Narrow Results

In this paper, we carry out the canonical quantization of the field theory of an interacting tachyonic Majorana neutrino. We show how micro-causality is preserved in the physical scattering matrix elements between the in and out vacua.

The phenomenology of this radical proposal is nevertheless compatible with normal timelike oscillations.

For the first time the expected pulse shapes to be observed for neutrinoless double beta events in a big ⁷⁶Ge detector have been calculated starting from their Monte Carlo calculated time history and spatial energy distribution. It is shown that with the spatial resolution of a large size Ge detector for the majority of 0νββ events it is not possible to differentiate between the contributions of different particle physics parameters entering into the 0νββ decay process — in the mass mechanism the effective neutrino mass and the right-handed weak current parameters λ, η. It is shown that on the other hand it is possible in a ⁷⁶Ge double beta decay experiment to reject a background of larger sizes (high multiplicity) gamma events by selecting low size (low multiplicity) events. First comparison of the theoretical ββ pulses to events from the line observed at^3,4Q_ββ shows very good agreement. It is shown further that a rather good radial position determination of ββ events in the detector is possible. By the same type of calculation it is shown that use of the pulse shapes of the 1592 keV double escape line of the 2614 keV γ-transition from ²²⁸Th for calibrating a neuronal net for search of events of neutrinoless double beta decay should be helpful.

In this brief review, a description of the observed evidence for neutrinoless double beta^3–5 in the ⁷⁶Ge experiment in Gran Sasso (Heidelberg–Moscow experiment) which has been operated with 11 kg enriched ⁷⁶Ge detectors in the period 1990–2003, is provided. Two different methods of pulse shape analysis have been used to select potential 0νββ events from the γ background of the measured spectrum — a selection by a neuronal net approach,^3,4,16 and a selection by a new method comparing measured pulses with a library of pulse shapes of point-like events calculated from simulation of the electric field distribution in the detectors (see Refs. 6–8 and 37). The latter method also allows spatial localization of measured events. Both methods lead to selections of events at Q_ββ with almost no γ-background. The observed line at Q_ββ is identified as a 0νββ signal. It has a confidence level of more than 6σ.

This is a brief review of spectroscopic studies of neutrino-less double beta decays (0νββ) and the MOON (Mo Observatory Of Neutrinos) project. It aims at studying the Majorana nature of neutrinos and the mass spectrum by spectroscopic studies of 0νββ with ν-mass sensitivity of 〈m_ν〉 ≈ 30 meV. The solid scintillator option of the MOON detector is a super ensemble of multi-layer modules, each being composed by a scintillator plate and two tracking detector planes. Thin ββ source films are interleaved between the detector planes. High localization of the two β tracks enables one to select true signals and reject BG ones by spatial and time correlation analyses. MOON with detector ≠ ββ source is used for studying 0νββ decays from ¹⁰⁰Mo, ⁸²Se and other ββ isotopes with large nuclear sensitivity (large Q_ββ). Real-time exclusive measurements of low energy solar neutrinos can also be made by observing inverse β rays from solar-ν captures of ¹⁰⁰Mo in delayed coincidence with the subsequent β decay of ¹⁰⁰Tc.

The GERmanium Detector Array, GERDA, is designed to search for neutrinoless double-beta (0νββ) decay of ⁷⁶Ge and it is installed in the Laboratori Nazionali del Gran Sasso (LNGS) of INFN, Italy. In this review, the detection principle and detector setup of GERDA are described. Also, the main physics results by GERDA Phase I, are discussed. They include the measurement of the half-life of 2νββ decay, the background decomposition of the energy spectrum and the techniques for the discrimination of the background, based on the pulse shape of the signal. In the last part of this review, the estimation of a limit on the half-life of 0νββ ( at 90% C.L.) and the comparison with previous results are discussed. GERDA data from Phase I strongly disfavor the recent claim of 0νββ discovery, based on data from the Heidelberg–Moscow experiment.

We give a review on neutrino models in which Majorana neutrino masses are generated radiatively through loop diagrams. In particular, we concentrate on the two-loop models which contain extra doubly charged singlet $\Phi$ and triplet $\Delta$ scalars beyond the Standard Model so that the new Yukawa $\Psi {\bar{\ell }}_R^c{\ell }_R$ and effective ${\Psi }^{\pm \pm }{W}^{\mp }{W}^{\mp }$ couplings can be induced. In these two-loop models, we find that the neutrino mass spectrum is a normal hierarchy and the rate of the neutrinoless double beta decay $(0\nu \beta \beta )$ can be large as it is dominated by the short-distance tree contribution. In addition, by using the neutrino oscillation data and comparing with the global fitting result in the literature, we find a unique neutrino mass matrix and predict the Dirac and two Majorana CP phases to be $3(\pi -\eta )∕2$, $\pi +3\eta ∕2$ and $(3\pi -\eta )∕2$ with $\eta =0.07\pi$, respectively.

