Majorana neutrinos, <Emphasis Type="Italic">CP</Emphasis> violation,neutrinoless double beta and tritium beta decays

If the present or upcoming searches for neutrinoless double beta ((ββ)_0ν) decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the (ββ)_0ν-decay effective Majorana mass parameter (|〈m〉|), it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-ν mixing and massive Majorana neutrinos, we discuss the information that a measurement of, or an upper bound on, |〈m〉| can provide on the value of the lightest neutrino mass m₁. With additional data on the neutrino masses obtained in ³H β-decay experiments, it might be possible to establish whether the CP symmetry is violated in the lepton sector. This would require very high precision measurements. If CP invariance holds, the allowed patterns of the relative CP parities of the massive Majorana neutrinos would be determined.     

Neutrinoless double-beta decay and double-electron capture

The fundamental importance of searching for neutrinoless double-beta decay is widely recognized. Observation of the decay would tell us that the total lepton number is not conserved and that, consequently, neutrinos are massive Majorana fermions. The same statement could be made in the case of observing neutrinoless double-electron capture. We address the question of the sensitivity of the 0νεε decay to the effective mass of the Majorana neutrino. According to our estimates, in the case of ¹⁵²Gd and ¹⁶⁴Er the sensitivity can be comparable to the favored 0νββ decays of nuclei. The main uncertainty in the prediction of half-lives of the 0νεε decay stems from the lack of sufficient precision in measuring the mass difference between the parent and daughter atoms. More accurate measurements can be accomplished using the modern high-precision ion traps.     

Investigation of double-beta decay at the Institute of Theoretical and Experimental Physics (ITEP, Moscow)

Investigation of neutrinoless double-beta (2β0ν) decay is presently being considered as one of the most important problems in particle physics and cosmology Interest in the problem was quickened by the observation of neutrino oscillations. The results of oscillation experiments determine the mass differences between different neutrino flavors, and the observation of neutrinoless decay may fix the absolute scale and the hierarchy of the neutrino masses. Investigation of 2β0ν decay is the most efficient method for solving the problem of whether the neutrino is a Dirae or a Majorana particle, Physicists from the Institute of Theoretical and Experimental Physics (ITEP, Moscow) have been participating actively in solving this problem. They initiated and pioneered the application of semiconductor detectors manufactured from enriched germanium to searches for the double-beta decay of ⁷⁶Ge. Investigations with ⁷⁶Ge provided the most important results. At present, ITEP physicists are taking active part in four very large projects, GERDA. Majorana, EXO, and NEMO, which are capable of recording 2β0ν decay at a Majorana neutrino mass of 〈m _ν〉 ≈ 10^?2 eV.     

Theory of neutrinoless double beta decay—A brief review

Neutrinoless double decay (0νββ-decay) is a unique probe for lepton number conservation and neutrino properties. This is a process with long and interesting history with important implications for particle physics and cosmology, but its observation is still elusive. The search for the 0νββ-decay represents the new frontiers of neutrino physics, allowing to determine the Majorana nature of neutrinos and to fix the neutrino mass scale and possible CP violation effects, which could explain the matter-antimatter asymmetry in the Universe. At present a complete theory is missing and, thus, to motivate and guide the experiments the mechanism mediated by light neutrinos is mostly considered. The subject of interest is an effective mass of Majorana neutrinos, which can be deduced from the measured half-life, once this process is definitely observed. The accuracy of the determination of this quantity is mainly determined by our knowledge of the nuclear matrix elements. There is a request to evaluate them with high precision, accuracy and reliability. Recently, there is an increased interest to the resonant neutrinoless double electron capture, which may also establish the Majorana nature of neutrinos. This possibility is considered as alternative and complementary to searches for the 0νββ-decay.     

