Correlations exhibited by neutrino oscillations are studied via quantum information theoretic quantities. We show that the strongest type of entanglement, genuine multipartite entanglement, is persistent in the flavour changing states. We prove the existence of Bell-type nonlocal features, in both its absolute and genuine avatars. Finally, we show that a measure of nonclassicality, dissension, which is a generalization of quantum discord to the tripartite case, is nonzero for almost the entire range of time in the evolution of an initial electron-neutrino. Via these quantum information theoretic quantities capturing different aspects of quantum correlations, we elucidate the differences between the flavour types, shedding light on the quantum-information theoretic aspects of the weak force.
We show that, in the relativistic limit, the quantum theory of neutrino oscillations can be described through the theory of weak measurements with pre and post-selection. The weak nature of neutrino detection allows simultaneous determination of flavor and energy without problems related to the collapse of the wavefunction. Together with post-selection, a non-trivial quantum interference emerges, allowing one to describe a flavor neutrino as one single particle, despite its superposition of masses. We write down the flavor equation of motion and calculate the flavor oscillation probability by …
Spontaneous collapse models aim at solving the measurement problem of quantum mechanics by introducing collapse of wave function as an ontologically objective mechanism that suppresses macroscopic superpositions. In particular, the strength of collapse depends on the mass of the system. Flavor oscillating systems such as neutral mesons feature superpositions of states of different masses and, hence, could be used to test the validity of spontaneous collapse models. Recently, it has been shown that the mass-proportional CSL model causes exponential damping of the neutral meson oscillations whic…
We demonstrate that sizable neutrino flavor oscillations can be generated in a model with large extra spacetime dimensions even if the physics on the brane is flavor-diagonal, the bulk neutrino theory is flavor-neutral, and the brane/bulk couplings are flavor-blind. This is thus a compact model for addressing neutrino flavor oscillations in higher dimensions. We also discuss several phenomenological aspects of the ``bulk-mediated'' neutrino oscillations inherent in this model, and show that this model contains some potentially important new phenomenological features in the limit of large brane…
We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between non-orthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CP conservation, our study shows for the first time that there is a geometri…
We comment on the paper ``Remarks on flavor-neutrino propagators and oscillation formulae'' [Phys. Rev. D64, 013011 (2001)]. We show that the conclusions presented in that paper do not apply to the exact field theoretical oscillation formulae obtained in the BV formalism (for three flavors) which are free from the dependence on arbitrary mass parameters, account for CP violation and reduce to the usual quantum mechanical (Pontecorvo) three flavor oscillation formulae in the relativistic limit.
In a recent paper [arXiv:0901.0790], we showed that there is a neat geometric interpretation of two flavor neutrino oscillation formulae, and that the geometric phase involved in the physics of oscillations is restricted to be topological as long as CP is conserved. This paper has been criticised by Bhandari [arXiv:1006.5935]. In the present note, we show that the criticisms are not valid and only reflect his failure to understand some crucial points.
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.
Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum mixing for neutrinos. Once the mass-eigenstates that support flavor oscillations are identified as three-{\em qubit} modes, a decoherence scale can be extracted from correlation quantifiers, namely the entanglement of formation and the logarithmic negativity. Such a decoherence scale is compared with the coherence length of damped oscillations. Damping signat…
We consider neutrino oscillations as non stationary phenomenon based on Schrodinger evolution equation and mixed states of neutrinos with definite flavors. We show that time-energy uncertainty relation plays a crucial role in neutrino oscillations. We compare neutrino oscillations with $B_{d}^{0}\leftrightarrows\bar B_{d}^{0}$ oscillations.
A short review on studies of neutrino flavor oscillations in moving with a constant speed matter is presented. Then neutrino flavor oscillations in matter moving with acceleration are considered. We develop an approach that is valid for both non-relativistic and relativistic matter motion. For both these cases the effective neutrino potentials in accelerating matter are obtained and neutrino flavor oscillation probabilities and the Mikheyev-Smirnov-Wolfenstein resonance conditions are evaluated. The obtained results in the limit of zero matter acceleration reproduce the corresponding expressio…
In the context of quantum field theory, we derive flavor energy uncertainty relations for neutrino oscillations. By identifying the non conserved flavor charges with the clock observables, we arrive at the Mandelstam Tamm version of time energy uncertainty relations. In the ultrarelativistic limit these relations yield the well known condition for neutrino oscillations. Ensuing non relativistic corrections to the latter are explicitly evaluated. The analogy among flavor states and unstable particles and a novel interpretation of our uncertainty relations, based on the unitary inequivalence of …
As a possible approach to the neutrino oscillation on the basis of quantum field theory, the expectation values of the flavor-neutrino currents are investigated by employing the finite-time transition matrix in the interaction representation. Such expectation values give us in the simplest form a possible way of treating the neutrino oscillation without recourse to any one flavor-neutrino states. The present paper is devoted to presenting the formulation and the main structures of the relevant expectation values.