We examine the possibility of vanishing effective Majorana mass $M_{ee}$ in the presence of one or two sterile neutrinos taking into account the recent data on neutrino masses and mixings, particularly, on ${\theta }_{13}$. Also, within the framework of standard three active neutrinos, we find that effective Majorana mass $M_{ee}$ can be vanishingly small if neutrino masses observe normal hierarchy. However, the same is not valid for inverted hierarchical neutrino masses. The predictions for Majorana phases $\alpha$ and $\beta$ have also been obtained and shown as scatter plots. We also examine the condition $M_{ee}=0$ within the framework wherein fermion sector has been extended by the addition of either one or two sterile neutrinos. The condition of vanishing effective Majorana mass is found to be inconsistent with the recent measurement of ${\theta }_{13}$ in these classes of models except for $1+3$, $2+3$ neutrino mass scheme for small values of the lightest neutrino mass, $m_{\mathrm{\text{light}}}$.

Assuming that one neutrino type with definite mass is described by a massive Dirac field operator, it is shown that the physical one-particle states for particles and antiparticles can be rotated to each other, irrespective of their helicity. This result is used to prove that the neutrino must necessarily be a Majorana particle.

We give some new insights into the effective Majorana neutrino mass ${〈m〉}_{ee}^{}$ responsible for the neutrinoless double-beta $(0\nu 2\beta )$ decays. We put forward a three-dimensional way of plotting $\left|{〈m〉}_{ee}^{}\right|$ against the lightest neutrino mass and the Majorana phases, which can provide more information as compared with the two-dimensional one. With the help of such graphs we discover a novel threshold of $\left|{〈m〉}_{ee}^{}\right|$ in terms of the neutrino masses and flavor mixing angles: $|{〈m〉}_{ee}^{}{|}_{\ast }^{}=m_3^{}{sin}^2{𝜃}_{13}^{}$ in connection with $tan{𝜃}_{12}^{}=\sqrt{m_1^{}/m_2^{}}$ and $\rho =\pi$, which can be used to signify observability of the future $0\nu 2\beta$-decay experiments. Fortunately, the possibility of $\left|{〈m〉}_{ee}^{}\right|<|{〈m〉}_{ee}^{}{|}_{\ast }^{}$ turns out to be very small, promising a hopeful prospect for the $0\nu 2\beta$-decay searches.

In this review for the first time a theoretical description of the tracks of events of nuclear double beta decay in a large Ge detector is presented. It is obvious that in principle the shapes and sizes of these tracks — and the corresponding time structure of pulses — depend on particle physics and nuclear physics parameters such as neutrino mass, right-handed current parameters, and nuclear matrix elements. The knowledge of this dependence is of importance, since the key to probe the existence of 0νββ decay beyond observation of a signal at the Q value of the process, Q_ββ, is the discrimination of ββ events from background γ events (or other events), in almost any double beta decay experiment (see Refs. 2 and 3). In this review Monte-Carlo simulations of tracks of neutrino-accompanied (2νββ) and neutrinoless double beta decay (0νββ) events, and of various kinds of background processes such as multiple and other γ interactions are reported for a large Ge detector. The time history of the evolution of the individual events is followed and the sizes of the events (volumes in the detector inside which the energy of the event is released) are investigated. Effects of the angular correlations of the two electrons in ββ decay, which again depend on the above nuclear and (for 0νββ decay) particle physics parameters, are taken into account and have been calculated for this purpose for the first time on basis of the experimental half-life of ⁷⁶Ge and of realistic nuclear matrix elements.

It is shown for ββ decay of ⁷⁶Ge, that 0νββ events are to a large extent separable from Compton scattering of γ events of the same energy, while double escape peaks of γ-lines show very similar behavior as 0νββ events, and in that sense can be useful for corresponding "calibration" of pulse shapes of the detector. The possibility to distinguish 0νββ events from γ events is found to be essentially independent of the particle physics parameters of the 0νββ process. A brief outlook is given on the potential of future experiments with respect to determination of the particle physics parameters 〈m_ν〉, 〈λ〉, 〈η〉. It is suggested, that the strategy in future 0νββ research should be, to combine confirmation of the HEIDELBERG-MOSCOW result with determination of the mechanism of the dominating decay, instead of repeating earlier experiments or ideas. The future experiment thus should not use ⁷⁶Ge or ¹³⁶Xe, but instead ¹²⁴Xe.

