Oscillations of three generations of neutrinos and the solar neutrino problem

The resonant neutrino oscillations in matter are assumed to be responsible for the observed reduction in the capture rate for the ³⁷Cl detector. The expression of the probability that a solar v_e reaches the Earth as a v_e is given in the case of three generations. In the small mixing angle approximation, we describe all the regions of neutrino parameters which give rise to a capture rate of 2.1 SNU for ³⁷Cl and we give the corresponding prediction for the ⁷¹Ga detector.     

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.     

The effect of random matter density perturbations on the MSW solution to the solar neutrino problem

We consider the implications of solar matter density random noise upon resonant neutrino conversion. The evolution equation describing MSW-like conversion is derived in the framework of the Schrödinger approach. We study quantitatively the effect of such matter perturbations upon both large and small mixing angle MSW solutions to the solar neutrino problem. This is carried out both for the active-active v_e → v_μ,τ as well as active-sterile v_e → v_s conversion channels. We find that the small mixing MSW solution is much more stable (especially in Δm² than the large mixing solution. The possible existence of solar matter density noise at the few percent level could be tested at future solar neutrino experiments, especially Borexino.     

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.     

Radiative neutrino decay and the unusual X-ray flux from Sn 1987A

The radiative neutrino decay in the mass and a lifetime range, m_v=10–100 keV and τ_v=10³–10⁵ s, is often argued to be forbid by γ-ray data from past supernovas. We demonstrate that this argument is not always correct, and accordingly attempt to explain via radiative neutrino decay the unusual soft component of the X-ray spectrum from SN 1987A, observed by the satellite Ginga. Our fit to the data suggests that τ_v=(1–3)×10⁴s·(m_v/50 keV).     

Statistical theory of nuclear neutrino capture: (II). Inclusion of first-forbidden transitions

The statistical theory of nuclear neutrino capture is extended to include first-forbidden transitions. A comparison with the theory of Bahcall and Frautschi is made. It is found that the present theory predicts neutrino capture cross sections which are smaller than those of Bahcall and Frautschi by a factor 2–3 for neutrino energies less than 50 MeV when first-forbidden transitions are dominant. Calculation of the cross section is made for the process in which ³⁷Cl nuclei capture electron neutrinos that are emitted in muon decay. The present calculation gives a cross section which is around one half of that of Donnelly and Haxton. Finally the contributions of the highly excited states in ³⁷Ar to the neutrino capture cross section are evaluated. It is shown that the contributions from the highly excited states (E > 6.02 MeV) to the neutrino capture cross section amount to 60% for E_v = 50 MeV.     

The mixing angles in matter for three generations of neutrinos and the MSW mechanism

Mikheyev and Smirnov have recently shown that oscillations between two species of neutrinos may be amplified in matter. We give analytic expressions for the energy eigenvalues, all the mixing angles and the CP-violating phase in matter for three generations of neutrinos using the Fritzsch parametrization for the flavor mixing matrix. For clearly separated neutrino masses Δm ₃₁ ² ?Δm ₂₁ ² we find two MSW resonance effects—one forv _e ?v _µ and one forv _e ?v _τ conversions —which can each be approximated by a separate two neutrino treatment as has been recently shown by Kuo and Pantaleone. Nearly degenerate neutrino masses Δm ₃₁ ² ～Δm ₂₁ ² on the other hand lead to only one resonance region withs _{1 2} ^{m 2} no longer necessarily approaching 1 for very high densities.     

Superstring induced mass and magnetic moment of the neutrino and the time modulation of the solar neutrino flux

The new Yukawa couplings involving heavy matter E₆ fields predicted in the framework of superstring theories are considered as a source of mass and magnetic moment for the neutrino. Given the experimental bound m_ve < 46 eV bounds are derived on the neutrino magnetic moment thus generated. Finally, a scenario is produced where the induced magnetic moment has the correct magnitude (∼10⁻¹¹ μ_B) to explain an alleged depletion or solar neutrino flux during periods of maximum solar activity.     

