Recent work has shown that neutrino oscillations in matter can be greatly enhanced by flips between mass eigenstates if the medium is fluctuating with a period equal to the neutrino oscillation length. Here we investigate the effect of the primordial fluctuations on the neutrino oscillations in the early universe. We calculate the oscillation probability in the case of a general power law fluctuation spectrum and for a more realistic spectrum predicted by inflation. We also include the effect of the amplification of fluctuations resulting from the QCD phase transition. We find that there is a region of parameter space where this mechanism would be the dominant mechanism for producing sterile neutrinos. However this conclusion does not take account of the damping of fluctuations on the neutrino oscillation scale when the neutrinos decouple from the plasma. We find that this reduces the probability of flips between the mass eigenstates to an unobservable level.
We studied nonequilibrium oscillations between left-handed electron neutrinos and nonthermalized sterile neutrinos in medium for resonant and nonresonant cases. The exact kinetic equations for neutrinos, written in terms of neutrino density matrix in {\it momentum space} were analyzed. The evolution of neutrino density matrix was numerically calculated. This allowed to study precisely the evolution of the neutrino number densities, energy spectrum distortion and the asymmetry between neutrinos and antineutrinos for each momentum mode. The influence of nonequilibrium oscillations on the primord…
We studied nonequilibrium oscillations between left-handed electron neutrinos and nonthermalized sterile neutrinos. The exact kinetic equations for neutrinos, written in terms of neutrino density matrix in momentum space were analyzed. The evolution of neutrino density matrix was numerically calculated. This allowed to study precisely the evolution of the neutrino number densities, energy spectrum distortion and the asymmetry between neutrinos and antineutrinos for each momentum mode. Both effects of distortion and asymmetry, which cannot be accounted for correctly when working in terms of par…
In this article we discuss lepton asymmetry effect on BBN with neutrino oscillations. We argue that asymmetry much smaller than 0.01, although not big enough to influence directly the nucleosynthesis kinetics, can effect considerably BBN indirectly via neutrino oscillations. Namely, it distorts neutrino spectrum and changes neutrino density evolution and the pattern of oscillations (either suppressing or enhancing them), which in turn effect the primordial synthesis of elements. We show that the results of the paper X. Shi et al., Phys. Rev. D 60, 063002 (1999), based on the assumption that on…
We consider random primordial magnetic fields and discuss their dissipation, coherence length $L_0$, scaling behaviour and constraints implied by the primoridal nucleosynthesis. Such magnetic fields could excite the right-helicity states of Dirac neutrinos, with adverse consequences for nucleosynthesis. We present solutions to the spin kinetic equation of a Dirac neutrino traversing a random magnetic field in the cases of large and small $L_0$, taking also into account elastic collisions. Depending on the scaling behaviour and on the magnetic coherence length, the lower limit on the neutrino m…
The influence of a massive Majorana tau-neutrino on primordial nucleosynthesis is rigorously calculated. The system of three integro-differential kinetic equations is solved numerically for the tau-neutrino mass in the interval from 0 to 20 MeV. It is found that the usual assumption of kinetic equilibrium is strongly violated and non-equilibrium corrections considerably amplify the effect. Even a very weak restriction from nucleosynthesis, allowing for one extra massless neutrino species, permits to conclude that m_ν_τ< 1 MeV. For a stricter bound, e.g. for dN < 0.3, the limit is m_ν_τ< 0.35 M…
The connection between cosmological observations and neutrino physics is discussed in detail. Neutrinos decouple from thermal contact in the early Universe at a temperature of order 1 MeV which coincides with the temperature where light element synthesis occurs. Observation of light element abundances therefore provides important information on such properties as neutrino energy density and chemical potential. Precision observations of the cosmic microwave background and large scale structure of galaxies can be used to probe neutrino masses with greater precision than current laboratory experi…
The impact of unstable Majorana tau neutrinos on primordial nucleosynthesis is considered. The mass and lifetime of nu_tau are taken in the intervals 0.1-20 MeV and 0.001-400 sec respectively. The studied decay modes are nu_tau -> nu_mu + phi and nu_tau -> nu_e + phi, where phi is a massless (or light) scalar. Integro-differential kinetic equations are solved numerically without any simplifying assumptions. Our results deviate rather strongly from earlier calculations. Depending on mass, lifetime, and decay channels of the nu_tau, the number of effective neutrino species (found from He4), in a…
The primordial black holes (PBHs) play as a novel source to radiate light elementary particles of energies in the region of a few hundred MeV. We explore the possibility that the axion-like particles (ALPs) with mass less than 1 MeV are produced from PBH evaporation. The absorption of light ALPs in the underground detector targets then induces energetic photoelectron signatures in current and future neutrino experiments. Utilizing the PBH ALP event rate, we place general exclusion limits on the axion couplings at Super-K and Hyper-K. We also translate these limits into the upper bound on the f…
Primordial nucleosynthesis constrains the properties of light, stable neutrinos. Apart from the well--known limit on the number of neutrino species, there are also bounds on neutrino masses and magnetic moments. I discuss also sterile neutrinos and neutrino propagation in a primordial magnetic field, such as could be the origin of the observed galactic magnetic fields.