We study spin and spin-flavor oscillations of Dirac neutrinos in a plane electromagnetic wave with circular polarization. The evolution of massive neutrinos with nonzero magnetic moments in the field of an electromagnetic wave is based on the exact solution of the Dirac-Pauli equation. We formulate the initial condition problem to describe spin-flavor oscillations in an electromagnetic wave. The transition probabilities for spin and spin-flavor oscillations are obtained. In case of spin-flavor oscillations, we analyze the transition and survival probabilities for different neutrino magnetic mo…
We analyze phenomenological aspects of the quantum field theoretical formulation of meson mixing and obtain the exact oscillation formula in the presence of the decay. This formula is different from quantum mechanical formula by additional high-frequency oscillation terms. In the infinite volume limit, the space of the flavor quantum states is unitarily inequivalent to the space of energy eigenstates.
Extreme conditions present in the interiors of the core-collapse supernovae make neutrino-neutrino interactions not only feasible but dominant in specific regions, leading to the non-linear evolution of the neutrino flavor. Results obtained when such collective neutrino oscillations are treated in the mean-field approximation deviate from the results using the many-body picture because of the ignored quantum correlations. We present the first three flavor many-body calculations of the collective neutrino oscillations. The entanglement is quantified in terms of the entanglement entropy and the …
Neutrino flavor oscillations are discussed in terms of two coupled Dirac fields. The interacting Lagrangian is diagonalized to obtain the exact eigenvalues and eigenfunctions. Flavor wave functions are then derived directly from the quantized neutrino fields. Probability density obtained by squaring these wave functions upon taking into account the neutrino chirality are in agreement with the standard neutrino oscillation probabilities.
Recently, it was pointed out that the solar and atmospheric neutrino deficits can be explained by oscillations between electroweak doublet and singlet neutrinos in the model of Majorana neutrinos. However, since the model includes no flavor mixing, it cannot explain the recent LSND result. We extend the model to include the flavor mixing, and obtain the explanation of the LSND result together with the solar and atmospheric neutrino deficits. The requirement for the neutrinos to be the hot dark matter selects out only the vacuum oscillation solution to the solar neutrino deficit.
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.
We derive the reduction formula, which expresses the survival rate for the three-flavor neutrino oscillation by the two-flavor one, to the next-to-leading order in case there is one resonance due to the matter effect. We numerically find that the next-to-leading reduction formula is extremely accurate and the improvement is relevant for the precision test of solar neutrino oscillation and the indirect measurment of CP violation in the leptonic sector. We also derive the reduction formula, which is slightly different from that previously obtained, in case there are two resonances. We numericall…
We present a formalism for the flavor oscillation of unstable particles that relies only upon the structure of the time Fourier-transformed two-point Green's function. We derive exact oscillation probability and integrated oscillation probability formulae, and verify that our results reproduce the known results for both neutrino and neutral meson oscillation in the expected regimes of parameter space. The generality of our approach permits us to investigate flavor oscillation in exotic parameter regimes, and present the corresponding oscillation formulae.
We compare the effectiveness of various tests of three-flavor mixing in future long-baseline neutrino oscillation experiments. We analyze a representative case of mixing in a simplified three-flavor scheme, whose relevant parameters are one neutrino mass-square difference, $m^2$, and two mixing angles, $ψ$ and $ϕ$. We show that an unambiguous determination of $ψ$ and $ϕ$ requires flavor-appearance tests in accelerator experiments, as well as supplementary information from reactor experiments.
The standard theory of neutrino oscillations is reviewed, highlighting the main assumptions: the definition of the flavor states, the equal-momentum assumption and the time = distance assumption. It is shown that the standard flavor states are correct approximations of the states that describe neutrinos in oscillation experiments. The equal-momentum assumption is shown to be unnecessary for the derivation of the oscillation probability. The time = distance assumption derives from the wave-packet character of the propagating neutrinos. We present a simple quantum-mechanical wave-packet model wh…
A brief survey of the history of the neutrino oscillation is presented. Here emphasis is laid on the topics around the first proposal of neutrino flavor oscillation by Nagoya group in 60's. Main contents are presented in my opening address "Birth of Neutrino Oscillation" at the NOW' 98, Amsterdam, hep-ph/9811358, but added some detail of the other topics, especially a first calculation of decay processes $μ\to e + γ$ and $ν_2 \to ν_1 + γ$ in terms of neutrino flavor mixing, and some arguments relating to the massive neutrino.