Photons as para-fermion composites-limitations

A large class of neutrino theories of light has not previously been eliminated. Every model in which a photon is a superposition of non-interacting v_μv?_μ, v_βv?_β, v?_μv_β and v_μv?_β states still succumbs to the pitfalls uncovered by Pryce.Using a natural para-statistical place convention, it is seen that possible bi-linear constructions of photon operators from para-Fermion operators are more general than those already ruled out in the neutrino theory of light. Previous extensions of Pryce's theorem have not excluded the possibility that cross terms involving both pair annihilation terms and Raman terms may give the required Bose commutation relations in a para-statistical construction. Here it is established that the only parastatistical constructions still open for investigation are those in which the underlying lepton numbers are not conserved.It is impossible to bilinearly construct a para-Boson algebra on a representative neutrino space. Nevertheless, it is pointed out that it will be possible to derive a para-Boson representation from any composite photon field.     

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.     

The magnetic moments of (vg 9/2)-levels in odd Zn isotopes

^69m,71mZn have been implanted with an isotope separator on-line into a cold iron host matrix. Nuclear magnetic resonance of the low-temperature oriented isotopes has been observed. The resonance frequencies for zero external magnetic field are v_L(^69mZnFe@#@) =36.814(35) MHz andv _L (^71mZnFe)=33.47(19) MHz. From these the magnetic moments of the 9/2⁺ iosmeric states have been derived as μ(^69mZn)=(?)1.138(18) n.m. andμ(^71mZn)=(?)1.035(18) n.m. The experimentally known magnetic moments of (vg _9/2)-levels in odd zinc isotopes are compared to theoretical estimates.     

An upper limit on the tau neutrino mass from leptonic tau decays

The partial width of the τ → e ^- v _e v _τ can be calculated from the tau mass, lifetime and branching ratio. The increasing precision on these measurements is making the partial width sensitive to the mass of the tau neutrino. We present the tau neutrino mass dependence on the partial width and show that this leads to a limit of m _r < 71 MeV at the 95% confidence level. We show that the limit is determined by the uncertainty in the tau lifetime and τ → e?v _e v _τ branching ratio. Additional measurements of these values are expected in the next few years and we show that the limit could become competitive with the direct measurements.     

Physics potential of searching for 0vββ decays in JUNO

In the past few decades, numerous searches have been made for the neutrinoless double-beta decay (0vββ) process, aiming to establish whether neutrinos are their own antiparticles (Majorana neutrinos), but no 0vββ decay signal has yet been observed. A number of new experiments are proposed but they ultimately suffer from a common problem: the sensitivity may not increase indefinitely with the target mass. We have performed a detailed analysis of the physics potential by using the Jiangmen Underground Neutrino Observatory (JUNO) to improve the sensitivity to 0vββ up to a few meV, a major step forward with respect to the experiments currently being planned. JUNO is a 20 kton low-background liquid scintillator (LS) detector with 3%E(MeV) energy resolution, now under construction. It is feasible to build a balloon filled with enriched xenon gas (with ¹³⁶Xe up to 80%) dissolved in LS, inserted into the central region of the JUNO LS. The energy resolution is ～1.9% at the Q-value of ¹³⁶Xe 0vββ decay. Ultra-low background is the key for 0vββ decay searches. Detailed studies of background rates from intrinsic 2vββ and ⁸B solar neutrinos, natural radioactivity, and cosmogenic radionuclides (including light isotopes and ¹³⁷Xe) were performed and several muon veto schemes were developed. We find that JUNO has the potential to reach a sensitivity (at 90% C. L.) to T_1/2^0vββ of 1.8×10²⁸ yr (5.6×10²⁷ yr) with ～50 tons (5 tons) of fiducial ¹³⁶Xe and 5 years exposure, while in the 50-ton case the corresponding sensitivity to the effective neutrino mass, m_ββ, could reach (5-12) meV, covering completely the allowed region of inverted neutrino mass ordering.     

Calculation of double beta decay rates and the neutrino mass

Predictions for 2v and 0v double beta decay rates are given for all nuclei with A ⩾ 70, for which double beta decay is energetically allowed. These predictions are based on detailed nuclear structure studies of the beta strength distribution and replace earlier estimates basing mostly on phase space considerations. New and more stringent limits on the Majorana neutrino mass are deduced from existing double beta decay experiments. Since the collective effects arising from spin-isospin as well as quadrupole-quadrupole forces are found to lead to a strong reduction of the nuclear matrix elements for two-neutrino double beta decay, but to have only minor influence on the matrix elements M^0v for the neutrinoless decay mode, the smaller limits for m_v result mainly from the fact that the widely used scaling procedure underestimates the 0_v matrix elements. It is further discussed to what extent interference between different neutrinos affects the obtained mass limits.     

