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.     

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.     

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.     

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.     

Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m₀ and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN ²〉/V on the particle mass m₀ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym ₀c² is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_BT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N _v〉/V but also the mean square fluctuation 〈Δ _v ² 〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino massm _v instead of the actual massm _0v .     

A search for neutrino oscillations

We present here the final results of experiments searching for neutrino oscillations, carried out by the CHARM Collaboration. The data — taking took place in 1983. The first experiment was performed by exposing two detectors simultaneously to the CERN PS low energyv _µ beam. In the second experiment the full CHARM detector was exposed to the wide-band horn-focusedv _µ beam of the CERN SPS. Complete details of the experiments and data reduction are presented. No statistically significant signals for neutrino oscillations were observed. Our 90% CL limits in the appearance experiment (v _µ→v _e ) exclude Δm ²≧0.19 eV² for complete mixing (sin²2θ=1), and sin²2θ≧0.008 for the region Δm ²≧30 eV². These results, and the limits observed for (v _µ→v _x ) (disappearance of (v _µ), are in agreement with those of most other experiments but exclude part of the region previously reported as a possible indication ofv _µ→v _e oscillations.     

What can we learn from high precision measurements of neutrino mixing angles?

Many experiments are being planned to measure the neutrino mixing angles more precisely. In this note, the theoretical significance of a high precision measurement of these parameters is discussed. It is emphasized that they can provide crucial information about different ways to understand the origin of large atmospheric neutrino mixing and move us closer towards determining the neutrino mass matrix. They may also be able to throw light on the question of lepton-quark unification as well as the existence of any leptonic symmetries. For instance if exact μ↔ τ symmetry in the neutrino mass matrix is assumed to be the reason for maximalv _μ-v_gt mixing, one gets θ₁₃ = 0 and {ie1295-01} can provide information about the way the μ↔ τ symmetry breaking manifests in the case of normal hierarchy.     

Double-beta decay: Present status

The present status of double-beta-decay experiments (including the search for 2β ⁺, ECβ ⁺, and ECEC processes) are reviewed. The results of the most sensitive experiments are discussed. Average and recommended half-life values for two-neutrino double-beta decay are presented. Conservative upper limits on effective Majorana neutrino mass and the coupling constant of the Majoron to the neutrino are established as 〈m _ν 〉 < 0.75 eV and 〈g _ee 〉 < 1.9 × 10⁻⁴, respectively. Proposals for future double-betadecay experiments with a sensitivity for the 〈m _ν 〉 at the level of 0.01–0.1 eV are considered.     

Neutrino oscillations: Present status and outlook

The status of neutrino oscillations from global data is summarized, with the focus on the three-flavour picture. The status of sterile neutrino oscillation interpretations of the LSND anomaly in the light of recent MiniBooNE results is also discussed. Furthermore, an outlook on the measurement of the mixing angle ϑ ₁₃ in the near term future, as well as prospects to discover CP violation in neutrino oscillations and to determine the type of the neutrino mass ordering by long-baseline experiments in the long term future are given.      

Gemma experiment: Three years of the search for the neutrino magnetic moment

The result of the 3-year neutrino magnetic moment measurement at the Kalinin Nuclear Power Plant (KNPP) with the GEMMA spectrometer is presented. Antineutrino-electron scattering is investigated. A high-purity germanium detector of 1.5 kg placed at a distance of 13.9 m from the 3 GW_th reactor core is exposed to the antineutrino flux of 2.7 × 10¹³ cm⁻² s⁻¹. The scattered electron spectra taken in (5184 + 6798) and (1853 + 1021) h for the reactor ON and OFF periods are compared. The upper limit for the neutrino magnetic moment μ_v < 3.2 × 10⁻¹¹μ _B at 90% CL is derived from the data processing.     

Future of neutrino experiments

Atmospheric, solar, reactor and accelerator neutrino oscillation experiments have measured Δm ₁₂², sin² θ ₁₂, |Δm ₂₃²| and sin² 2θ ₂₃. The next stage of the oscillation studies should be the observation of a finite sin² 2θ ₁₃. If a non-zero sin² 2θ ₁₃ is observed, the subsequent goals should be the observation of the CP violation and the determination sign of Δm ₂₃². Possible future neutrino oscillation experiments that could assess these questions are discussed.      

