If neutrinos are Majorana fermions, the lepton mixing parameter space consists of six mixing parameters: three mixing angles and three CP-odd phases. A related issue concerns the physical range of the mixing parameters. What values should these take so that all physically distinguishable mixing scenarios are realized? We present a detailed discussion of the lepton mixing parameter space in the case of two and three active neutrinos, and in the case of three active and N sterile neutrinos. We emphasize that this question, which has been a source of confusion even among "neutrino" physicists, is connected to an unambiguous definition of the neutrino mass eigenstates. We find that all Majorana phases can always be constrained to lie between 0 and pi, and that all mixing angles can be chosen positive and at most less than or equal to pi/2 provided the Dirac phases are allowed to vary between -pi and pi. We illustrate our results with several examples. Finally, we point out that, in the case of new flavor-changing neutrino interactions, the lepton mixing parameter space may need to be enlarged. We properly qualify this statement, and offer concrete examples.
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…
Majorana neutrino. Is double neutrinoless beta decay possible in the framework of the weak interactions? How to prove that neutrino is Majorana particle
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…
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.
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 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 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.
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.
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 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…
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.
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…
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 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.
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.
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…
The article investigates the possibility that right-handed neutrinos are Majorana particles embedded in an abelian multiplicative $U(1)_R$ factor, with the Lagrangian in the new factor being invariant under chiral gauge transformations. Majorana neutrinos couple to charged and neutral currents, producing new signatures to (anti)neutrino-electron elastic scattering and an additional term to coherent scattering of neutrinos on atomic nuclei. The model is ultraviolet complete and depends on one extra hypercharge correlating the reactions and providing upper bounds for the new coupling constant.