Present and future strategies for neutrinoless double beta decay searches

The renewed interest shown in these days towards neutrinoless double beta decay, a lepton number violating process which can take place only if neutrinos are Majorana particles (ν = \(\bar \nu \)) with a nonvanishing mass, is justified by the fact that the Majorana nature of neutrinos is expected in many theories beyond the Standard Model. We also now know, thanks to the neutrino oscillation experiments, that neutrinos are in fact massive, as expected in these theories and not requested in the Standard Model. Moreover, since neutrino oscillation experiments measure only the absolute value of the difference of the square of the neutrino masses, the discovery of neutrinoless double beta decay would help to disentangle questions that still remain unsolved: what is the absolute mass scale of the neutrinos and which mass hierarchy (normal, inverted or quasi-degenerate) is the correct one?The scope of this paper is not only to review the present results reached in the field by the different groups and technologies worldwide, but also to illustrate and comment on the (near and long-term) future strategies that experimentalists are trying to pursue to reach the needed sensitivity required to explore the inverted hierarchy neutrino mass scale.     

Bimaximal mixing in an SO(10) minimal Higgs model

An SO(10) SUSY GUT model was previously presented based on a minimal set of Higgs fields. The quark and lepton mass matrices derived fitted the data extremely well and led to large ν_μ−ν_τ mixing in agreement with the atmospheric neutrino data and to the small-angle MSW solution for the solar neutrinos. Here we show how a slight modification leading to a non-zero up quark mass can result in bimaximal mixing for the atmospheric and solar neutrinos. The “just-so” vacuum solution is slightly favored over the large-angle MSW solution on the basis of the hierarchy required for the right-handed Majorana matrix and the more nearly-maximal mixing angles obtained.     

Sterile neutrinos in lepton number and lepton flavor violating decays

We study the contribution of massive dominantly sterile neutrinos, N, to the lepton number and lepton flavor violating semileptonic decays of τ and B, D, K-mesons. We focus on special domains of sterile neutrino masses mN where it is close to its mass-shell. This leads to an enormous resonant enhancement of the decay rates of these processes. This allows us to derive stringent limits on the sterile neutrino mass mN and its mixing UαN with active flavors. We apply a joint analysis of the existing experimental bounds on the decay rates of the studied processes. In contrast to other approaches in the literature our limits are free from ad hoc assumptions on the relative size of the sterile neutrino mixing parameters. We analyze the impact of this sort of assumptions on the extraction of the limits on mN and UαN, and discuss the effect of finite detector size. Special attention was paid to the limits on meson decays with e^±e^± in final state, derived from non-observation of 0νββ-decay. We point out that observation of these decays may, in particular, shed light on the Majorana phases of the neutrino mixing matrix.     

Neutrino-less double beta decays and Majorana neutrinos

Neutrino-less double beta decays (0??? ??) are sensitive and realistic probes for studying the Majorana nature of neutrinos, the ?? mass spectrum and the absolute mass scale, the lepton sector CP and others beyond the standard electro-weak theory. This report reviews briefly 0??? ?? processes and Majorana neutrinos, the present and future 0??? ?? experiments and 0??? ?? nuclear matrix elements.     

Dirac vs. Majorana neutrino masses from a TeV interval

We investigate the nature (Dirac vs. Majorana) and size of left-handed neutrino masses in a supersymmetric five-dimensional model compactified in the interval [0,πR], where quarks and leptons are localized on the boundaries while the gauge and Higgs sectors propagate in the bulk of the fifth dimension. Supersymmetry is broken by Scherk–Schwarz boundary conditions and electroweak breaking proceeds through radiative corrections. Right-handed neutrinos propagate in the bulk and have a general five-dimensional mass M, which localizes the zero modes towards one of the boundaries, and arbitrary boundary terms. We have found that for generic boundary terms left-handed neutrinos have Majorana masses. However for specific boundary configurations left-handed neutrinos are Dirac fermions as the theory possesses a conserved global U(1) symmetry which prevents violation of lepton number. The size of neutrino masses depends on the localization of the zero-modes of right-handed neutrinos and/or the size of the five-dimensional neutrino Yukawa couplings. Left-handed neutrinos in the sub-eV range require either MR10 or Yukawa couplings 10⁻³R, which make the five-dimensional theory perturbative up to its natural cutoff.     