In this work we present the results of our numerical analysis of the effect of lepton asymmetries L on neutrino oscillations and consequently on helium production in a model of cosmological nucleosynthesis with active-sterile neutrino oscillations. We performed detail calculations of the neutron-proton ratio till its freezing and the subsequent synthesis of helium-4 for a wide range of values of the initial lepton asymmetry 10^{-4}-10^{-10} and for the complete set of mixing parameters of the oscillation model described in hep-ph/9707282: δm^2 \le 10^{-7} eV^2 and any \vartheta. We have found …
We use the constraints arising from primordial nucleosynthesis to bound the strength $F$ of non-standard neutrino-neutrino interactions, when the right-handed neutrinos participate in the interaction. We find $F < 3 \times 10^{-3}\ G_F$, which is five orders of magnitude more stringent than the limit obtained using LEP data. We also show that secret interactions of neutrinos mediated by massless particles must have a coupling $f$ less than $2 \times 10^{-5}$. This also ameliorates previous limits in the literature.
Recent measurements of deuterium abundances from QSO absorption spectra show two conflicting numbers, which differ by an order of magnitude. Allowing the neutrino degeneracy together with gravitational constant variation at the epoch of primordial nucleosynthesis, the implication of these observations on the ^6Li, ^9Be and ^11B abundances will be discussed. Within the permitted ranges consistent with D, ^4He and ^7Li, we observe the strong ηdependence of ^11B as in SBBN but no significant dependence of ^6Li and ^9Be on the baryon number density is observed. The predictions of ^6Li and ^9Be for…
We present one point of contact between the standard theory of neutrino oscillations and the alternative one, in which flavor neutrinos are described by states with definite masses. We show that both theories give the same results for static neutrinos only.
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.
A primordial black hole in the last stages of evaporation and located in the local neighborhood can produce a detectable signal in gamma ray and neutrino telescopes. We re-evaluate the expected gamma ray and neutrino fluxes from these transient point events and discuss the consequences for existing constraints. For gamma rays we improve the current bounds by a factor of few, while for neutrinos we obtain significantly different results than the existing literature. The capability and advantages of neutrino telescopes in the search for primordial black holes is discussed thoroughly. The correla…
In the Standard theory of neutrino oscillations it is supposed that physical observed neutrino states $ν_{e}, ν_μ, ν_τ$ have no definite masses and that neutrinos are initially created as mixture of $ν_{1}, ν_{2}, ν_{3}$ neutrino states and that neutrino oscillations are the real ones even when neutrino masses are different. It is shown that these suppositions lead to violation of the law of energy and momentum conservation and then the neutrino states are unstable ones and they must disintegrate. Then the development of the standard theory of neutrino oscillations in the framework of particle…
We demonstrate that combining Cosmic Microwave Background anisotropy measurements from the 1st year WMAP observations with clustering data from the SLOAN galaxy redshift survey yields an indication for primordial anisotropies in the cosmological Neutrino Background.
