Neutrinoless double-beta decay, which is a very old and yet elusive process, is reviewed. Its observation will signal that the lepton number is not conserved and that the neutrinos are Majorana ...particles. More importantly it is our best hope for determining the absolute neutrino-mass scale at the level of a few tens of meV. To achieve the last goal certain hurdles must be overcome involving particle, nuclear and experimental physics. Nuclear physics is important for extracting useful information from the data. One must accurately evaluate the relevant nuclear matrix elements--a formidable task. To this end, we review the sophisticated nuclear structure approaches which have recently been developed, and which give confidence that the required nuclear matrix elements can be reliably calculated employing different methods: (a) the various versions of the quasiparticle random phase approximations, (b) the interacting boson model, (c) the energy density functional method and (d) the large basis interacting shell model. It is encouraging that, for the light neutrino-mass term at least, these vastly different approaches now give comparable results. From an experimental point of view it is challenging, since the life times are long and one has to fight against formidable backgrounds. One needs large isotopically enriched sources and detectors with high-energy resolution, low thresholds and very low background. If a signal is found, it will be a tremendous accomplishment. The real task then, of course, will be the extraction of the neutrino mass from the observations. This is not trivial, since current particle models predict the presence of many mechanisms other than the neutrino mass, which may contribute to or even dominate this process. In particular, we will consider the following processes: The neutrino induced, but neutrino-mass independent contribution. Heavy left and/or right-handed neutrino-mass contributions. Intermediate scalars (doubly charged, etc). Supersymmetric (SUSY) contributions. We will show that it is possible to disentangle the various mechanisms and unambiguously extract the important neutrino-mass scale, if all the signatures of the reaction are searched for in a sufficient number of nuclear isotopes.
Within left-right symmetric model a generalization of the Majorana neutrino mass for the case of light and and heavy neutrinos is introduced and analyzed. Further, current status of calculation of ...the neutrinoless double beta decay matrix elements is shortly reviewed. An important connection between them and matrix element of double Gamow-Teller operator is established. A new way of fixing quenching of axial-vector coupling constant gA is presented.
Techniques are developed for constructing amplitudes of neutrino-related processes in terms of the neutrino mass matrix, with no reference to the neutrino mixing matrix. The amplitudes of neutrino ...oscillations in vacuum and medium, quasi-elastic neutrino scattering,
decays and double-
decays are considered. The proposed approach makes extensive use of Frobenius covariants within the framework of Sylvester’s theorem on matrix functions. The in-medium dispersion laws are found in quadratures for three flavors of Majorana neutrinos as an application of the developed formalism. The in-medium dispersion laws for Dirac neutrinos can be determined in the general case by searching for the roots of a polynomial of degree 6. In the rest frame of baryonic matter, the minimum energy of both Majorana and Dirac neutrinos is achieved at a neutrino momentum equal to half the mean-field potential. In such cases, Dirac neutrinos occupy a hollow Fermi sphere at zero temperature and low chemical potentials. Fitting experimental data in terms of the neutrino mass matrix can provide better statistical accuracy in determining the neutrino mass matrix compared to methods using the neutrino mixing matrix at intermediate stages.
An explicit expression is derived for the mixing matrix of Majorana neutrinos in terms of the mass matrix and its Frobenius covariants. Illustrative scenarios are taken as examples where the ...suggested formula is used to obtain the mixing matrix from the mass matrix.
The nuclear matrix elements
M
0
ν
of the neutrinoless double beta decay (
0
ν
β
β
) of most nuclei with known
2
ν
β
β
-decay rates are systematically evaluated using the quasiparticle random phase ...approximation (QRPA) and renormalized QRPA (RQRPA). The experimental
2
ν
β
β
-decay rate is used to adjust the most relevant parameter, the strength of the particle–particle interaction. New results confirm that with such procedure the
M
0
ν
values become essentially independent on the size of the single-particle basis. Furthermore, the matrix elements are shown to be also rather stable with respect to the possible quenching of the axial vector strength parametrized by reducing the coupling constant
g
A
, as well as to the uncertainties of parameters describing the short range nucleon correlations. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. Furthermore, a discussion of other implicit and explicit parameters, inherent to the QRPA method, is presented. Comparison is made of the ways these factors are chosen by different authors. It is suggested that most of the spread among the published
0
ν
β
β
decay nuclear matrix elements can be ascribed to these choices.
We show that the presence in the nuclear medium of lepton number violating four-fermion interactions of neutrinos with quarks from a decaying nucleus could account for an apparent incompatibility ...among the 0 νββ searches in the laboratory, the direct neutrino mass measurement with the nuclear β-decay and cosmological data.
The influence of a neutrinoless electron to positron conversion on a cooling of strongly magnetized iron white dwarfs is studied. It is shown that they can be good candidates for soft gamma-ray ...repeaters and anomalous X-ray pulsars.
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