We numerically solve the evolution equations of neutrino three-flavor density matrices, and show that, even if neutrino oscillations mix neutrino flavors, large lepton number asymmetries are still allowed in certain limits by Big Bang Nucleosynthesis (BBN).
Analytic formulas are presented for three flavor neutrino oscillations in matter in the plane wave approximation. We calculate in particular the time evolution operator in both mass and flavor bases. We also find the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter. The application of this to neutrino oscillations for both atmospheric and long baseline neutrinos in a mantle-core-mantle step function model of the Earth's matter density profile is discussed.
In this talk, we consider the interplay of fundamental and matter-induced T-violating effects in neutrino oscillations in matter. We present a simple approximative analytical formula for the T-violating probability asymmetry for three flavor neutrino oscillations in matter with an arbitrary density profile. We also discuss some implications of the obtained results. Since there are no T-violating effects in two flavor neutrino case (in the limit of vanshing $θ_{13}$ or $Δm_{21}^2$, the three flavor neutrino oscillations reduces to the two flavor ones), the T-violating probability asymmetry can,…
A unique description avoiding confusion is presented for all flavor oscillation experiments in which particles of a definite flavor are emitted from a localized source. The probability for finding a particle with the wrong flavor must vanish at the position of the source for all times. This condition requires flavor-time and flavor-energy factorizations which determine uniquely the flavor mixture observed at a detector in the oscillation region; i.e. where the overlaps between the wave packets for different mass eigenstates are almost complete. Oscillation periods calculated for ``gedanken'' t…
We clarify the domain needed for the mixing angles in three flavor neutrino oscillations. By comparing the ranges of the transition probabilities as functions of the domains of the mixing angles, we show that it is necessary and sufficient to let all mixing angles be in $[ 0, π/2 ]$. This holds irrespectively of any assumptions on the neutrino mass squared differences.
If one assumes solar and LSND neutrino oscillations to explain the corresponding data, then the atmospheric neutrino deficit cannot be accommodated within the Standard Model with three light flavors, unless one ignores the data's zenith-angle dependence. We propose a novel solution to this problem by postulating large anomalous diagonal $ν_τ$-quark interactions which affect $ν_μ- ν_τ$ oscillations traversing the Earth and induce the observed zenith-angle dependence.
We formulate direct, neutrino flavor-changing interactions in a framework that fits smoothly with the parameterization of two-and three-state mixing of massive neutrino states. We show that even small direct interaction strengths could have important consequences for the interpretation of currently running and proposed oscillation experiments. The oscillation amplitude and the borders of the allowed regions in two-and three-flavor mixing parameter space can be sensitieve to the presence of direct interactions when the transition probability is small. We use extensively the high sensitivity of …
A unique description avoiding confusion is presented for all flavor-oscillation experiments in which particles of a definite flavor are emitted from a localized source. The probability for finding a particle with the wrong flavor must vanish at the position of the source for all times. This condition requires flavor-time and flavor-energy factorizations which determine uniquely the flavor mixture observed at a detector in the oscillation region; i.e. where the overlaps between the wave packets for different mass eigenstates differ negligibly from 100\%. The translation of a ``gedanken'' experi…
Recent experimental research progress of solar neutrino and neutrino oscillation reveals that neutrinos do have nonzero mass, which poses a serious challenge to theoretical physics. Two symmetries, the common invariance under the space-time inversion and the invariance or violation to maximum under the space inversion are analyzed for Dirac equation or the equation for superluminal neutrino respectively. Then a simple three-flavor model containing only one parameter is proposed and the relations among neutrino oscillation, parity violation and superluminal property are emphasized.