In the standard theory of neutrino oscillations it is supposed that physical observed neutrino states $ν_{e}, ν_μ, ν_τ$ have no definite masses, that they are initially produced as a mixture of the $ν_{1}, ν_{2}, ν_{3}$ neutrino states (are produced as a wave packet), and that neutrino oscillations are the real ones. Then this wave packet must decompose at a definite distance into constituent parts and neutrino oscillations must disappear. It was shown that these suppositions lead to violation of the law of energy and momentum conservation. An alternative scheme of neutrino oscillations obtain…
A massive long-lived tau neutrino in the MeV regime modifies the primordial light-element abundances predicted by big-bang nucleosynthesis (BBN) calculations. This effect has been used to derive limits on the tau neutrino mass. Because recently the observational situation has become somewhat confusing and, in part, intrinsically inconsistent, we reconsider the BBN limits on the tau neutrino mass. To this end we use our newly developed BBN code to calculate the primordial abundances as a function of the tau neutrino mass and of the cosmic baryon density eta. We derive concordance regions in the…
We review the current status of the solar neutrino oscillation parameters. We discuss the conditions under which measurements from future solar neutrino experiments would determine the oscillation parameters precisely. Finally we expound the potential of long baseline reactor anti-neutrino experiments in measuring the solar neutrino oscillation parameters.
An analysis of 3-flavour neutrino oscillations inside the Earth is presented in terms of the oscillograms -- contour plots of oscillation probabilities in the plane neutrino energy -- nadir angle. Special attention is paid to CP violation in neutrino oscillations in the Earth.
A brief review of the problem of neutrino masses and oscillations is given. In the beginning we present an early history of neutrino masses, mixing and oscillations. Then we discuss all possibilities of neutrino masses and mixing (neutrino mass terms). The phenomenology of neutrino oscillations in vacuum is considered in some details. We present also the neutrino oscillation data and the seesaw mechanism of the neutrino mass generation.
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.
In the Standard theory of neutrino oscillations is used scheme of mass mixings, i.e., oscillation parameters are expressed via terms of mass matrix. In this work neutrino oscillations generated by charge (the weak interaction couple constants) mixings are considered. Expressions for angle mixings and lengths of oscillations are obtained. The expressions of the probability for three neutrino oscillations are given. Neutrino oscillations in this scheme (mechanism) are virtual if neutrino masses are not equal and real if neutrino masses are equal.
We include the coupling of a heavy sterile neutrino with active neutrinos in the calculation of primordial abundances of light-nuclei. We calculate neutrino distribution functions and primordial abundances, as functions depending on a renormalization of the sterile neutrino distribution function $(a)$, the sterile neutrino mass $(m_s)$ and the mixing angle $(ϕ)$. Using the observable data, we set constrains on these parameters, which have the values $a < 0.60$, $\sin^2 ϕ=0.15$ and $m_s \approx 4$ keV, for a fixed value of the baryon to photon ratio. When the baryon to photon ratio is allowed t…
The maximum overproduction of helium-4 in cosmological nucleosynthesis with active--sterile neutrino oscillations, nu_e -> nu_s, efficient after decoupling of electron neutrino, is analyzed. The kinetic effects on primordial nucleosynthesis due to neutrino spectrum distortion, caused by oscillations, are precisely taken into account. The maximum overproduction of primordial He-4 as a function of oscillation parameters is obtained from the analysis of the kinetics of the nucleons and the oscillating neutrinos, for the full range of parameters of the discussed oscillation model. A maximum relati…
It is shown that in the two schemes with four massive neutrinos which are compatible with the results of all neutrino oscillation experiments, the probabilities of nu_e disappearance and nu_mu->nu_e appearance in long-baseline experiments are severely constrained.
