Majorana neutrino oscillations in a magnetic field are considered using the wave packets formalism. The modified Dirac equation for Majorana neutrinos with non-zero transition magnetic moments propagating in a magnetic field is solved analytically in the two flavour case. The expressions for the oscillations probabilities are derived accounting for the decoherence effect emerging at distances exceeding the coherence length. It is shown that for Majorana neutrinos propagating in a magnetic field the coherence length coincides with the coherence length for neutrino oscillations in vacuum when the vacuum frequency is much greater than the magnetic frequency ($ω_{vac} \gg ω_B$), while it is proportional to the cube of the average neutrino momentum if ($ω_{vac} \ll ω_B$). We show that the decoherence effect may appear during neutrino propagation in a magnetic field of supernova.
We present the possibility that Dirac and Majorana neutrino wave packets can be distinguished when subject to spin-gravity interaction while propagating through vacuum described by the Lense-Thirring metric. By adopting the techniques of gravitational phase and time-independent perturbation theory following the Brillouin-Wigner method, we generate spin-gravity matrix elements from a perturbation Hamiltonian and show that this distinction is easily reflected in well-defined gravitational corrections to the neutrino oscillation length for a two-flavour system. Explicit examples are presented usi…
In this paper, we carry out the canonical quantization of the field theory of an interacting tachyonic Majorana neutrino. We show how micro-causality is preserved in the physical scattering matrix elements between the in and out vacua. The phenomenology of this radical proposal is nevertheless compatible with normal timelike oscillations.
Geometric (Aharonov--Anandan) phases in neutrino oscillations have been claimed [Phys. Lett. B 780 (2018) 216] to be sensitive to the Majorana phases in neutrino mixing. More recently, however, it has been pointed out [Phys. Lett. B 818 (2021) 136376] that the proposed phases are not gauge invariant. Using both kinematic and geometric approaches, we show that all gauge-invariant Aharonov--Anandan phases (including the off-diagonal geometric phases associated with flavor transitions) are independent of the Majorana phases. This finding, which generalizes the well-known fact that conventional os…
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.
We review and remark on models of radiatively induced neutrino Majorana masses and oscillations. It is pointed out that while the models are capable of accounting for the observed solar and atmospheric neutrino oscillation, some of them can also induce neutrinoless double beta decay and $μ^-$ -- $e^+$ conversion in nuclei large enough to be potentially observable in the near future.
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.
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 …
It is shown that the Majorana phases of the neutrino mixing matrix cannot have any effect in neutrino oscillations, contrary to the argument presented in arXiv:0912.5266. It is also shown that in a charged-current weak interaction process it is not possible to create a coherent superposition of different flavor neutrinos which is independent of the associated charged leptons.
If the massive neutrinos are Majorana particles, neutrinoless double beta ($0νββ$) decay experiments are not enough to determine the Majorana phases. We carry out a systematic study of CP violation in neutrino-antineutrino oscillations. In these processes, CP-conserving parts involve six independent $0νββ$-like mass terms $\langle m\rangle_{αβ}$ and CP-violating parts are associated with nine independent Jarlskog-like parameters ${\cal V}^{ij}_{αβ}$ (for $α, β= e, μ, τ$ and $i, j = 1, 2,3$). With the help of current neutrino oscillation data, we illustrate the salient features of six independe…
Quantum correlations provide a fertile testing ground for investigating fundamental aspects of quantum physics in various systems, especially in the case of relativistic (elementary) particle systems as neutrinos. In a recent paper, Ming et al. (Ming et al. Eur.Phys.J.C 80 (2020) 275), in connection with results of Daya-Bay and MINOS experiments, have studied the quantumness in neutrino oscillations in the framework of plane-wave approximation. We extend their treatment by adopting the wave packet approach that accounts for effects due to localization and decoherence. This leads to a better ag…
General arguments in favor of the necessity of a wave packet description of neutrino oscillations are presented, drawing from analogies with other wave phenomena. We present a wave packet description of neutrino oscillations in stationary beams using the density matrix formalism. Recent claims of the necessity of an equal energy of different massive neutrinos are refuted.
The complete description of neutrino oscillations require the wave packet treatment. For terrestrial experiments the contribution from the interaction of neutrino with the Earth matter would modify oscillation pattern, i.e., the dependence of the flavor transition probability on baseline $L$ and energy $E$. We thus combine the wave packet approach and the matter effects, in order to have more accurate descriptions of neutrino oscillation. The general expression for the transition probability of oscillations with arbitrary numbers of neutrinos are derived. As an example the two-neutrino oscilla…
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…
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.