Neutrinos in the time of Higgs

In this paper, the recent progress in the determination of neutrino oscillation parameters and future prospects have been discussed. The tiny neutrino masses as inferred from oscillation data and cosmology cannot be explained naturally by the Higgs mechanism and warrant some new physics. The latter can be connected to the Majorana nature of the neutrinos which can be probed by neutrinoless double beta decay (0 νββ). The paper also summarizes the latest experimental results in 0 νββ and discusses some implications for the left–right symmetric model which could be a plausible new physics scenario for the generation of neutrino masses.     

Resonance enhancement of neutrinoless double electron capture

The process of neutrinoless double electron (0νECEC$0\nu \text{ECEC}$) capture is revisited for those cases where the two participating atoms are nearly degenerate in mass. The theoretical framework is the formalism of an oscillation of two atoms with different total lepton number (and parity), one of which can be in an excited state so that mass degeneracy is realized. In such a case and assuming light Majorana neutrinos, the two atoms will be in a mixed configuration with respect to the weak interaction. A resonant enhancement of transitions between such pairs of atoms will occur, which could be detected by the subsequent electromagnetic de-excitation of the excited state of the daughter atom and nucleus. Available data of atomic masses, as well as nuclear and atomic excitations are used to select the most likely candidates for the resonant transitions. Assuming an effective mass for the Majorana neutrino of 1 eV, some half-lives are predicted to be as low as 10²² years in the unitary limit. It is argued that, in order to obtain more accurate predictions for the 0νECEC$0\nu \text{ECEC}$ half-lives, precision mass measurements of the atoms involved are necessary, which can readily be accomplished by today?s high precision Penning traps. Further advancements also require a better understanding of high-lying excited states of the final nuclei (i.e. excitation energy, angular momentum and parity) and the calculation of the nuclear matrix elements.     

具有整体代对称性的左右对称模型中的中微子质量

本文基于具有整体U(1)代对称性的SU(2)_L×SU(2)_R×U(1)模型推导了轻子的味混合矩阵,对中微子的质量问题进行了研究.在本文的模型中,产生轻子Dirac质量的汤川耦合拉格朗日密度具有整体U(1)代对称性,所以,模型中的带电轻子质量矩阵和中微子Dirac质量矩阵是Fritzsch形式的.但是,中微子除了具有Dirac质量,一般还具有Majorana质量,在这种一般情况下, 关键词： 中微子质量 轻子味混合矩阵 左右对称模型 代对称性     

Hierarchical matrices in the see-saw mechanism,large neutrino mixing and leptogenesis

We consider the see-saw mechanism for hierarchical Dirac and Majorana neutrino mass matrices m _D and M _R, including the CP violating phases. Simple arguments about the structure of the neutrino mass matrix and the requirement of successful leptogenesis lead to the situation that one of the right-handed Majorana neutrinos is much heavier than the other two, which in turn display a rather mild hierarchy. It is investigated how for the neutrino mixing one small and two large mixing angles are generated. The mixing matrix element |U _e3|² is larger than 10^-3 and a characteristic ratio between the branching ratios of lepton flavor violating charged lepton decays is found. Successful leptogenesis implies sizable CP violation in oscillation experiments. As in the original minimal see-saw model, the signs of the baryon asymmetry of the universe and of the CP asymmetry in neutrino oscillations are equal and there is no connection between the leptogenesis phase and the effective mass as measurable in neutrinoless double beta decay.Received: 28 May 2003, Revised: 13 September 2003, Published online: 26 November 2003     

Lepton mixing under the lepton charge nonconservation, neutrino masses and oscillations and the “forbidden” decay µ− → e − + γ

The lepton-charge (L _e , L _μ , L _τ ) nonconserving interaction leads to the mixing of the electron, muon, and tau neutrinos, which manifests itself in spatial oscillations of a neutrino beam, and also to the mixing of the electron, negative muon, and tau lepton, which, in particular, may be the cause of the “forbidden” radiative decay of the negative muon into the electron and γ quantum. Under the assumption that the nondiagonal elements of the mass matrices for neutrinos and ordinary leptons, connected with the lepton charge nonconservation, are the same, and by performing the joint analysis of the experimental data on neutrino oscillations and experimental restriction for the probability of the decay µ^? → e ^? + γ per unit time, the following estimate for the lower bound of neutrino mass has been obtained: m ^(ν) > 1.5 eV/c ².     