Direct neutrino mass measurements

The determination of the neutrino rest mass plays an important role at the intersections of cosmology, particle physics and astroparticle physics. This topic is currently being addressed by two complementary approaches in laboratory experiments. Neutrinoless double beta decay experiments probe whether neutrinos are Majorana particles and determine an effective neutrino mass value. Single beta decay experiments such as KATRIN and MARE investigate the spectral shape of β-decay electrons close to their kinematic endpoint in order to determine the neutrino rest mass with a model-independent method. Owing to neutrino flavour mixing, the neutrino mass parameter appears as an average of all neutrino mass eigenstates contributing to the electron neutrino. The KArlsruhe TRItium Neutrino experiment (KATRIN) is currently the experiment in the most advanced status of commissioning. Applying an ultra-luminous molecular windowless gaseous tritium source and an integrating high-resolution spectrometer of MAC-E filter type, it allows β-spectroscopy close to the T ₂ end-point with unprecedented precision and will reach a sensitivity of 200 meV/c ² (90% C.L.) on the neutrino rest mass.     

Neutrino physics at the turn of the millennium

I discuss the implications of the latest data on solar and atmospheric neutrinos which strongly indicate the need for physics beyond the Standard Model. I review the theoretical options for reconciling these data in terms of three-neutrino oscillations. Even though not implied by the data, bimaximal models of neutrino mixing emerge as an attractive possibility. Supersymmetry with broken R-parity provides a predictive way to incorporate it, opening the possibility of testing neutrino anomalies at high-energy collider experiments such as the LHC or at the upcoming long-baseline or neutrino factory experiments. Reconciling, in addition, the hint provided by the LSND experiment requires a fourth, light sterile, neutrino. The simplest theoretical scenarios are the most symmetric ones, in which two of the four neutrinos are maximally mixed and lie at the LSND scale, while the others are at the solar mass scale. The lightness of the sterile neutrino, the nearly maximal atmospheric neutrino mixing, and the generation of Δm _⊙ ² &; Δm _atm ² all follow naturally from the assumed lepton-number symmetry and its breaking. These two basic schemes can be distinguished at neutral-current-sensitive solar &; atmospheric neutrino experiments such as the Sudbury Neutrino Observatory. However, underground experiments have not yet proven neutrino masses, since there is a variety of alternative mechanisms. For example, flavor changing interactions can play an important role in the explanation of solar and of contained atmospheric data and could be tested through effects such as μ → e+γ, μ-e conversion in nuclei, unaccompanied by neutrino-less double beta decay. Conversely, the room is still open for heavy unstable neutrinos. A short-lived ν_μ might play a role in the explanation of the atmospheric data. Finally, in the presence of a sterile neutrino v_s, a long-lived ν_τ in the MeV range could delay the time at which the matter and radiation contributions to the energy density of the Universe become equal, reducing the density fluctuations on the smaller scales and rescuing the standard cold-dark-matter scenario for structure formation. In this case, the light v_e ν_μ, and v_s would account for the solar and atmospheric data.     

Do Two Flavour Oscillations Explain both KamLAND Data and the Solar Neutrino Spectrum?

The recent measurement of Δ _sol by the KamLAND experiment with very small errors, makes definitive predictions for the energy dependence of the solar neutrino survival probability P _ee . We fix Δ _sol to be the KamLAND best fit value of 8×10⁻⁵ eV² and study the energy dependence of P _ee for solar neutrinos, in the framework of two flavour oscillations and also of three flavour oscillations. For the case of two flavour oscillations, P _ee has a measurable slope in the 5–8 MeV range but the solar spectrum measurements in this range find P _ee to be flat. The predicted values of P _ee , even for the best fit value of θ _sol , differ by 2–3 σ from the Super-K measured values in each of the three energy bins of the 5–8 MeV range. If future measurements of solar neutrinos by Super-K and SNO find a flat spectrum with reduced error bars (by a factor of 2), it will imply that two flavour oscillations can no longer explain both KamLAND data and the solar spectrum. However a flat solar neutrino spectrum and the Δ _sol measured by KamLAND can be reconciled in a three flavour oscillation framework with a moderate value of θ ₁₃≈13°.     