We show that discovery of baryon number violation in two processes with at least one obeying the selection rule Δ(B-L) = \pm 2 can determine the Majorana character of neutrinos. Thus observing p \to e^+ π^0 and n \to e^- π^0 decays, or p \to e^+ π^0 and n-nbar oscillations, or n \to e^- π^+ and n-nbar oscillations would establish that neutrinos are Majorana particles. We discuss this in a model-independent effective operator approach.
We analyze neutrino oscillation for the general case when the initial neutrino is not in a pure flavor state. We show that, after such a neutrino beam propagates for a while, the probability of detecting any pure flavor state depends even on the CP-violating Majorana phases in the mixing matrix. The dependence remains even when energy spectrum of the initial beam is taken into account. We discuss various implications of this dependence.
Manipulation with ill-defined notions creates an illusion of a simple derivation of the standard phase of neutrino oscillations in hep-ph/0311241 and hep-ph/0312180.
The plane-wave approximation is widely used in the practical calculations concerning neutrino oscillations. A simple derivation of this approximation starting from the neutrino wave-packet framework is presented.
Majorana CP Violation Insights from Decaying Neutrinos
Jawaharlal Nehru University（贾瓦哈拉尔·尼赫鲁大学）；Oklahoma State University（俄克拉荷马州立大学）；Institut de Física Corpuscular – CSIC/Universitat de València（粒子物理研究所 - 西班牙国家研究委员会/巴伦西亚大学）；Indian Institute of Technology (BHU)（印度理工学院（贝拿勒斯））；Indian Institute of Science Education and Research Berhampur（贝拉姆普尔科学教育与研究所）
We study the neutrino oscillation problem in the framework of the wave packet formalism. The neutrino state is described by a packet located initially in a region S (source) and detected in another region D at a distance R from S. We examine how the oscillation probability as a function of variable R can be derived from he oscillation probability as a function of time t, the latter being found by using the Schrodinger equation. We justify the known prescription "t --> R/c" without referring to a specific form of the neutrino wave packet and only assuming the finiteness of its support. The effe…
We present a parity-doublet theorem for the representation of the intrinsic parity of Majorana fermions, which is expected to be useful also in condensed matter physics, and it is illustrated to provide a criterion of neutron-antineutron oscillation in a BCS-like effective theory with $ΔB=2$ baryon number violating terms. The CP violation in the present effective theory causes no direct CP violating effects in the oscillation itself, which is demonstrated by the exact solution, although it influences the neutron electric dipole moment in the leading order of small $ΔB=2$ parameters. An analogu…
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.
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 consider a class of models for the relativistic covariant wave packets which can be used as asymptotically free in and out states in the quantum field theoretical formalisms for description of the neutrino flavor oscillation phenomenon. We demonstrate that the new "asymmetric" wave packet (AWP) is an appropriate alternative for the more convenient "symmetric" wave packets, like the so-called relativistic Gaussian packet (RGP) widely used in the QFT-based approaches to neutrino oscillations. We show that RGP is not a particular case of AWP, although many properties of these models are almost…
Using the recent measurement of SNO salt phase experiment, we investigate how much the solar neutrino flux deficit observed at SNO could be due to $ν_e$ transition into antineutrino. Our analysis leads to rather optimistic conclusion that the SNO salt phase data may indicate the existence of Majorana magnetic moment. The prospect for the future BOREXINO experiment is also discussed.
We introduce an approximation scheme to perform an analytic study of the oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian wave packets, we show that the oscillation is bounded by a time-dependent vanishing function which characterizes the slippage between the mass-eigenstate wave packets. We also demonstrate that the wave packet spreading represents a secondary effect which plays a significant role only in the non-relativistic limit. In our analysis, we note the presence of a new time-dependent phase and calculate how this additional term modifies the oscillating…
We analyze the possibility of encountering resonant transitions of high energy Majorana neutrinos produced in Active Galactic Nuclei (AGN). We consider gravitational, electromagnetic and matter effects and show that the latter are ignorable. Resonant oscillations due to the gravitational interactions are shown to occur at energies in the PeV range for magnetic moments in the $10^{-17} μ_B$ range. Coherent precession will dominate for larger magnetic moments. The alllowed regions for gravitational resonant transitions are obtained.
