Neutrino Oscillations In Vacuum Research Articles

Neutrino oscillations as a single Feynman diagram

We propose an approach to neutrino oscillations in vacuum, based on quantum field theory (QFT). The neutrino emission and detection are identified with the charged-current vertices of a single second-order Feynman diagram for the underlying process, enclosing neutrino propagation between these two points. The key point of the presented approach is the definition of the space-time setup typical for neutrino oscillation experiments, implying macroscopically large but finite volumes of the source and detector separated by a sufficiently large distance L. We derive an L-dependent master formula for the charged lepton production rate, which provides the QFT basis for the analysis of neutrino oscillations. This formula depends on the underlying process and is not reducible to the conventional approach resorting to the concept of neutrino oscillation probability, which originates from non-relativistic quantum mechanics. We demonstrate that for some particular choice of the underlying process the derived master formula approximately coincides with the conventional one under some assumptions. In support to presented approach we show that it provides the QFT framework not only for neutrino–neutrino but also neutrino-antineutrino oscillations. It is also argued that the proposed formalism allows us to consistently incorporate medium effects, when neutrinos oscillate in dense matter.

Neutrino oscillations by a manifestly coherent mechanism and massless vs. massive neutrinos

The neutrino oscillations in vacuum are derived in a manifestly coherent scheme. The mechanism is operative in a quantum field theoretical framework, justifying nevertheless a formal analogy with quantum mechanical two- (or more) level systems and their oscillatory behaviour. Both the flavour states and the massive states are eigenstates of certain Hamiltonians which, in special conditions, can be argued to share the same Hilbert space of states. In this scheme, flavour neutrinos are massless and play the role of asymptotic states for any interactions, including the weak interactions, while massive neutrinos are effective propagation states. The vacuum is interpreted as a medium, where the flavour neutrinos undergo coherent forward scatterings which modify their energy and mix their flavours. The treatment of matter conversion and MSW effect fits in naturally; the extension to other neutral particle oscillations, like K0−K¯0, is straightforward. The scheme is eclectic insofar as it combines seamlessly quantum field theory and quantum mechanics.

Inference of bipolar neutrino flavor oscillations near a core-collapse supernova based on multiple measurements at Earth

Neutrinos in compact-object environments, such as core-collapse supernovae, can experience various kinds of collective effects in flavor space, engendered by neutrino-neutrino interactions. These include "bipolar" collective oscillations, which are exhibited by neutrino ensembles where different flavors dominate at different energies. Considering the importance of neutrinos in the dynamics and nucleosynthesis in these environments, it is desirable to ascertain whether an Earth-based detection could contain signatures of bipolar oscillations that occurred within a supernova envelope. To that end, we continue examining a cost-function formulation of statistical data assimilation (SDA) to infer solutions to a small-scale model of neutrino flavor transformation. SDA is an inference paradigm designed to optimize a model with sparse data. Our model consists of two mono-energetic neutrino beams with different energies emanating from a source and coherently interacting with each other and with a matter background, with time-varying interaction strengths. We attempt to infer flavor transformation histories of these beams using simulated measurements of the flavor content at locations in vacuum (that is, far from the source), which could in principle correspond to earth-based detectors. Within the scope of this small-scale model, we found that: (i) based on such measurements, the SDA procedure is able to infer \textit{whether} bipolar oscillations had occurred within the protoneutron star envelope, and (ii) if the measurements are able to sample the full amplitude of the neutrino oscillations in vacuum, then the amplitude of the prior bipolar oscillations is also well predicted. This result intimates that the inference paradigm can well complement numerical integration codes, via its ability to infer flavor evolution at physically inaccessible locations.

Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes

Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries of the oscillation parameters. We elucidate the ${2}^{7}$ parameter symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an additional set of ${2}^{7}$ parameter symmetries of the matter parameters exists. Due to the complexity of the exact expressions for neutrino oscillations in matter, numerous approximations have been developed; we show that under certain assumptions approximate expressions have at most ${2}^{6}$ additional parameter symmetries of the matter parameters. We also include one parameter symmetry related to the large mixing angle (LMA)-dark degeneracy that holds under the assumption of $CPT$ invariance; this adds one additional factor of 2 to all of the above cases. Explicit, nontrivial examples are given of how physical observables in neutrino oscillations, such as the probabilities, $CP$ violation, the position of the solar and atmospheric resonance, and the effective $\mathrm{\ensuremath{\Delta}}{m}^{2}$'s for disappearance probabilities, are invariant under all of the above symmetries. We investigate which of these parameter symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.

