In this paper, we investigate lepton mass spectra, flavor mixing and CP violation with a modular $S^{}_4$ symmetry under the assumption that neutrinos are Dirac fermions. We find that the Majorana mass term can be forbidden by adjusting the weight of the right-handed neutrino superfields. We study the scenarios where modular forms in the neutrino sector take the lowest non-trivial weight two, while those in the charged-lepton sector vary from two to six. The corrections from renormalization-group running effects to our model have also been discussed in detail. We totally obtain twelve different classes of models and find that ten of them can accommodate current neutrino oscillation data.
If neutrinos are Dirac, the conditions for cobimaximal mixing, i.e. $θ_{23}=π/4$ and $δ_{CP}=\pm π/2$ in the $3 \times 3$ neutrino mixing matrix, are derived. One example with $A_4$ symmetry and radiative Dirac neutrino masses is presented.
A significant signal of neutrinoless double beta decay can be consistent with the existence of light quasi-Dirac neutrinos. To demonstrate this possibility, we consider a realistic model where the neutrino masses and the neutrinoless double beta decay can be simultaneously generated after a Peccei-Quinn symmetry breaking.
The possibility to verify the pseudo-Dirac nature of neutrinos is investigated here via the detection of ultra high energy neutrinos from distant cosmological objects like GRBs. The very long baseline and the energy range from $\sim$ TeV to $\sim$ EeV for such neutrinos invokes the likelihood to probe very small pseude-Dirac splittings. The expected secondary muons from such neutrinos that can be detected by a kilometer scale detector such as ICECUBE is calculated. The pseudo-Dirac nature, if exists, will show a considerable departure from flavour oscillation scenario in the total yield of the…
The theory of neutrino flavor rotations is discussed in terms of wave function solutions to the Dirac equation with a neutrino mass matrix. We give a critical review of the nature of neutrino oscillations.
The oscillations of pseudo-Dirac neutrinos in matter are discussed and applied to the solar neutrino problem. Several scenarios such as both $ν_e$ and $ν_μ$ being pseudo-Dirac and only $ν_e$ or $ν_μ$ being pseudo-Dirac are examined. It is shown that the allowed region in the mass-mixing angle parameter space obtained by comparing the solar neutrino data with the calculations based on the standard solar model and the MSW effect is not unique. The results depend on the nature of neutrinos; for example, if both $ν_e$ and $ν_μ$ are pseudo-Dirac, the allowed region determined by the current solar n…
In this talk, we discuss the idea of how Dirac or Pseudo-Dirac neutrino masses arise naturally with a correct size, after the breaking of local N=1 supersymmetry.
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.
We propose a model where sterile neutrinos are introduced to make light neutrinos to be pseudo-Dirac particles. It is shown how tiny mass splitting necessary for realizing pseudo-Dirac neutrinos can be achieved. Within the model, we show how leptogenesis can be successfully generated. Motivated by the recent observation of very high energy neutrino events at IceCube, we study a possibility to observe the effects of the pseudo-Dirac property of neutrinos by performing astronomical-scale baseline experiments to uncover the oscillation effects of very tiny mass splitting. Using the result of glob…
The Zee model for Dirac neutrinos is one of the simplest models featuring one-loop Dirac neutrino masses. The interactions between the new scalars (two singly-charged fields) and neutrinos induce general neutrino interactions (GNI) which, as a generalisation of the non standard neutrino interactions, constitute an additional tool to probe models beyond the SM like this. In this work, we consider a $U(1)_{B-L}$ gauge symmetry as the responsible for the Diracness of the neutrinos and the radiative character of the neutrino masses. We determine the viable parameter space consistent with neutrino …
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 PTOLEMY experiment, implementing a $100~{\rm g}$ surface-deposition tritium target, is promising to detect cosmic neutrino background via $ν^{}_e + {^3}{\rm H} \to {^3}{\rm He} + e^-$. In this talk, I consider a thermal production of right-handed Dirac neutrinos in the early Universe, and investigate their impact on the capture rate of cosmic relic neutrinos at PTOLEMY.