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.     

Futurev τ oscillation experiments and present data

Our goal in this paper is to examine the discovery covery potential of laboratory experiments searching for the oscillationv _μ(ν _e)→v _τ, in the light of recent data on solar and atmospheric neutrino experiments, which we analyse together with the most restrictive results from laboratory experiments on neutrino oscillations. In order to explain simultaneouslyall present results we use a four-neutrino framework, with an additional sterile neutrino. Our predictions are rather pessimistic for the upcoming experiments NOMAD and CHORUS, which, we find, are able to explore only a small area of the oscillation parameter space. On the other hand, the discovery potential of future experiments is much larger. We consider three examples. E803, which is approved to operate in the future Fermilab main injector beam line, MINOS, a proposed long-baseline experiment also using the Fermilab beam, and NAUSICAA, an improved detector which improves by an order of magnitude the performance of CHORUS/NOMAD and can be operated either at CERN or at Fermilab beams. We find that those experiments can cover a very substantial fraction of the oscillation parameter space, having thus a very good chance of discoveringboth v _μ→v _τ andν _e→v _τ oscillation modes.     

Futurev �� oscillation experiments and present data

Our goal in this paper is to examine the discovery covery potential of laboratory experiments searching for the oscillationv _??(?? _e)??v _??, in the light of recent data on solar and atmospheric neutrino experiments, which we analyse together with the most restrictive results from laboratory experiments on neutrino oscillations. In order to explain simultaneouslyall present results we use a four-neutrino framework, with an additional sterile neutrino. Our predictions are rather pessimistic for the upcoming experiments NOMAD and CHORUS, which, we find, are able to explore only a small area of the oscillation parameter space. On the other hand, the discovery potential of future experiments is much larger. We consider three examples. E803, which is approved to operate in the future Fermilab main injector beam line, MINOS, a proposed long-baseline experiment also using the Fermilab beam, and NAUSICAA, an improved detector which improves by an order of magnitude the performance of CHORUS/NOMAD and can be operated either at CERN or at Fermilab beams. We find that those experiments can cover a very substantial fraction of the oscillation parameter space, having thus a very good chance of discoveringboth v _????v _?? and?? _e??v _?? oscillation modes.     

Uniqueness of the standard model neutral current predictions

In view of an excellent agreement between the recently determinedv _μ-hadron couplings and predictions of the standard model, the basic question discussed is how far its neutral current predictions can be mimiced in going either from the isodoublet to an isotriplet (or an even higher isospin) left-handed representation or from SU _L (2) × U(1) toG × U(1), whereG is a simple group of rank two. This question is addressed with reference to a sufficiently broad class of schemes. Their most distinctive properties are: in the higher isospin scheme, neutrino couplings are precisely in the form obtainable with standard l.h. representation; the higher g.g. scheme isL+R type in which, to each light fermion of evenRU parity, a superheavy fermion of the same charge and oddRU parity is associated, parity conservation forbidding their mixing. Reasons for excluding theL-type andG ₂ higher g.g. schemes are given. Their neutral current predictions are compared with those of the standard model. A higher isospin representation can mimic the predictions of the standard model in inclusive and semi-inclusivev _μ-hadron reactions but is conclusively discriminated from the isodoublet representation by elasticv _μ ⁽⁻ p scattering. TheG × U(1) scheme can mimic standard model neutrino sector but is conclusively discriminated from minimal scheme by parity violating effects.     

Mesonic decays of τ− lepton: Effects of neutrino mass and mass mixing

Experimentally established mesonic decays ofτ ⁻ lepton have been reexamined with the inclusion of the effects of finite neutrino mass and the associated mass mixing in the form of Kobayashi-Maskawa mixing matrix. A comparison with the experimentally predicted decay probabilities provides limits for thev _τ mass which are finite in all decays except for the lower limit in mass mixing case of the decayτ ⁻→K*⁻ (892)+v _τ for which MeV. The large error in this value is because of (i) large errors in the experimental values of life time and branching ratio for this decay and (ii) thekm mixing used in the calculations. The ratio of parity-violating to parity-conserving terms in the differential decay probabilities of various decays differs slightly from their values corresponding to those with varishingv _τ mass.