity for the next generations of the neutrinoless double beta decay searches …
Neutrino mass matrix via a seesaw mechanism is constructed by assuming that the underlying symmetry of both heavy Majorana and Dirac mass matrices is the discrete subgroup $Δ(27)$ symmetry of SU(3). Using the experimental data of neutrino oscillation, the neutrino mass matrix exhibits maximal $ν_μ-ν_τ$ mixing and has a specific prediction on the effective neutrino mass in neutrinoless double beta decay which can be tested in future experiment.
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…