The seesaw mechanism explains the exclusive smallness of neutrino masses by the presence of very heavy Majorana masses and leads to the appearance of Majorana particles and to the direct lepton number violation. The author proposes a seesaw scenario that produces only Dirac neutrinos with the same violation. This scenario appears possible for heavy neutrinos with non-perturbative Higgs boson H couplings. Such a scenario could be accomplished in the model describing the structure of weak mixing matrices for quarks and leptons through the existence of very heavy mirror analogs of Standard Model …
We propose a simple radiative neutrino mass scenario with a Dirac dark matter candidate, which is minimally realized by a Z3 symmetry. We introduce two Dirac neutrinos and two inert doublets. We demonstrate that the model has a large allowed region that satisfies the constraints from neutrino oscillation data, lepton flavor violations, direct/indirect detection of dark matter and dark matter relic density. We also propose an efficient parameterization of the neutrino Yukawa couplings, which reproduces a desired active neutrino mass matrix.
It is shown how a mechanism which allows naturally small Dirac neutrino masses is linked to the existence of dark matter through an anomaly-free U(1) gauge symmetry of fermion singlets.
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.
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.
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.
The magic texture is one of the successful textures of the flavor neutrino mass matrix for the Majorana type neutrinos. The name "magic" is inspired by the nature of the magic square. We estimate the compatibility of the magic square with the Dirac, instead of the Majorana, flavor neutrino mass matrix. It turned out that some parts of the nature of the magic square are appeared approximately in the Dirac flavor neutrino mass matrix and the magic squares prefer the normal mass ordering rather than the inverted mass ordering for the Dirac neutrinos.
We propose a Standard Model extension with underlying A4 flavour symmetry where small Dirac neutrino masses arise from a Type-II seesaw mechanism. The model predicts the "golden" flavour-dependent bottom-tau mass relation, requires an inverted neutrino mass ordering and non-maximal atmospheric mixing angle. Using the latest neutrino oscillation global fit we derive restrictions on the oscillation parameters, such as a correlation between Dirac CP phase and the lightest neutrino mass.
The intent of this paper is to convey a new primary physical idea of a Dirac-Majorana neutrino duality in relation to the topical problem of neutrino oscillations. In view of the new atmospheric, solar and the LSND neutrino oscillation data, the Pontecorvo $ν- K^0$ oscillation analogy is generalized to the notion of neutrino duality with substantially different physical meaning ascribed to the long-baseline and the short-baseline neutrino oscillations. At the level of CP-invariance, the suggestion of dual neutrino properties defines the symmetric two-mixing-angle form of the widely discussed f…
We explore a new origin of neutrino dark energy and baryon asymmetry in the universe. The neutrinos acquire small masses through the Dirac seesaw mechanism. The pseudo-Nambu-Goldstone boson associated with neutrino mass-generation provides a candidate for dark energy. The puzzle of cosmological baryon asymmetry is resolved via neutrinogenesis.
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.
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…
Modular symmetries have been impeccable in neutrino and quark sectors. This motivated us, therefore, to propose a variant of scotogenic model based on modular $A_4$ symmetry to realize the neutrino mass generation at one-loop level through radiative mechanism. Alongside, the lepton flavour violating process $μ\to e γ$ and the muon $g-2$ anomaly are also addressed. The lightest Majorana fermions turn out to be potential dark matter candidates, made stable by suitable assignment of modular weights. The relic density of the same has been computed with annihilations mediated by inert scalars and n…
Light Dirac neutrino of mass of mass of the order of few eV is obtained in an $SU(2)_L\times U(1)_Y$ model with an extended Higgs sector and right-handed neutrinos. Small neutrino mass is generated at the tree level through small effective coupling of the Dirac neutrino mass term due to soft discrete symmetry breaking. In order to remove the exact degeneracy in mass between the second and the third generation of neutrinos, one loop corrected mass terms are incorporated. The model can accommodate bi-maximal mixing scenario of neutrino which has been favoured by recent Solar and atmospheric neut…
We examine constraints on a simple neutrino model in which there are three massless and three massive Dirac neutrinos and in which the left handed neutrinos are linear combinations of doublet and singlet neutrinos. We examine constraints from direct decays into heavy neutrinos, indirect effects on electroweak parameters, and flavor changing processes. We combine these constraints to examine the allowed mass range for the heavy neutrinos of each of the three generations.