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 give a detailed analysis of the oscillation formula within the context of the wave packet formalism. Particular attention is made to insure flavor eigenstate creation in the physical cases (Delta p not equal 0). This requirement imposes non instantaneous particle creation in all frames. It is shown that the standard formula is not only exact when the mass wave packets have the same velocity, but it is a good approximation when minimal slippage occurs. For more general situations the oscillation formula contains additional arbitrary parameters, which allows for the unknown form of the wave p…
We investigate effects of non-zero Dirac and Majorana CP violating phases on neutrino-antineutrino oscillations in a magnetic field of astrophysical environments. It is shown that in the presence of strong magnetic fields and dense matter, non-zero CP phases can induce new resonances in the oscillations channels $ν_e \leftrightarrow \barν_e$, $ν_e \leftrightarrow \barν_μ$ and $ν_e \leftrightarrow \barν_τ$. We also consider all other possible oscillation channels with $ν_μ$ and $ν_τ$ in the initial state. The resonances can potentially lead to significant phenomena in neutrino oscillations acce…
The electron and muon number violating muonium-antimuonium oscillation process can proceed provided neutrinos have non-zero masses and mix among the various generations. Modifying the Standard Model only by the inclusion of singlet right handed neutrino fields and allowing for general neutrino masses and mixings, the leading order matrix element contributing to this process is computed. For the particularly interesting case where the neutrino masses are generated by a see-saw mechanism with a very large Majorana mass $M_R>>M_W$, it is found that both the very light and very heavy Majorana neut…
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…
Flavor oscillation of traveling neutrinos is treated by solving the one-dimensional Dirac equation for massive fermions. The solutions are given in terms of squeezed coherent state as mutual eigenfunctions of parity operator and the corresponding Hamiltonian, both represented in bosonic creation and annihilation operators. It was shown that a mono-energetic state is non-normalizable, and a normalizable Gaussian wave packet, when of pure parity, cannot propagate. A physical state for a traveling neutrino beam would be represented as a normalizable Gaussian wave packet of equally-weighted mixing…
We examine the potential of the future medium-baseline reactor neutrino oscillation (MBRO) experiments in studying neutrino wave-packet impact. In our study, we treat neutrinos as wave packets and use the corresponding neutrino flavor transition probabilities. The delocalization, separation and spreading of the wave packets lead to decoherence and dispersion effects, which modify the plane-wave neutrino oscillation pattern, by amounts that depend on the energy uncertainties in the initial neutrino wave packets. We find that MBRO experiments could be sensitive to the wave-packet impact, since t…
We derive the neutrino flavor transition probabilities with the neutrino treated as a wave packet. The decoherence and dispersion effects from the wave-packet treatment show up as damping and phase-shifting of the plane-wave neutrino oscillation patterns. If the energy uncertainty in the initial neutrino wave packet is larger than around 0.01 of the neutrino energy, the decoherence and dispersion effects would degrade the sensitivity of reactor neutrino experiments to mass hierarchy measurement to lower than 3 $σ$ confidence level.
In arXiv:2209.00561 our treatment arXiv:2208.03736 of effects of particles emitted together with neutrinos on neutrino wave packets is criticized on several grounds. We show here that this criticism is based on misinterpretation of our results and is invalid. Our conclusions and, in particular, the conclusion that neutrino wave packet separation effects are unobservable in reactor and neutrino source experiments, remain unchanged.
We analyze oscillations of intermediate neutrinos in terms of the scattering of particles described by Gaussian wave packets. We study a scalar model as in a previous paper (I) but in realistic situations, where the two particles of the initial state and final state are wave packets and neutrinos are in the intermediate state. The oscillation of the intermediate neutrino is found from the time evolution of the total transition probability between the initial state and final state. The effect of a finite lifetime and a finite relaxation time are also studied. We find that the oscillation patter…
We analyze both chirality-changing and chirality-preserving transitions of Dirac-Majorana neutrinos. In vacuum, the first ones are suppressed with respect to the others due to helicity conservation and the interactions with a (``normal'') medium practically does not affect the expressions of the probabilities for these transitions, even if the amplitudes of oscillations slightly change. For usual situations involving relativistic neutrinos we find no resonant enhancement for all flavour-conserving transitions. However, for very light neutrinos propagating in superdense media, the pattern of os…
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.