If massive neutrinos are the Majorana particles, how to pin down the Majorana CP-violating phases will eventually become an unavoidable question relevant to the future neutrino experiments. I argue that a study of neutrino–antineutrino oscillations will greatly help in this regard, although the issue remains purely academic at present. In this talk I first derive the probabilities and CP-violating asymmetries of neutrino–antineutrino oscillations in the three-flavor framework, and then illustrate their properties in two special cases: the normal neutrino mass hierarchy with m₁ = 0 and the inverted neutrino mass hierarchy with m₃ = 0. I demonstrate the significant contributions of the Majorana phases to the CP-violating asymmetries, even in the absence of the Dirac phase.

We consider extensions of the standard model with fourth generation fermions (SM4) in which extra symmetries are introduced such that the transitions between the fourth generation fermions and the ones in the first three generations are forbidden. In these models, the stringent lower bounds on the masses of fourth generation quarks from direct searches can be relaxed, and the lightest fourth neutrino is allowed to be stable and light enough to trigger the Higgs boson invisible decay. In addition, the fourth Majorana neutrino can be a subdominant but highly detectable dark matter component. We perform a global analysis of the current Large Hadron Collider (LHC) data on the Higgs production and decay in this type of SM4. The results show that the mass of the lightest fourth Majorana neutrino is confined in the range ~41–59 GeV. Within the allowed parameter space, the predicted effective cross-section for spin-independent DM–nucleon scattering is ~3×10^-48–6×10^-46cm², which is close to the current XENON100 upper limit and is within the reach of the XENON1T experiment in the near future. The predicted spin-dependent cross sections can also reach ~8×10^-40cm².

In the LHC era the issue of the origin and nature of neutrino mass has attained a new meaning and a renewed importance. The growing success of the Higgs–Weinberg mechanism behind the charged fermion masses paves the way for answering the question of neutrino mass. We have shown recently how the spontaneous breaking of parity in the context of the minimal left–right symmetric model allows to probe the origin of neutrino mass in complete analogy with the charged fermions masses in the Standard Model. We revisit here this issue and fill in the gaps left in our previous work. In particular we discuss a number of different mathematical approaches to the problem of disentangling the seesaw mechanism and show how a unique analytical solution emerges. Most important, we give all the possible expressions for the neutrino Dirac mass matrix for general values of light and heavy neutrino mass matrices. In practical terms what is achieved is an untangling of the seesaw mechanism with clear and precise predictions testable at hadron colliders such as LHC.

Nuclear double beta decay provides an extraordinarily broad potential to search for beyond-standard-model physics. The occurrence of the neutrinoless decay(0νββ) mode has fundamental consequences: first, the total lepton number is not conserved, and second, the neutrino is a Majorana particle. Furthermore, the measured effective mass provides an absolute scale of the neutrino mass spectrum. In addition, double beta experiments yield sharp restrictions for other beyond-standard-model physics. These include SUSY models (R-parity breaking and conserving), leptoquarks (leptoquark-Higgs coupling), compositeness, left-right symmetric models (right-handed W boson mass), test of special relativity and of the equivalence principle in the neutrino sector and others. First evidence for neutrinoless double beta decay was reported by the HEIDELBERG–MOSCOW experiment in 2001. The HEIDELBERG–MOSCOW experiment is by far the most sensitive0νββ experiment since more than 10 years. It is operating 11 kg of enriched ⁷⁶Ge in the GRAN SASSO Underground Laboratory. The analysis of the data taken from 2 August 1990–20 May 2003 is presented here. The collected statistics is 71.7 kg y. The background achieved in the energy region of the Q value for double beta decay is 0.11 events/kg y keV. The two-neutrino accompanied half-life is determined on the basis of more than 100,000 events to be years. The confidence level for the neutrinoless signal has been improved to a 4.2σ level. The half-life is years. The effective neutrino mass deduced is (0.2–0.6) eV (99.73% C.L.), with the consequence that neutrinos have degenerate masses. The sharp boundaries for other beyond SM physics, mentioned above, are comfortably competitive to the corresponding results from high-energy accelerators like TEVATRON, HERA, etc.

This paper describes the lessons we have to draw after the observation of neutrinoless ββ decay by the enriched ⁷⁶Ge experiment, for present and future experiments so as (a) to fulfill the task to confirm the present result (b) to deliver additional information on the main contributions of effective neutrino mass and right-handed weak currents etc. to the 0νββ amplitude. It is shown that presently running and planned experiments are probably not sensitive enough to check the evidence on a reasonable time scale. It is further demonstrated that, the only way to get more information on the individual contributions of m, η, λ etc. to the 0νββ amplitude is to go to completely different types of experiments, rather than those under construction and preparation at present, e.g. to mixed-mode β⁺/EC decay experiments, such as ¹²⁴Xe decay. It is pointed out that the sometimes observed "tension" between the result of 0νββ decay and cosmological experiments like WMAP, SDSS etc. does not exist and is an artificial product of improper analysis of the latter.