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…
Within the "pseudo-Dirac" scenario for massive neutrinos the existence of sterile neutrinos which are almost degenerate in mass with the active ones is hypothesized. The presence of these sterile neutrinos can affect the flavor composition of cosmic neutrinos arriving at Earth after traveling large distances from astrophysical objects. We examine the prospects of neutrino telescopes such as IceCube to probe the very tiny mass squared differences 10^(-12) eV^2<Δm^2<10^(-19) eV^2, by analyzing the ratio of $μ$-track events to shower-like events. Considering various sources of uncertainties which…
We argue how pseudo-Dirac scenario for neutrinos leads to rich neutrino oscillation phenomena, including oscillation inside each generation. The pseudo-Dirac scenario is generalized by incorporating generation mixings and formulae for the various neutrino oscillations are derived. As the application we compare the formulae with the corresponding data. We find that observed pattern of mixings, such as almost maximal mixing in the atmospheric neutrino oscillation, is naturally explained in the generalized Pseudo-Dirac scenario with small generation mixings. We, however, also point out that there…
We propose a model with radiatively induced neutrino mass at two-loop level, applying modular $A_4$ symmetry. The neutrino mass matrix is formulated where the structure of associated couplings are restricted by the symmetry. Then we show several predictions in the lepton sector, satisfying lepton flavor violations as well as neutrino oscillation data. We also discuss muon anomalous magnetic moment and briefly comment on dark matter candidate.
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.
A new solution is presented where the right-handed neutrino $ν_R$ in $SO(10)$ pairs up with $ν_L$ to form a naturally light Dirac neutrino. It is based on the framework of $E_6 \to SO(10) \times U(1)_ψ$, then $SO(10) \to SU(5) \times U(1)_χ$.
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.
Using a mechanism which allows naturally small Dirac neutrino masses and its linkage to a dark gauge $U(1)_D$ symmetry, a realistic Dirac neutrino mass matrix is derived from $S_3$. The dark sector naturally contains a fermion singlet having a small seesaw mass. It is thus a good candidate for freeze-in dark matter from the decay of the $U(1)_D$ Higgs boson.
We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. We find that the modular forms of integral weights and level $N$ can be arranged into irreducible representations of the homogeneous finite modular group $Γ'_N$ which is the double covering of $Γ_N$. The lowest weight 1 modular forms of level 3 are constructed in terms of Dedekind eta-function, and they transform as a doublet of $Γ'_3 \cong T'$. The modular forms of weights 2, 3, 4, 5 and 6 are presented. We build a model of lepton masses and mixing based on $T'$ modular symmetry.
Non-zero leptonic CP phases in the neutrino sector are clear evidence for physics beyond the Standard Model and have many implications in particle physics and cosmology. Some clues to maximal Dirac CP violation $δ_{CP}=3π/2$ are reviewed. An approach to connect the Dirac CP violation phase and the neutrino mass hierarchy in terms of the measurement of CP asymmetry is proposed. Under appropriate requirements for baseline distance and beam energy, the problem of neutrino mass hierarchy can be revealed at maximal Dirac CP violation. General allowed parameter spaces are investigated, within which …
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 provide a complete systematic classification of all two-loop realizations of the dimension four operator for Dirac neutrino masses. Our classification is multi-layered, starting first with a classification in terms of all possible distinct two-loop topologies. Then we discuss the possible diagrams for each topology. Model-diagrams originating from each diagram are then considered. The criterion for genuineness is also defined and discussed at length. Finally, as examples, we construct two explicit models which also serve to highlight the intimate connection between the Dirac nature of neutr…
If neutrinos are truly Dirac fermions, the smallness of their masses may still be natural if certain symmetries exist beyond those of the standard model of quarks and leptons. We perform a systematic study of how this may occur at tree level and in one loop. We also propose a scotogenic version of the left-right gauge model with naturally small Dirac neutrino masses in one loop.
A sterile neutrino in the $3+1$ scheme, where the sterile accounts for neutrino anomalies not explained solely by the weak active neutrinos, arises as a natural source for the breaking of the $μ-τ$ symmetry suggested by oscillation neutrino data. We explore the predictions for the Dirac CP phases in this scenario, with and without sterile neutrino decay, and show that current limits on $δ_{CP}$ suggest a normal hierarchy and a lightest neutrino scale below 0.1~eV as the most plausible explanation for that, when Majorana phases are null. Other Dirac phases turn out to be non zero as well.
