Remarks to the standard scheme (theory) of neutrino oscillations. Corrected scheme of neutrino oscillations

In the standard theory of neutrino oscillations, it is supposed that physically observed neutrino states ν _e , ν_μ, ν_τ, have no definite masses, that they are initially produced as a mixture of the ν₁, ν₂, ν₃ neutrino states (i.e., they 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 obtained within the framework of particle physics has been considered, where the above mentioned shortcomings are absent, the oscillations of neutrinos with equal masses are the real ones, and the oscillations of neutrinos with different masses are the virtual ones. Expressions for probabilities of neutrino transitions (oscillations) in the alternative (corrected) scheme are given. The text was submitted by the author in English.     

Majorana neutrino masses in the three-flavor Pauli model

A special Majorana model for three neutrino flavors is developed on the basis of the Pauli transformation group. In this model, the neutrinos possess a partially conserved generalized lepton (Pauli) charge that makes it possible to discriminate between neutrinos of different type. It is shown that, within the model in question, a transition from the basic “mass” representation, where the average value of this charge is zero, to the representation associated with physical neutrinos characterized by specific Pauli “flavor” charges establishes a relation between the neutrino mixing angles θ _{mix, 12}, θ _{mix, 23}, and θ _{mix, 13} and an additional relation between the Majorana neutrino masses. The Lagrangian mass part, which includes a term invariant under Pauli transformations and a representation-dependent term, concurrently assumes a “quasi-Dirac” form. With allowance for these relations, the existing set of experimental data on the features of neutrino oscillations makes it possible to obtain quantitative estimates for the absolute values of the neutrino masses and the 2β-decay mass parameter m _ββ and a number of additional constraints on the neutrino mixing angles.     

New neutrino experiments

Following incredible recent progress in understanding neutrino oscillations, many new ambitious experiments are being planned to study neutrino properties. The most important may be to find a non-zero value of θ₁₃. The most promising way to do this appears to be to measurev _μ →v _e oscillations with anE/L near Δm _atmo ² . Future neutrino experiments are great.     

Supernova constraints on neutrino mass and mixing

In this article I review the constraints on neutrino mass and mixing coming from type-II supernovae. The bounds obtained on these parameters from shock reheating, r-process nucleosynthesis and from SN1987A are discussed. Given the current constraints on neutrino mass and mixing the effect of oscillations of neutrinos from a nearby supernova explosion in future detectors will also be discussed.     

Results from Super-Kamiokande and K2K

Results from Super-Kamiokande-I’s entire 1496 live days of solar neutrino data are presented, including the absolute flux, energy spectrum, zenith angle (day/night) and seasonal variation. The possibility of MSW and vacuum oscillations is discussed in light of these results. Results from the first 1289 days of Super-K-I’s atmospheric neutrino analysis are also presented, including the evidence for ν_μ →ν _τ oscillations, against ν_μ → ν_sterile oscillations, and the current limits on proton decay. Finally, results based on 56 × 10¹⁹ protons on target are given for the K2K long-baseline neutrino oscillation experiment.     

Is realization of Majorana neutrino and neutrinoless double beta decay possible in the framework of standard weak interactions?

Usually it is supposed that Majorana neutrino produced in the superposition state χ _L = ν _L + (ν _L ) ^c and then follows the neutrinoless double beta decay. But since the standard weak interactions are chiral invariant then neutrino at production has definite helicity (ν _L and (ν _L ) ^c have opposite spirality). Then these neutrinos are separately produced and their superposition state cannot appear. Thus we see that for unsuitable helicity the neutrinoless double β decay is not possible even if it is supposed that neutrino is a Majorana particle (i.e. there is not a lepton number which is conserved). Also transition of Majorana neutrino ν _L into antineutrino (ν _L ) ^c at their oscillations is forbidden since helicity in vacuum holds. Transition Majora neutrino ν _L into (ν _R ) ^c (i.e., ν _L → (ν _R ) ^c ) at oscillations is unobserved since it is supposed that mass of (ν _R ) ^c is very big. If neutrino is a Dirac particle there can be transition of ν _L neutrino into (sterile) antineutrino $ \bar v_R $ \bar v_R (i.e., ν _L → $ \bar v_R $ \bar v_R ) at neutrino oscillations if there takes place double violation of lepton number. It is necessary also to remark that introducing of a Majorana neutrino implies violation of global and local gauge invariance in the standard weak interactions.     