Revisiting the quantum field theory of neutrino oscillations in vacuum

We consider neutrino oscillations in vacuum in the framework of quantum field theory in which neutrino production and detection processes are part of a single Feynman diagram and the corresponding cross section is computed in the standard way, i.e. with final states represented by plane waves. We use assumptions which are realized in actual experiments and concentrate on the detection process. Moreover, we also allow for a finite time interval of length τ during which the detector records neutrino events. In this context we are motivated by accelerator-neutrino oscillation experiments where data taking is synchronized in time with the proton spill time of the accelerator. Given the final momenta and the direction of neutrino propagation, we find that in the oscillation amplitude—for all practical purposes—the neutrino energy Q is fixed, apart from an interval of order 2πℏ/τ around a mean energy this is an expression of energy non-conservation or the time-energy uncertainty relation in the detection process due to . We derive in excellent approximation that in the amplitude the oscillation effect originates from massive neutrinos with the same energy , i.e. oscillations take place in space without any decoherece effect, while the remaining integration over Q in the interval of order 2πℏ/τ around results in a time-correlation function expressing the time delay between neutrino production and detection.

Neutrinos in curved spacetime: Particle mixing and flavor oscillations

We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the non--trivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulae. We compute the formulae explicitly in the spatially flat FLRW metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of previous analyses when the quantum mechanical limit is considered.

Flavor Mixing and the Permutation Symmetry among Generations

In the standard model, the permutation symmetry among the three generations of fundamental fermions is usually regarded to be broken by the Higgs couplings. It is found that the symmetry is restored if we include the mass matrix parameters as physical variables which transform appropriately under the symmetry operation. Known relations between these variables, such as the renormalization group equations, as well as formulas for neutrino oscillations (in vacuum and in matter), are shown to be covariant tensor equations under the permutation symmetry group.

Neutrino oscillations in accelerated frames

We discuss neutrino oscillations in vacuum from the point of view of a uniformly accelerated observer. A covariant definition of quantum phase is introduced with the aim of generalizing the standard expression of the oscillation amplitude to the accelerating frame. By way of illustration, we address a simplified two-flavor model with relativistic neutrinos, showing that inertial effects on the usual Pontecorvo formula are intimately related to the energy redshift. Phenomenological aspects are preliminarily analyzed in the context of atmospheric neutrinos. Finally, we discuss a gedanken experiment in order to investigate our formalism in the regime of extreme acceleration.

On neutrino mixing in matter and CP and T violation effects in neutrino oscillations

Aspects of 3-neutrino mixing and oscillations in vacuum and in matter with constant density are investigated working with a real form of the neutrino Hamiltonian. We find the (approximate) equalities θ23m=θ23 and δm=δ, θ23 (θ23m) and δ (δm) being respectively the atmospheric neutrino mixing angle and the Dirac CP violation phase in vacuum (in matter) of the neutrino mixing matrix, which are shown to represent excellent approximations for the conditions of the T2K (T2HK), T2HKK, NOνA and DUNE neutrino oscillation experiments. A new derivation of the known relation sin⁡2θ23msin⁡δm=sin⁡2θ23sin⁡δ is presented and it is used to obtain a correlation between the shifts of θ23 and δ due to the matter effect. A derivation of the relation between the rephasing invariants which determine the magnitude of CP and T violating effects in 3-flavour neutrino oscillations in vacuum, JCP, and of the T violating effects in matter with constant density, JTm≡Jm, reported in [1] without a proof, is presented. It is shown that the function F which appears in this relation, Jm=JCPF, and whose explicit form was given in [1], coincides with the function F˜ in the similar relation Jm=JCPF˜ derived in [2], although F and F˜ are expressed in terms of different sets of neutrino mass and mixing parameters and have completely different forms.