We report about recent results on Dirac wave packets in the treatment of neutrino flavor oscillation where the initial localization of a spinor state implies an interference between positive and negative energy components of mass-eigenstate wave packets. A satisfactory description of fermionic particles requires the use of the Dirac equation as evolution equation for the mass-eigenstates. In this context, a new flavor conversion formula can be obtained when the effects of chiral oscillation are taken into account. Our study leads to the conclusion that the fermionic nature of the particles, wh…
The temporal and spatial coherence widths of the microscopic process by which a neutrino is detected are incorporated in the quantum mechanical wave packet treatment of neutrino oscillations, confirming the observation of Kiers, Nussinov and Weiss that an accurate measurement of the energies of the particles participating in the detection process can increase the coherence length. However, the wave packet treatment presented here shows that the coherence length has an upper bound, determined by the neutrino energy and the mass-squared difference, beyond which the coherence of the oscillation p…
In the recent note we argued that most of the available positive and negative neutrino oscillation data can be incorporated in a four-neutrino weak interaction model with one physical condition: thorough maximal mixing of the neutrino components in each of the two mass doublets. On the level of CP-invariance an extended Pontecorvo analogy between the neutrino oscillations and the K^0-meson oscillations, which implied maximal violation of the lepton charge conservation in the neutrino mass matrix exclusively, can afford a physical clue to the three data dictated assumptions in a model with thre…
The wave-packet treatment of neutrino oscillation developed previously is extended to the case in which momentum distribution functions are taken to be a Gaussian form with both central values and dispersions depending on the mass eigenstates of the neutrinos. It is shown among other things that the velocity of the neutrino wave packets does not in general agree with what one would expect classically and that relativistic neutrinos emitted from pions nevertheless do follow, to a good approximation, the classical trajectory.
A quantum wave packet treatment of neutrino and neutral K and B meson oscillations is presented which incorporates the recoil particle in the production process, and includes the effect of the localization and lifetime of the source assumed to be a resonance or unstable particle. This approach removes the ambiguities in the conventional single particle treatment of these oscillations with the recoil particle. A fundamental connection between the stochastic decay time of the source and the space-time coordinates of the correlated final state particles is derived.
We point out three apparent inconsistencies in the treatment of oscillation coherence from reactor neutrino and source neutrino experiments in recent paper "Damping of neutrino oscillations, decoherence and the lengths of neutrino wave packets''. First, that the dependence of the oscillation probability upon the subsequent interactions of entangled recoil particles implies causality violations and in some situations superluminal signaling; second, that integrating over a non-orthogonal basis for the entangled recoil leads to unphysical effects; and third, that the question of what interactions…
We derive the effective Hamiltonian describing collective oscillations of Majorana neutrinos with a transition magnetic moment, allowing for the presence of scalar and pseudoscalar nonstandard neutrino self-interactions (NSSIs). Using this Hamiltonian, we analyze new flavor instability channels of collective oscillations in a core-collapse supernova environment that open up in the presence of a small but nonzero neutrino magnetic moment. It turns out that, contrary to certain claims in the literature, within the minimally extended Standard Model (i.e., without NSSIs), no new instabilities aris…
Assuming the Majorana masses of $ν_e$ and the linear combination $c ν_τ- s ν_μ$ to be equal from their couplings to a heavy scalar triplet $ξ$, I show that their radiative splitting is given by $Δm^2/m_ν^2 = (3 c^2/4 π^2) (G_F/\sqrt 2) m_τ^2 \ln (m_ξ^2/m_W^2)$. This is applicable to the small-angle matter-enhanced oscillation solution of the solar neutrino deficit and restricts $m_ν$ to be between 0.20 and 0.36 eV if $c^2 = 0.7$ and $m_ξ= 10^{14}$ GeV.
The effects originated in dispersion with time on spreading of wave packets for the time-integrated two-flavor neutrino oscillation probabilities in vacuum are studied in the context of a field theory treatment. The neutrino flavor states are written as superpositions of neutrino mass eigenstates which are described by localized wave packets. This study is performed for the limit of nearly degenerate masses and considering an expansion of the energy until third order in the momentum. We obtain that the time-integrated neutrino oscillation probabilities are suppressed by a factor $1/L^2$ for th…
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 study the impact of the dynamical Lorentz symmetry breaking induced by the auxiliary gauge fields of neutrino on the oscillations probability at DUNE. The DLSB introduces an alternative energy-momentum relation of the neutrinos and thus results in a new oscillation probability. We extend the previously proposed four-Majorana fermion model that gives rise to DLSB after the type II seesaw mechanism by considering the electron neutrino forward scattering when passing through a medium. Moreover, we incorporate the three-flavor neutrino states, which introduce the CP-violation term inside the os…
We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavour system, as shown explicitly for SN1987A.
We study the implications of neutrino oscillations with maximal mixing for the neutrino Dirac and Majorana matrices in the see-saw mechanism for three non degenerate neutrino masses. We find the form of the Dirac matrix for a structure-less Majorana matrix and, conversely, the structure of the Majorana matrix if the Dirac matrix is according to our naive intuition. We give some examples of Majorana matrices that, in a 3 X 3 context, lead to maximal mixing without too much fine tuning and cross talk with the Dirac input.