Deviation from Tetra-Maximal Neutrino Mixing Above the GUT scale

We consider non-renormalizable interaction term as perturbation of the conventional neutrino mass matrix. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck scale and the electroweak breaking scale. We also assume that, just above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is tetra-maximal. Quantum gravity (Planck scale effects) lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On electroweak symmetry breaking, this operator gives rise to correction to the above masses and mixing. These additional term can be consider as a perturbation to the Tetra-maximal mass matrix. The nature of gravitational interaction demands that the element of this perturbation matrix should be independent of flavor indices. We compute the deviation of three neutrino mixing angles due to Planck scale effects. We find that there is no change in θ ₁₃ and θ ₂₃ but change in solar mixing angle θ ₁₂ is suppress by 3.0°.     

Resonant neutrino oscillations and the neutrino signature of supernovae

We examine the effects of resonant neutrino oscillations, proposed as a solution to the solar neutrino puzzle, on the neutrino signature of a Type II supernova. We find that, for parameters corresponding to an adiabatic conversion of most of the ⁸B neutrino flux, the supernova neutrino signal in a water-Čerenkov detector is altered in the following way: (1) The isotropic-to-directional event ratio increases; (2) The short time scale neutronization burst signal decreases by a factor 7, perhaps rendering it unobservable. Detection of these changes would allow one to distinguish between neutrino oscillations and solar model alterations as solutions to the solar neutrino problem. We also note that mixing of the higher energy ν_μ and ν_r's to ν_e's will enhance detection of the thermally produced ν-flux.     

Neutrino Mixing Matrix and Leptogenesis from Quantum Gravity

We consider non renormalization 1/M _x interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. The perturbation generates a non zero value of θ ₁₃, which is within reach of the high performance neutrino factory. In this paper, we find that the non zero value of θ ₁₃ due to Planck scale effects indicates the possibility of CP violation.     

Future atmospheric neutrino data from Super-Kamiokande

Expected sensitivity of future atmospheric neutrino data from Super-Kamiokande on neutrino oscillation physics is discussed. We expect that the accuracy of the sin ²θ₂₃ measurement will be improved with (exposure time) . By analyzing high energy fully contained events, it could be possible to statistically demonstrate the existence of charged current ν_τ interactions at the 3 standard deviation level with a few more years of data. Subdominant ν_μ → ν_e oscillations could be observed if θ₁₃ is near the present limit. However, significantly more data will be required to observe a 3 standard deviation effect.     

Non-standard neutrino interactions in the Zee–Babu model

We investigate non-standard neutrino interactions (NSIs) in the Zee–Babu model. The size of NSIs predicted by this model is obtained from a full scan over the parameter space, taking into account constraints from low-energy experiments such as searches for lepton flavor violation (LFV) and the requirement to obtain a viable neutrino mass matrix. The dependence on the scale of new physics as well as on the type of the neutrino mass hierarchy is discussed. We find that NSIs at the source of a future neutrino factory may be at an observable level in the ν_e→ν_τ and/or ν_μ→ν_τ channels. In particular, if the doubly charged scalar of the model has a mass in reach of the LHC and if the neutrino mass hierarchy is inverted, a highly predictive scenario is obtained with observable signals at the LHC, in upcoming neutrino oscillation experiments, in LFV processes, and for NSIs at a neutrino factory.     

Relativistic wave packets in the quantum field approach to the theory of neutrino oscillations

A covariant theory of wave packets and its application to the quantum field method of calculation of the probabilities of neutrino oscillations in vacuum that is based on the technique of macroscopic Feynman diagrams, which describe the processes of emission and absorption of virtual massive neutrinos ν _i (i = 1, 2, 3) at macroscopicly separated space-time points, is considered. The effect of flavor oscillations is reduced to an interference of amplitudes with different vi in an intermediate state. A macroscopic amplitude is calculated that describes a class of processes which go with nonconservation of leptonic numbers, and statistical averaging of the squared modulus of this amplitude is performed. The averaged probability of a process with ultrarelativistic neutrino exchange is representable in the form of an integral of the product of three factors: the flux of massless neutrinos from the source, the differential cross-section for the interaction of a neutrino with the detector, and a dimensionless factor that describes the flavor transition. The conditions under which the last factor can be interpreted as the probability of the flavor transition in the conventional quantummechanical sense are analyzed.     