The recent observations of atmospheric nu events from the Super-Kamiokande experiment are compatible with three-flavor neutrino oscillations, occurring dominantly in the nu_mu<--->nu_tau channel and subdominantly in the nu_mu<--->nu_e channel. We present an updated analysis of the three-flavor mass-mixing parameters consistent with the present phenomenology, including the latest 45 kTy data sample from Super-Kamiokande. A comparison with our previous results, based on 33 kTy data, shows that the oscillation evidence is strengthened, and that the neutrino mass-mixing parameters are constrained …
On the basis of quantum field theory, we consider a unified description of various processes accompanied by neutrinos, namely weak decays and oscillation processes. The structures of the expectation values of flavor-neutrino numbers with respect to neutrino-source hadron state are investigated. Due to the smallness of neutrino masses, we naturally obtain the old (i.e. pre-mixing) formulas of decay probabilities. Together, it is shown that the oscillation formulas, similar to the usual ones, are applied irrespectively of the details of neutrino-producing processes. The derived oscillation formu…
Neutrinos can undergo flavor--oscillations if they possess flavor--dependent couplings to the surrounding gravitational field (the VEP mechanism). The neutrino fields can be massless, in accord with the Minimal Standard Model, but at the expense of the Einstein Equivalence Principle. We show that it is possible to explain the observed Solar Neutrino data from the various experiments using the VEP solution in a realistic three--generation framework, and further note how the three--flavor model can offer larger allowed regions of parameter space over the two--flavor models.
We discuss here some flavor structure aspects of the complete theory of supersymmetry without R-parity addressed from the perspective of fitting neutrino oscillation data based on the recent Super-Kamiokande result. The single-VEV parametrization of supersymmetry without R-parity is first reviewed, illustrating some important features not generally appreciated. For the flavor structure discussions, a naive, flavor model independent, analysis is presented, from which a few interesting things can be learned.
The general formalism for the description of neutrino oscillations in arbitrary rapidly varying external fields is elaborated. We obtain the new effective Hamiltonian which determines the evolution of the averaged neutrino wave function. The general technique is applied to the neutrino oscillations in rapidly varying magnetic fields. We evaluate the transition probabilities of the neutrino spin-flavor oscillations in magnetic fields of the Sun and compare them with the numerical solutions of the Schroedinger equation with the exact Hamiltonian.
Oscillation studies play a central role in elucidating at least some aspects of the flavor problem. Here we examine the status of the predictions of a lepton quarticity flavor theory of neutrino oscillations against the existing global sample of oscillation data. By performing quantitative simulations we also determine the potential of the upcoming DUNE experiment in narrowing down the currently ill-measured oscillation parameters $θ_{23}$ and $δ_{\text{CP}}$. We present the expected improved sensitivity on these parameters for different assumptions.
Superkamiokande atmospheric neutrino data for 535 days are analyzed in the framework of three flavor oscillations with mass hierarchy. It is shown that the best fit point is very close to the pure maximal $ν_μ\leftrightarrowν_τ$ case and $Δm^2 \simeq 7\times10^{-3}$ eV$^2$. The allowed region at 90 %CL is given and the implications to the long baseline experiments are briefly discussed.
We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits to give a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrate some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and tha…
The physics of a superconductor subjected to a magnetic field is known to be equivalent to neutrino oscillations. Examining the properties of singlet-triplet oscillations in the magnetic field, a sterile neutrino--shown to be a Majorana fermion--is suggested to be represented by singlet Cooper pairs and moderates flavor oscillations between three flavor neutrinos (triplet Cooper pairs). A superconductor-exchange spring system's rotating magnetization profile is used to simulate the mass-flavor oscillations in the neutrino case and the physics of neutrino oscillations are discussed. Symmetry pr…
Abstract We study the analytic expression for four flavor neutrino oscillation in the presence of matter. We calculate the time evolution operator on flavor and mass basis. We find the matter dependent mass square difference and neutrino transition probabilities for (3+1) four flavor neutrino oscillation.
The three neutrino mass matrices in the $SU(5)\times U(2)$ model are studied focusing on the neutrino oscillation experiments. The atmospheric neutrino anomaly could be explained by the large $ν_μ - ν_τ$ oscillation. The long baseline experiments are expected to detect signatures of the neutrino oscillation even if the atmospheric neutrino anomaly is not due to the neutrino oscillation. However, the model cannot solve the solar neutrino deficit while it could be reconciled with the LSND data.
We review the application of the relativistic quantum mechanics method for the description of neutrino oscillations for the studies of spin-flavor oscillations in background matter under the influence of a plane electromagnetic wave. Basing on the new exact solution of the Dirac-Pauli equation for a massive neutrino in the given external fields, we derive the transition probabilities for spin and spin-flavor oscillations. The obtained expressions are analyzed for different types of the neutrino magnetic moments. Our results are compared with findings of other authors.