The observation of neutrinoless double beta decay (DBD) will have important consequences. First it will signal that lepton number is not conserved and the neutrinos are Majorana particles. Second, it represents our best hope for determining the absolute neutrino mass scale at the level of a few tens of meV. To achieve the last goal, however, certain hurdles have to be overcome involving particle, nuclear and experimental physics. Particle physics is important since it provides the mechanisms for neutrinoless DBD. In this review, we emphasize the light neutrino mass mechanism. Nuclear physics is important for extracting the useful information from the data. One must accurately evaluate the relevant nuclear matrix elements (NMEs), a formidable task. To this end, we review the recently developed sophisticated nuclear structure approaches, employing different methods and techniques of calculation. We also examine the question of quenching of the axial vector coupling constant, which may have important consequences on the size of the NMEs. From an experimental point of view it is challenging, since the life times are extremely long and one has to fight against formidable backgrounds. One needs large isotopically enriched sources and detectors with good energy resolution and very low background.

The neutrinoless double beta decay is not allowed in the Standard Model (SM) but it is allowed in most Grand Unified Theories (GUT's). The neutrino must be a Majorana particle (identical with its antiparticle) and must have a mass to allow the neutrinoless double beta decay. Apart of one claim that the neutrinoless double beta decay in ⁷⁶Ge is measured, one has only upper limits for this transition probability. But even the upper limits allow to give upper limits for the electron Majorana neutrino mass and upper limits for parameters of GUT's and the minimal R-parity violating supersymmetric model. One further can give lower limits for the vector boson mediating mainly the right-handed weak interaction and the heavy mainly right-handed Majorana neutrino in left-right symmetric GUT's. For that one has to assume that the specific mechanism is the leading one for the neutrinoless double beta decay and one has to be able to calculate reliably the corresponding nuclear matrix elements. In the present contribution, one discusses the accuracy of the present status of calculating the nuclear matrix elements and the corresponding limits of GUT's and supersymmetric parameters.

We give some new insights into the effective Majorana neutrino mass 〈m〉_ee responsible for the neutrinoless double-beta (0v2β) decays. We put forward a three-dimensional way of plotting |〈m〉_ee| against the lightest neutrino mass and the Majorana phases, which can provide more information as compared with the two-dimensional one. With the help of such graphs we discover a novel threshold of |〈m〉_ee| in terms of the neutrino masses and flavor mixing angles: |〈m〉_ee|_* = m₃ sin²θ₁₃ in connection with $\tan {\theta }_{12}=\sqrt{m_1/m_2}$ and ρ = π, which can be used to signify observability of the future 0v2β-decay experiments. Fortunately, the possibility of |〈m〉_ee| < |〈m〉_ee|_* turns out to be very small, promising a hopeful prospect for the 0v2β-decay searches.

The following sections are included:

• Basics
  • Friedmann–Lemaître–Robertson–Walker Universe
  • Energy forms
  • Future
  • Density perturbation
• Thermal production
  • Number density history
  • Decoupling temperature
  • Interaction and decay rates
• Cosmological nucleosynthesis
• Baryon number in the Universe
• Thermal WIMP production in the Universe
  • Heavy neutrino
  • Forces for weakly interacting massive particles
  • WIMP relic density
• Nonthermal production
  • Non-thermal WIMP production
  • E-WIMP production
  • ADM production
  • Axion production
  • Heavy lepton as WIMP
• References

Nuclear double beta decay, an extremely rare radioactive decay process, is - in one of its variants - one of the most exciting means of research into particle physics beyond the standard model. The large progress in sensitivity of experiments searching for neutrinoless double beta decay in the last two decades - based largely on the use of large amounts of enriched source material in "active source experiments" - has lead to the observation of the occurrence of this process in nature (on a 6.4 sigma level), with the largest half-life ever observed for a nuclear decay process (2.2×10²⁵ y). This has fundamental consequences for particle physics - violation of lepton number, Majorana nature of the neutrino. These results are independent of any information on nuclear matrix elements (NME)*. It further leads to sharp restrictions for SUSY theories, sneutrino mass, right-handed W-boson mass, superheavy neutrino masses, composite-ness, leptoquarks, violation of Lorentz invariance and equivalence principle in the neutrino sector.

The masses of light-neutrinos are found to be degenerate, and to be at least 0.22±0.02eV. This fixes the contribution of neutrinos as hot dark matter to ≥4.7% of the total observed dark matter. The neutrino mass determined might solve also the dark energy puzzle.