Majorana mass term,Dirac neutrinos and selective neutrino oscillations

In a theory of neutrino mixing via a Majorana mass term involving only the left-handed neutrinos there exist selection rules for neutrino oscillations if true Dirac and/or exactly zero mass eigenstates are present. In the case of three neutrino flavours no oscillation is allowed if the mass spectrum contains one Dirac and one nondegenerate Majorana massive neutrino. The origin of these selection rules and their implications are discussed and the number of possible CP-violating phases in the lepton mixing matrix when Dirac and Majorana mass eigenstates coexist is given.     

Double beta decay

Double beta decay is a rare nuclear process changing the nuclear charge by two units leaving atomic number unchanged. The detection of the neutrino accompanied mode (A,Z)→(A,Z + 2) + 2e^? + &;2v^? ₂ with half-lives around 10²⁰ years is among the rarest decays ever observed. Of outmost importance for particle physics and especially neutrino physics, is the neutrinoless mode (A,Z)→(A,Z + 2) + 2e^?. This process is violating lepton number by two units and requires massive Majorana neutrinos, i.e. neutrino and antineutrino are identical. The current experimental status is reviewed and an outlook towards future activities is given.     

Leptogenesis from first principles in the resonant regime

The lepton asymmetry generated by the out-of-equilibrium decays of heavy Majorana neutrinos with a quasi-degenerate mass spectrum is resonantly enhanced. In this work, we study this scenario within a first-principle approach. The quantum field theoretical treatment is applicable for mass splittings of the order of the width of the Majorana neutrinos, for which the enhancement is maximally large. The non-equilibrium evolution of the mixing Majorana neutrino fields is described by a formal analytical solution of the Kadanoff–Baym equations, that is obtained by neglecting the back-reaction. Based on this solution, we derive approximate analytical expressions for the generated asymmetry and compare them to the Boltzmann result. We find that the resonant enhancement obtained from the Kadanoff–Baym approach is smaller compared to the Boltzmann approach, due to additional contributions that describe coherent transitions between the Majorana neutrino species. We also discuss corrections to the masses and widths of the degenerate pair of Majorana neutrinos that are relevant for very small mass splitting, and compare the approximate analytical result for the lepton asymmetry with numerical results.     

Heavy fourth-generation neutrino and flavour-changing neutral currents

We study the flavour-changing neutral currents in the case that the fourth-generation neutrino exists and the known three left-handed neutrino masses are at the experimental limits of the direct measurements. The fourth-generation neutrino has the mass of order a few ten GeV and the flavour-changing processes of the heavy neutrinos are expected to be observed onZ ⁰ ine ⁺ e ^? collisions. The heavy fourth-generation neutrino is significant to reveal the nature of the neutrino; Dirac or Majorana, the see-saw mechanism and the right-handed scale.     

Hierarchy of interactions and mass relations in asymptotically free E6 model of unified interactions

The hierarchy of gauge interactions within the E₆ model is proved, and the vector and spinor field masses are obtained. The mass spectrum of the charged W-bosons is found, and the mass scale is fixed so that the mass of the lightest of them is about 70 GeV. The lepton spectroscopy is studied and a new charged lepton, with mass of order 4–8 GeV is predicted. For the low-energy phenomenology, the model may be considered as a theory of 6 flavoured quarks and 4 charged leptons, each with its neutrino. Being 4-component the neutrinos are massive except for the ν_e (m_νe = 0, exactly) and ν_μ (m_νμ ≈ 0, approximately) particles. The problem of the “superfluous” particles which as a rule accompanies the asymptotic freedom in such theories is also briefly discussed.     

Leptonic minimal flavour violation in warped extra dimensions

Lepton mass hierarchies and lepton flavour violation are revisited in the framework of Randall?CSundrum models. Models with Dirac-type as well as Majorana-type neutrinos are considered. The five-dimensional c-parameters are fit to the charged lepton and neutrino masses and mixings using ?? ² minimization. Leptonic flavour violation is shown to be large in these cases. Schemes of minimal flavour violation are considered for the cases of an effective LLHH operator and Dirac neutrinos and are shown to significantly reduce the limits from lepton flavour violation.