Studies of limits on active-sterile neutrino mixing derived from big bang nucleosynthesis considerations are extended to consider the dependance of these constraints on the primordial deuterium abundance. This study is motivated by recent measurements of D/H in quasar absorption systems, which at present yield discordant results. Limits on active-sterile mixing are somewhat relaxed for high D/H. For low D/H ($\approx 2 \times 10^{-5}$), no active-sterile neutrino mixing is allowed by currently popular upper limits on the primordial $^4$He abundance $Y$. For such low primordial D/H values, the …
We study flavor oscillations in the early universe, assuming primordial neutrino-antineutrino asymmetries. Including collisions and pair processes in the kinetic equations, we not only estimate the degree of flavor equilibration, but for the first time also kinetic equilibration among neutrinos and with the ambient plasma. Typically the restrictive BBN bound on the nue-antinue asymmetry indeed applies to all flavors as claimed in the previous literature, but fine-tuned initial asymmetries always allow for a large surviving neutrino excess radiation that may show up in precision cosmological da…
The definition of `lepton flavour eigenstates' introduced in a recent paper hep-ph/0302045 is in disagreement with the Standard Model prediction for the structure of the leptonic charged current and implies the absence of neutrino oscillations following pion decay, in contradiction to experimental data
Neutrino mixing and basics of neutrino oscillations are considered. Recent evidences in favour of neutrino oscillations, obtained in the solar and atmospheric neutrino experiments, are discussed. Neutrino oscillations in the solar and atmospheric ranges of $Δm^{2}$ are considered in the framework of the minimal scheme with the mixing of three massive neutrinos.
This brief report is an extension of a prediction of neutrino oscillation with a sterile neutrino using parameters of the sterile neutrino mass and mixing angle recently extracted from experiment.
This is an extension of estimates of the probability of $ν$ to $e$ neutrino oscillation with one sterile neutrino to three sterile neutrinos, using a 6x6 matrix. Since the mixing angle for only one sterile neutrino has been experimentally determined, we estimate the $ν$ to $e$ neutrino oscillation probability with different mixing angles for two of the sterile neutrinos.
After some generalities on neutrino oscillations and on neutrinos, the recent experimental results presented by Soudan 2, MACRO and SuperKamiokande at the Neutrino'98 conference are summarized and discussed.
We explain the physics of neutrino oscillation in vacuum and in matter. We attempt to clarify several features of oscillation that can be puzzling when neutrinos are their own antiparticles.
Recently neutrino oscillation experiments have shown that it is very likely that there are one or two sterile neutrinos. In this review neutrino oscillations with one, two, three sterile and three active neutrinos, and parameters that are consistent with experiments, are reviewed.
Recent Super-Kamiokande data on the atmospheric neutrino anomaly are used to test various mechanisms for neutrino oscillations. It is found that the current atmospheric neutrino data alone cannot rule out any particular mechanism. Future long-baseline experiments should play an important role in identifying the underlying neutrino oscillation mechanism.
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.
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…
The basics of neutrino oscillations is presented. Existing evidences of neutrino oscillations, obtained in the atmospheric and solar neutrino experiments, are considered. The new CHOOZ bound on the element $|U_{e3}|^{2}$, obtained from the three-neutrino analysis of the data, is discussed. Decoupling of neutrino oscillations in the solar neutrino range of $Δm^{2}$ is considered.
We examine in detail the changes in the production of primordial helium resulting from nonthermal neutrino momentum distributions produced by resonant transformation of electron-type neutrinos to steriles. These transformations, anti-nu_e -> anti-nu_s (nu_e->nu_s), amplify a positive (negative) lepton number asymmetry. We find that the resulting supression relative to a thermal distribution of low energy nu_e reduces n -> p conversion to a greater extent than does the enhancement of n -> p from an identical suppression of anti-nu_e. Thus, equal lepton-number asymmetries of opposite sign have u…
It has been argued that any primordial B+L asymmetry existing at very high temperatures can be subsequently erased by anomalous electroweak effects. We argue that this is not necessarily the case in the supersymmetric standard model because, apart from B and/or L, there are, above a certain temperature $T_{SS}$, two other anomalous U(1) currents. As a consequence, anomalous electroweak effects are only able to partially transform a B+L excess into a generation of primordial sparticle (e.g. gaugino) density. This relaxes recent bounds on B,L-violating non-renormalizable couplings by several ord…
A consistent description of the results of the neutrino oscillation experiments carried out so far can be obtained from three basic properties of neutrinos and the parameters of the Hamiltonian matrix. Using these basic neutrino properties, an exact relation for the oscillation amplitudes of moving neutrinos is derived.