On the compatibility of the IceCube results with a universal neutrino spectrum

There is mounting evidence that the IceCube findings cannot be described simply invoking a single power-law spectrum for cosmic neutrinos. We discuss which the minimal modifications are of the spectrum that are required by the existing observations and we obtain a universal cosmic neutrino spectrum, i.e. valid for all neutrino flavors. Our approach to such task can be outlined in three points: (1) we rely on the throughgoing muon analysis above 200 TeV and on the high-energy starting events (HESE) analysis below this energy, requiring the continuity of the spectrum; (2) we assume that cosmic neutrinos are subject to three-flavor neutrino oscillations in vacuum; (3) we make no assumption on the astrophysical mechanism of production, except for no nu _tau (overline{nu }_tau ) component at the source. We test our model using the information provided by HESE shower-like events and by the lack of double pulses and resonant events. We find that a two-component power-law spectrum is compatible with all observations. The model agrees with the standard picture of pion decay as a source of neutrinos, and indicates a slight preference for a pgamma mechanism of production. We discuss the tension between the HESE and the “throughgoing muons” datasets around few tens TeV, focussing on the angular distributions of the spectra. The expected number of smoking-gun signatures of nu _tau -induced events (referred to as double pulses) is quantified: in the baseline model we predict 0.65 double pulse events in 5.7 years. Uncertainties in the predictions are quantified.

Collective neutrino oscillations and neutrino wave packets

Effects of decoherence by wave packet separation on collective neutrino oscillations in dense neutrino gases are considered. We estimate the length of the wave packets of neutrinos produced in core collapse supernovae and the expected neutrino coherence length, and then proceed to consider the decoherence effects within the density matrix formalism of neutrino flavour transitions. First, we demonstrate that for neutrino oscillations in vacuum the decoherence effects are described by a damping term in the equation of motion of the density matrix of a neutrino as a whole (as contrasted to that of the fixed-momentum components of the neutrino density matrix). Next, we consider neutrino oscillations in ordinary matter and dense neutrino backgrounds, both in the adiabatic and non-adiabatic regimes. In the latter case we study two specific models of adiabaticity violation—one with short-term and another with extended non-adiabaticity. It is demonstrated that, while in the adiabatic case a damping term is present in the equation of motion of the neutrino density matrix (just like in the vacuum oscillation case), no such term in general appears in the non-adiabatic regime.

Comments on the determination of the neutrino mass ordering in reactor neutrino experiments

We consider the problem of determination of the neutrino mass ordering via precise study of the vacuum neutrino oscillations in the JUNO and other future medium baseline reactor neutrino experiments. We are proposing to resolve neutrino mass ordering by determination of the neutrino oscillation parameters from analysis of the data of the reactor experiments and comparison them with the oscillation parameters obtained from analysis of the solar and KamLAND experiments.

Neutrino oscillations: from an historical perspective to the present status

The history of neutrino mixing and oscillations is briefly presented. Basics of neutrino mixing and oscillations and convenient formalism of neutrino oscillations in vacuum is given. The role of neutrino in the Standard Model and the Weinberg mechanism of the generation of the Majorana neutrino masses are discussed.

Neutrino oscillations: From a historical perspective to the present status

The history of neutrino mixing and oscillations is briefly presented. Basics of neutrino mixing and oscillations and convenient formalism of neutrino oscillations in vacuum are given. The role of neutrino in the Standard Model and the Weinberg mechanism of the generation of the Majorana neutrino masses are discussed.

Neutrino masses from modified bimaximal mixing

The bimaximal (BM) neutrino mixing matrix was formulated in order to accommodate the data of the experimental results which indicate that both solar and atmospheric neutrino oscillation in vacuum are near maximal. But, after the T2K and Daya Bay Collaborations reported that the mixing angle [Formula: see text] is nonzero and relatively large, many authors have modified the neutrino mixing matrix in order to accommodate experimental data. We modified the BM mixing matrix by introducing a simple perturbation matrix into BM mixing matrix. The modified BM mixing matrix can proceed the mixing angles which are compatible with the global fit analysis data and by imposing the [Formula: see text]–[Formula: see text] symmetry into mass matrix from modified BM, we have the neutrino mass in normal hierarchy (NH): [Formula: see text]. Using the neutrino masses that obtained from neutrino mass matrix in the scheme of modified BM and imposing the constraint exact [Formula: see text] symmetry into neutrino mass matrix, we cannot have compatible squared-mass differences for both [Formula: see text] and [Formula: see text] as dictated by experimental results. In order to proceed the neutrino masses that can predict correctly the squared-mass difference, we introduce a small parameter [Formula: see text] into neutrino mass matrix. The obtained neutrino masses are in agreement with the squared-mass difference as dictated by experimental results. The predicted neutrino effective mass: [Formula: see text] in this paper can be tested in the future neutrinoless double beta decay.