Searching the absolute neutrino mass in tritium β-decay—interplay between nuclear, atomic and molecular physics

The paper treats recent experiments measuring the endpoint region of tritium β-decay with high resolution, sensitivity and background rejection, using an electrostatic filter with adiabatic magnetic collimation. The spectra are analysed with respect to the neutrino mass. These results form the primary source for the present upper limit of the neutrino mass m _ν ?<?2 eV quoted by the particle data group. Particular attention is paid to the decisive influence which atomic and molecular physics effects take on the results. A brief outlook on future experiments is given.     

Direct neutrino mass measurements

Direct neutrino mass experiments are complementary to searches for neutrinoless double β-decay and to analyses of cosmological data. The previous tritium beta decay experiments at Mainz and at Troitsk have achieved upper limits on the neutrino mass of about 2 eV/c² . The KATRIN experiment under construction will improve the neutrino mass sensitivity down to 200 meV/c² by increasing strongly the statistics and—at the same time—reducing the systematic uncertainties. Huge improvements have been made to operate the system extremely stably and at very low background rate. The latter comprises new methods to reject secondary electrons from the walls as well as to avoid and to eject electrons stored in traps. As an alternative to tritium β-decay experiments cryo-bolometers investigating the endpoint region of ¹⁸⁷Re β-decay or the electron capture of ¹⁶³Ho are being developed. This article briefly reviews the current status of the direct neutrino mass measurements.     

Neutrino masses as a second-order effect in Higgs coupling

It is suggested that in the usual type of gauge theory all fermions, including neutrinos, have right-handed components. The smallness or vanishing of the observed neutrino masses is explained by the fact that the appropriate neutral Higgs boson does not develop a non-zero vacuum expectation value. In the case when the neutrino masses do not vanish they are finite, of order G_Fm³, where m is the mass of the charged lepton. Non-conservation of lepton flavor gives rise to an instability of all neutrinos except v_e and to μ→e+γ decay, but at a very low level.     

Spontaneous R parity violation in supersymmetry: A model for solar neutrino oscillations

Spontaneous breaking of R parity in the standard supergravity model implies the existence of a majoron which is strongly constrained by astrophysics. This is suggested as the origin of the small parameter required for the resonant amplification of neutrino oscillations to take place in the sun. To a good approximation only one neutrino type (most likely the tau neutrino) acquires a mass. Therefore the form of the leptonic charged current is very much restricted: it is fully described by two mixing angles and there is no CP violation. As a result, matter can only amplify oscillations in one channel which, for small mixings, is v_ℓv_τ. Agreement with the chlorine data on the one hand and the nonobservation of charged supersymmetric states in e⁺e^- collisions on the other, tightly restricts the parameters of the model in a way that will be directly tested by collider experiments.     

Overview on neutrinos and the Daya Bay experiment

Neutrinos are elementary particles in the Standard Model. Neutrino oscillation is a quantum mechanical phenomenon beyond the Standard Model. Neutrino oscillation can be described by two independent mass-squared differences Δm ₂₁ ² , Δm ₃₁ ² (or Δm ₃₂ ² ) and a 3 × 3 unitary matrix, containing three mixing angles θ ₁₂, θ ₂₃, θ ₁₃, and one charge-parity (CP) phase. θ ₁₂ is about 34° and determined by solar neutrino experiments and the reactor neutrino experiment KamLAND. θ ₂₃ is about 45° and determined by atmospheric neutrino experiments and accelerator neutrino experiments. θ ₁₃ can be measured by either accelerator or reactor neutrino experiments. On Mar. 8, 2012, the Daya Bay Reactor Neutrino Experiment reported the first observation of non-zero θ ₁₃ with 5.2 standard deviations. In June, with 2.5× previous data, Daya Bay improved the measurement of sin²2θ ₁₃ = 0.089 ± 0.010(stat) ± 0.005(syst).     

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.