We investigate neutrino flavor oscillations in vacuum within a general conformal coupling model. We first examine the flavor oscillations within the plane-wave description of neutrinos, and then we extend our analysis to the wavepacket-based formalism. In both cases, we derive the general formulas for the flavor transition probability in arbitrary static and spherically symmetric spacetimes. We thoroughly discuss and assess in both cases the different possible ways -- dictated by the presence of the conformal coupling -- of computing the flavor transition probability. We show that the conforma…
This is the report from the Snowmass NF01 topical group and colleagues on the current status and expected future progress to understand the three-flavor neutrino oscillation picture.
Neutrinos and antineutrinos emitted from a core collapse supernova interact among themselves, giving rise to collective flavor conversion effects that are significant near the neutrinosphere. We develop a formalism to analyze these collective effects in the complete three-flavor framework. It naturally generalizes the spin-precession analogy to three flavors and is capable of analytically describing phenomena like vacuum/MSW oscillations, synchronized oscillations, bipolar oscillations and spectral split. Using the formalism, we demonstrate that the flavor conversions may be "factorized" into …
By resorting to recent results on the relativistic currents for mixed (flavor) fields, we calculate a space-time dependent neutrino oscillation formula in Quantum Field Theory. Our formulation provides an alternative to existing approaches for the derivation of space dependent oscillation formulas and it also accounts for the corrections due to the non-trivial nature of the flavor vacuum. By exploring different limits of our formula, we recover already known results. We study in detail the case of one-dimensional propagation with gaussian wavepackets both in the relativistic and in the non-rel…
We study flavor oscillations of low energy neutrinos propagating in dense matter of a rotating neutron star. On the basis of the exact solutions of the wave equations for neutrinos mass eigenstates we derive the transition probability for neutrinos having big initial angular momentum. It is found that flavor oscillations of neutrinos with energies of several electron-Volts can be resonancely enhanced.
We have studied structures of the neutrino flavor mixing matrix focusing on the neutrino oscillations at CHORUS and NOMAD as well as the one at LSND(or KARMEN). We have assumed two typical neutrino mass hierarchies $m_3\simeq m_2\gg m_1$ and $m_3\gg m_2\gg m_1({\rm or}\simeq m_1)$. Taking into account the see-saw mechanism of neutrino masses, the reasonable neutrino flavor mixing patterns have been discussed. The observation of the neutrino oscillation at CHORUS and NOMAD presents us the important constraint for the structure of the neutrino flavor mixing matrix. The atomospheric neutrino anom…
We present an updated analysis of the current solar neutrino data in terms of three-flavor oscillations, including the additional constraints coming from terrestrial neutrino oscillation searches at the CHOOZ (reactor), Super-Kamiokande (atmospheric), and KEK-to-Kamioka (accelerator) experiments. The best fit is reached for the subcase of two-family mixing, and the additional admixture with the third neutrino is severely limited. We discuss the relevant features of the globally allowed regions in the oscillation parameter space, as well as their impact on the amplitude of possible CP-violation…
Downward going atmospheric tau neutrino flux is estimated in the presence of three neutrino flavor oscillations for 1 GeV < E < 10^3 GeV. The relative differences between the three and purely two neutrino flavor oscillations are elaborated. As an implication, the downward going atmospheric tau neutrino flux is compared with the galactic plane tau neutrino flux that is also estimated in the presence of three neutrino flavor oscillations. It is pointed out that the galactic plane tau neutrino flux dominates over the downward going atmospheric tau neutrino flux until E \sim 10 GeV.
In the early Universe, as well as in supernovae and merging neutron stars, neutrinos have such high densities that they affect each other and exhibit collective flavor oscillations. A crucial ingredient for fast collective flavor oscillations is that the electron lepton number (ELN) distribution changes its sign as a function of direction, i.e., has a zero crossing. We present a study in two dimensions and show how fast flavor oscillations depend on the ELN and its crossings. We show that a large number of crossings can inhibit flavor oscillations. This may be a natural self-limiting mechanism…
The Lagrangian that is normally associated with Dirac neutrinos is analyzed in a complete and simple way through field theory. It is found that the elements of the neutrino mass matrix are field strength renormalization constants and that the flavor fields can be directly applied to the one-particle energy states through these rescaling factors. Moreover this Lagrangian describes neutrinos which are in a state of mixed flavor at any space-time point and therefore does not describe the phenomenology of neutrino oscillations properly, except in the ultra-relativistic limit where such a descripti…