Testing Theories of Chiral Symmetry

We investigate various physical consequences of theories of chiral symmetry. Predictions of the symmetry are given for the meson electroproduction process at an on-shell kinematical point where unknown contributions are minimized. Sum rules are derived for the corrections. Then we present a sum rule for the ∑ term in meson-baryon scattering from the assumptions of Bjorken limit, precocious asymptopia, and finite-mass dispersion relations. We use the commutation relations of the gluon model as input for a numerical evaluation. Next the explicit canonical structure of the light-cone restriction of the commutator of the weak current with its divergence is considered in the interacting quark-gluon model quantized in the infinite–momentum frame. The implications on neutrino scattering are analyzed. W₄ and W₅ are predicted to scale nontrivially as v⁻²F₄(ω) and v⁻²F₅(ω), which provides a simple test of light-cone current algebra feasible in the near future. The ∑ term for weak currents is deduced from a causal representation near the light-cone, and a correction is also made in the W₅ – sum rule obtained by naive infinite momentum techniques. As a by-product we obtain improved derivations of the Adler neutrino sum rules.     

New MACRO results on atmospheric neutrino oscillations

The final results of the MACRO experiment on atmospheric neutrino oscillations are presented and discussed. The data concern different event topologies with average neutrino energies of ～3 and ～50 GeV. Multiple Coulomb scattering of the high-energy muons in absorbers was used to estimate the neutrino energy of each event. The angular distributions, the L/E_ν distribution, the particle ratios, and the absolute fluxes all favor ν_π?ν_τ oscillations with maximal mixing and Δm²=0.0023 eV². A discussion is made on the Monte Carlos used for the atmospheric neutrino flux. Some results on neutrino astrophysics are also briefly discussed.     

Neutrino oscillations and the early universe

The observational and theoretical status of neutrino oscillations in connection with solar and atmospheric neutrino anomalies is presented briefly. The effect of neutrino oscillations on the evolution of the early Universe is discussed in detail. A short review is given of the standard Big Bang Nucleosynthesis (BBN) and the influence of resonant and non-resonant neutrino oscillations on active neutrinos and on primordial synthesis of He-4. BBN cosmological constraints on neutrino oscillation parameters are discussed.     

Neutrino oscillations in the field of a linearly polarized electromagnetic wave

Neutrino oscillations ν _iL ? ν _jR in the field of a linearly polarized electromagnetic wave are studied on the basis of a recently proposed effective Hamiltonian that describes the evolution of a spin in an arbitrary electromagnetic field. The condition of resonance amplification of the oscillations is analyzed in detail. A method is developed for qualitatively studying solutions to the equation of neutrino evolution in the resonance region. This method can be used to explore neutrino oscillations in fields of various configurations.     

Two-detector reactor neutrino oscillation experiment Kr2Det at Krasnoyarsk: Status report

We consider the status of the Kr2Det project aimed at sensitive searches for neutrino oscillations in the atmospheric neutrino mass parameter region around Δm² ～ 3×10^?3 eV² and at obtaining new information on the electron neutrino mass structure (U_e3).     

Cherenkov effect in the weak interactions generated by the neutrinos and new approach for estimation of neutrino mass

It is shown that if weak interactions can generate masses and polarize matter, then the Cherenkov effect induced by these interactions at v _v > c/n appears. The effect of (resonance) enhancement of neutrino oscillations in matter (v _v < c/n) and the Cherenkov (v _v > c/n) effect are competitive processes and at definite neutrino energies the effect of (resonance) enhancement of neutrino oscillations in matter will change to the Cherenkov effect. Then neutrino vacuum oscillations will regenerate and we obtain an excellent possibility of estimating neutrino masses. And knowing estimation of mass for one (electron) neutrino we can obtain masses of the rest neutrinos by using the values for mass differences for neutrinos obtained in oscillation experiments.     

O(5)×U(1) electroweak gauge theory and the neutrino oscillations in matter

A study is made of the groupO(5)×U(1). The group is economical in the number of gauge bosons, which we associate with each of its generators, and is anomaly-free. The left-handed leptonsL _L ^T (v _e ,e,,v ) _L are assigned to the four-dimensional spinorial representations ofO(5). The right-handed particles are taken to be the singlets of the group. The theory has three sets of gauge bosons: (1) analogues of the GWS model, (2) additional charged gauge bosons, and (3) a set of three additional neutral gauge bosons as compared to the GWS model. We introduce neutrino mixing by mixing the additional charged gauge bosons. We develope a theory of neutrino oscillations in matter in such a way that in the absence of matter the scattering length reduces to the usual scattering length in vacuum. Even if the neutrino masses are equal or the neutrinos are massless, we still have neutrino oscillations in matter, a result already noted by Wolfenstein.