Lepton mixing and neutrino oscillations

The present article is a review of phenomena connected with neutrino oscillations. Mixing of two neutrinos (Majorana as well as Dirac) with masses m₁ and m₂ is considered in detail. It is shown that the hypothesis of lepton mixing is not in contradiction with the existing data if |m₁²?m₂²| ? 1 (eV)². Possible experiments designed to reveal neutrino oscillations at reactor, meson factory and high energy accelerator facilities are considered. In such experiments oscillation might be found if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 0.01}\text{(eV)}{}^2$. The possibilities of searching for oscillations by experiments on cosmic ray neutrinos and especially on solar neutrinos are discussed in detail. The last experiments have an incredible high sensitivity from the point of view of testing the lepton mixing hypothesis (oscillation effects might be observable if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 10}{}^{\mathrm{?12}}\text{(eV)}{}^2$). The “solar neutrino puzzle” is also discussed from the point of view of lepton mixing. Neutrino oscillations are considered then in the case where in nature there exist N ? 2 neutrino types.In conclusion the case of heavy lepton mixing is considered. It is shown that in a concrete scheme with right-handed currents, the probabilities of such processes as μ → eγ, μ → 3e etc. can be close to existing experimental upper limits, provided the heavy lepton masses are of an order of a few GeV, whereas the probabilities of the above processes are entirely negligible if only neutrinos are mixed.     

On Lepton asymmetry and BBN

The strongest available cosmological constraint on lepton asymmetry is L<0.01. We discuss in more detail a BBN model with late ν_e↔ν_s oscillations which is capable of measuring extremely small lepton asymmetry, L>10⁻⁸. This sensitivity is achieved through the influence of small L on the neutrino oscillations, suppressing or enhancing them, and thus decreasing or increasing the primordially produced ⁴He. The cases of asymmetry generated by late resonant electron-sterile oscillations and relic lepton asymmetry are considered. The influence of L on nucleons freezing in pre-BBN epoch is numerically analyzed in the full range of the oscillation parameters for the model and L≥10⁻¹⁰.     

Lepton flavour symmetry and the neutrino magnetic moment

With the standard model gauge group and the three standard left-handed Weyl neutrinos, two minimal scenarios are investigated where an arbitrary non-Abelian lepton flavour symmetry groupG _H is responsible for a light neutrino with a large magnetic moment. In the first case, with scalar fields carrying lepton flavour, some finetuning is necessary to get a small enough neutrino mass for _v =O(10)^–11 _B. In the second scenario, the introduction of heavy charged gauge singlet fermions with lepton flavour allows for a strictly massless neutrino to one-loop order. In both cases, the interference mechanism for smallm and large _v is unique, independently ofG _H . In explicit realizations of the two scenarios, the horizontal groups are found to be non-Abelian extensions of a Zeldovich-Konopinski-Mahmoud lepton number symmetry. Only a discrete part ofG _H is spontaneously broken leading to a light Dirac neutrino with a large magnetic moment.     

Lepton family symmetries for neutrino masses and mixing

I review some of the recent progress (up to December 2005) in applying non-Abelian discrete symmetries to the family structure of leptons, with particular emphasis on the tribimaximal mixing ansatz of Harrison, Perkins and Scott.     

Charged lepton and neutrino oscillations

Problems long present in the conventional formalism employed for neutrino oscillations are discussed. We here develop a more satisfactory framework based on the Dirac equation and its propagators. When 4-momentum conservation is strictly enforced, there will be induced oscillations in space (but not between generations) for the charged leptons, e.g. and , produced in association with the neutrinos. The oscillations are computed explicitly for the pion decay . Leptonic decays of the are also briefly discussed. Received: 15 October 1996 / Revised version: 15 June 1997 / Published online: 20 February 1998     

CP violation and neutrino oscillations

We review the basic mechanisms of neutrino mass generation and the corresponding structure of the lepton mixing matrix. We summarize the status of three-neutrino oscillation parameters as determined from current observations, using state-of-the-art solar and atmospheric neutrino fluxes, as well as latest experimental data as of September 2007. We also comment on recent attempts to account for these results and to understand flavour from first principles. We discuss extensively the prospects of probing the strength of CP violation in two near term accelerator neutrino oscillation experiments, T2K and , as well as possible extensions such as T2KK and a second large off-axis detector near the detector. We also briefly discuss the possibility of probing the effect of Majorana phases in future neutrinoless double beta decay searches and discuss other implications of leptonic CP violation such as leptogenesis. Finally we comment on the issue of robustness of the current oscillation interpretation and possible ways of probing for non-standard neutrino interactions in precision oscillation studies.     

Lepton mixing, μ → e + γ decay and neutrino oscillations

The μ → eγ decay is investigated in a gauge theory with lepton mixing under the assumption that in nature there exist heavy leptons. It is shown that for lepton masses of the order of a few GeV the μ → eγ decay probability may well be close to its experimentally determined upper limit. The relation between such a decay process and neutrino oscillations is briefly considered.     

Phenomenology of neutrino oscillations

The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.     

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.     

Paradoxes of neutrino oscillations

Despite the theory of neutrino oscillations being rather old, some of its basic issues are still being debated in the literature. We discuss a number of such issues, including the relevance of the “same energy” and “same momentum” assumptions, the role of quantum-mechanical uncertainty relations in neutrino oscillations, the dependence of the coherence and localization conditions that ensure the observability of neutrino oscillations on neutrino energy and momentum uncertainties, the question of (in)dependence of the oscillation probabilities on the neutrino production and detection processes, and the applicability limits of the stationary-source approximation. We also develop a novel approach to calculation of the oscillation probability in the wave-packet approach, based on the summation/integration conventions different from the standard one, which allows a new insight into the “same energy” vs. “same momentum” problem. We also discuss a number of apparently paradoxical features of the theory of neutrino oscillations. The text was submitted by the authors in English.