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 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 …
We present a mechanism that naturally produces light Dirac neutrinos. The basic idea is that the right-handed neutrinos are composite. Any realistic composite model must involve `hidden flavor' chiral symmetries. In general some of these symmetries may survive confinement, and in particular, one of them manifests itself at low energy as an exact $B-L$ symmetry. Dirac neutrinos are therefore produced. The neutrinos are naturally light due to compositeness. In general, sterile states are present in the model, some of them can naturally be warm dark matter candidates.
We write out the generic Dirac neutrino mass operator which possesses the Friedberg-Lee (FL) symmetry and find that its corresponding neutrino mass matrix is asymmetric. Following a simple way to break the FL symmetry, we calculate the neutrino mass eigenvalues and show that the resultant neutrino mixing pattern is nearly tri-bimaximal. Imposing the Hermitian condition on the neutrino mass matrix, we also show that the simplified ansatz is consistent with current experimental data and favors the normal neutrino mass hierarchy.
An overview of pseudo-Dirac neutrino framework is given starting from general spinor phenomenology. The framework is then tested by simulation of oscillations for T2K experiment parameters. Two possible derivations of oscillation parameters are indicated to have the same result.
The standard model of quarks and leptons is extended to include the gauge symmetry $U(1)_χ$ which comes from $SO(10) \to SU(5) \times U(1)_χ$. The radiative generation of Dirac neutrino masses through dark matter is discussed in two examples. One allows for light Dirac fermion dark matter. The other allows for self-interacting scalar dark matter with a light scalar mediator which decays only to two neutrinos.
We generalize the modular invariance approach to include the half-integral weight modular forms. Accordingly the modular group should be extended to its metaplectic covering group for consistency. We introduce the well-defined half-integral weight modular forms for congruence subgroup $Γ(4N)$ and show that they can be decomposed into the irreducible multiplets of finite metaplectic group $\widetildeΓ_{4N}$. We construct concrete expressions of the half-integral/integral modular forms for $Γ(4)$ up to weight 6 and arrange them into the irreducible representations of $\widetildeΓ_4$. We present …
So far we have not been able to establish that, as theoretically expected, neutrinos are their own anti-particles. Here we propose a dynamical way to account for the Dirac nature of neutrinos and the smallness of their mass in terms of a new variant of the seesaw paradigm in which the energy scale of neutrino mass generation could be accessible to the current LHC experiments.
We consider the Affleck-Dine mechanism for leptogenesis in the minimal MSSM with Dirac or Pseudo-Dirac neutrinos. The rolling of scalars along D-flat directions generates a left-right asymmetry in the sneutrino sector, only the left part of which is transferred to a baryon asymmetry via sphaleron transitions. In the pure Dirac case the baryon asymmetry of the Universe is thus mirrored by an equal and opposite asymmetry in the leptons. The mechanism is also found to work when the neutrinos are pseudo-Dirac. No additional field needs to be added to the MSSM other than the right-handed neutrino.
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 …
Operating with the bilarge neutrino mixing, we show that in the option of Dirac neutrinos the fermion universality -- expressed by the proportionality of neutrino masses to charged-lepton masses -- predicts $Δm_{21}^2$ of the order $10^{-5} {\rm eV}^2$, consistently with the LMA MSW solar solution. In contrast, in the option of Majorana neutrinos the fermion universality -- introduced as the seesaw proportionality of neutrino masses to charged-lepton masses squared -- predicts $Δm_{21}^2$ of the order $10^{-8} {\rm eV}^2$, what is consistent rather with the LOW MSW solar solution. Thus, the fa…
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.
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.
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.
We present a neutrino mass model based on modular symmetry with the fewest input parameters to date, which successfully accounts for the 12 lepton masses and mixing parameters through 6 real free parameters including the modulus. The neutrino masses are predicted to be normal ordering, the atmospheric angle $θ_{23}$ is quite close to maximal value and the Dirac CP phase $δ_{CP}$ is about $1.34π$. We also study the soft supersymmetry breaking terms due to the modulus $F$-term in this minimal model, which are constrained to be the non-holomorphic modular forms. The radiative lepton flavor violat…