This work estimates the probability of $μ$ to $e$ neutrino oscillation with two sterile neutrinos using a 5x5 U-matrix, an extension of the previous estimate with one sterile neutrino and a 4x4 U-matrix. The sterile neutrino-active neutrino mass differences and the mixing angles of the two sterile neutrinos with the three active neutrinos are taken from recent publications, and the oscillation probability for one sterile neutrino is compared to the previous estimate.
The bicycle model of Lorentz noninvariant neutrino oscillations without neutrino masses naturally predicts maximal mixing and a 1/E dependence of the oscillation argument for $ν_μ\to ν_τ$ oscillations of atmospheric and long-baseline neutrinos, but cannot also simultaneously fit the data for solar neutrinos and KamLAND. We examine all nineteen possible structures of the Standard Model Extension for Lorentz noninvariant oscillations of massless neutrinos that naturally have a 1/E dependence at high neutrino energy. Due to the lack of any evidence for direction dependence, we consider only direc…
Using the Mandelstam-Tamm method we derive time-energy uncertainty relations for neutrino oscillations. We demonstrate that the small energy uncertainty of antineutrinos in a recently considered experiment with recoilless resonant (Mössbauer) production and absorption of tritium antineutrinos is in conflict with the energy uncertainty which, according to the time-energy uncertainty relation, is necessary for neutrino oscillations to happen. A Mössbauer neutrino experiment could provide a unique possibility to test the applicability of the time-energy uncertainty relation to neutrino oscillatio…
This is a reply to the preprint "On Neutrino-Mixing-Generated Lepton Asymmetry and the Primordial Helium-4 Abundance" by M. V. Chizhov and D. P. Kirilova (hep-ph/9908525), which criticised our recent publication (X. Shi, G. M. Fuller and K. Abazajian Phys. Rev. D 60, 063002 (1999)). Here we point out factual errors in their description of what our paper says. We also show that their criticisms of our work have no merit.
Neutrino oscillations is a phenomenon which is characterized by a finite oscillation time (length). For such phenomena time-energy uncertainty relation is valid. This means that energy uncertainty is needed for oscillations to occur. We consider neutrino oscillations from this point of view. We demonstrate that for mixed neutrino states, which describe flavor neutrinos $ν_{e}$, $ν_μ$ and $ν_τ$, translational invariance does not take place.
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.
We comment on the paper "On application of the time-energy uncertainty relation to Mössbauer neutrino experiments" (see arXiv: 0803.1424) in which our paper "Time-energy uncertainty relations for neutrino oscillation and Mössbauer neutrino experiment" (see arXiv: 0803.0527) has been criticized. We argue that this critique is a result of misinterpretation: The authors of (arXiv: 0803.1424) do not take into account (or do not accept) the fact that at present there exist different schemes of neutrino oscillations which can not be distinguished in usual neutrino oscillation experiments. We stress …
Predictions are presented for the oscillation phase in neutrino oscillations following pion decay at rest and in flight, muon decay and nuclear $β-$decay at rest as well as for muon oscillations following pion decay at rest and in flight. The neutrino oscillation phases found disagree with the conventionally used value: $ϕ_{12} = Δm^2 L/(2P)$. The same oscillation phase is found for neutrino and muon oscillations following pion decay at rest. Shortcomings of previous treatments of the quantum mechanics of neutrino oscillations are commented on.
We analyze the consequences of Lorentz violation (LV) to three-generation neutrino oscillation in the massless neutrino sector. We present a general formalism of three-family neutrino oscillation with neutrino flavor states being mixing states of energy eigenstates. It is also found that the mixing parts could strongly depend on neutrino energy by special choices of Lorentz violation parameters. By confronting with the existing experimental data on neutrino oscillation, the upper bounds on LV parameters are derived. Because the oscillation amplitude could vary with the neutrino energy, neutrin…
In the framework of the three-neutrino mixing the neutrino oscillations in the atmospheric and solar ranges of neutrino mass-squared differences are considered in the leading approximation. Neutrinoless double $β$- decay is also discussed.