Phenomenology of Neutrino Mixing in Vacuum and Matter

The current status and some perspectives of the phenomenology of massive neutrinos is reviewed. We start with the phenomenology of neutrino oscillations in vacuum and in matter. We summarize the results of neutrino experiments using solar, atmospheric. The fundamental theory of flavor changing neutrinos that has confirmed the neutrino oscillations and the various parameters affecting these oscillations have been discussed in detail. Specifically we will take the solar and atmospheric neutrino case. The oscillation plots will be discussed in detail, based on their behavior in vacuum and matter. Both normal and inverted mass hierarchy hypotheses are tested and both are consistent with observation. Finally the sensitivity of theta 13 over these probability oscillations has been analyzed and commented.

Novel results on low energy neutrino physics

Many progresses have been achieved in the study of low energy neutrinos from Sun and Earth. In the solar neutrinos the flux from 7Be has been measured with a total error <5% (introducing strong constraints also on the pp flux), while the day/night effect in that energy region has been determined at 1%. The 8B neutrinos have been detected with a threshold down to 3 MeV, while the solar neutrinos flux from pep reaction has been measured together with a stringent limit on CNO. These results give the experimental proof of the neutrino oscillation in vacuum and the validation of the MSW-LMA model in that region, while the day/night allows the isolation of the LMA solution by means of the solar neutrinos only, without the assumption of CPT symmetry. The evidence of the antineutrinos produced within the Earth by radioactive decays is now very robust, but more statistics is needed to clearly estimate the radiogenic contribution to the terrestrial caloric energy.

Majorana Neutrino Oscillations in Vacuum

In the context of a type I seesaw scenario which leads to get light left-handed and heavy right-handed Majorana neutrinos, we obtain expressions for the transition probability densities between two flavor neutrinos in the cases of left-handed and right-handed neutrinos. We obtain these expressions in the context of an approach developed in the canonical formalism of Quantum Field Theory for neutrinos which are considered as superpositions of mass-eigenstate plane waves with specific momenta. The expressions obtained for the left-handed neutrino case after the ultra-relativistic limit is taking lead to the standard probability densities which describe light neutrino oscillations. For the right-handed neutrino case, the expressions describing heavy neutrino oscillations in the non-relativistic limit are different respect to the ones of the standard neutrino oscillations. However, the right-handed neutrino oscillations are phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets.

Neutrino oscillations: theory and phenomenology

A brief overview of selected topics in the theory and phenomenology of neutrino oscillations is given. These include: oscillations in vacuum and in matter; phenomenology of 3-flavour neutrino oscillations; CP and T violation in neutrino oscillations in vacuum and in matter; matter effects on ν μ ↔ ν τ oscillations; parametric resonance in neutrino oscillations inside the earth; oscillations below and above the MSW resonance; unsettled issues in the theory of neutrino oscillations.

Expressions for Neutrino Wave Functions and Transition Probabilities at Three Neutrino Oscillations in Vacuum and Some of Their Applications

We have considered three neutrino transitions and oscillations in the general case and obtained expressions for neutrino wave functions in three cases: with CP violation, without CP violations and the case when $\nu_e \leftrightarrow \nu_\tau$ transitions are absent (some works indicate on this possibility). Then using the existing experimental data some analysis has been fulfilled. This analysis definitely has shown that transitions $\nu_e \leftrightarrow \nu_\tau$ cannot be closed for the Solar neutrinos. However, this possibility may be realized by using the mechanism of resonance enhancement neutrino oscillations in matter (the Sun). But this possibility is not confirmed by the Solar neutrinos spectrum (the Solar neutrinos spectrum is not distorted) and the Day-Night effect (this effect is not observed). It was found out that the probability of $\nu_e \leftrightarrow \nu_e$ neutrino transitions is positive defined value only if the angle of $\nu_e, \nu_\tau$ mixing $\beta \le 15^o \div 17^o$.