Abstract
The problem of the nature of massive neutrinos ν i (Dirac or Majorana?) is one of the most fundamental problem of neutrino physics. The solution of this problem will have an important impact on the understanding of the origin of neutrino masses and mixing. If it will be proved that ν i are Majorana particles, it will be a strong argument in favor of the seesaw mechanism of neutrino mass generation which is commonly considered as the most natural explanation of the smallness of neutrino masses.
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Notes
- 1.
Thus, in (8.27) the strong interaction are taking into account.
- 2.
Notice that in the case of the Dirac neutrinos \(\langle 0|\nu_{i\!L}(x_{1}) \nu^{T}_{i\!L}(x_{2})|0\rangle=\frac{1-\gamma_{5}}{2} \langle 0|\nu_{i}(x_{1}) \nu^{T}_{i}(x_{2})|0\rangle\frac{1-\gamma^{T}_{5}}{2}=0\). The neutrinoless double β-decay is obviously forbidden in the Dirac case.
- 3.
It is assumed that in the propagator \(m^{2}_{i} = m^{2}_{i}-i\varepsilon\).
- 4.
The pseudoscalar term in the one-nucleon matrix element of the hadronic charged current induces a tensor term. From numerical calculations follow that its contribution to the matrix element can be significant.
- 5.
An additional factor \(\frac{1}{2}\) is due to the fact that in the final state we have two identical electrons.
- 6.
In order to have the same notation \(\varDelta m^{2}_{12}\) for the solar-KamLAND neutrino mass-squared difference and to determine this quantity as a positive one the neutrino masses are usually labeled differently in the cases of the normal and inverted neutrino mass spectra. In the case of the normal spectrum \(\varDelta m^{2}_{23}>0\) and in the case of the inverted spectrum \(\varDelta m^{2}_{13}<0\). Thus, with such a notation the character of the neutrino mass spectrum is determined by the sign of the larger (atmospheric) neutrino mass-squared difference. It clear, however, that the sign of the atmospheric mass-squared difference has no physical meaning: it is a convention based on the labeling of the neutrino masses and the way how the neutrino mass-squared difference is determined \((\varDelta m^{2}_{ik}= m^{2}_{k}- m^{2}_{i})\). In both cases of the neutrino mass spectrum for the mixing angles the same notations can be used.
- 7.
Let us notice that these three neutrino mass spectra correspond to different mechanisms of neutrino mass generation. Masses of quarks and charged leptons satisfy hierarchy of the type (8.68). Hierarchy of neutrino masses is a typical feature of GUT models (like SO(10)) in which quarks and leptons are unified. Inverted spectrum and quasi-degenerate spectrum require specific symmetries of the neutrino mass matrix.
- 8.
Some participants of the Heidelberg-Moscow collaboration claim that they obtained an evidence for the \(0\nu\beta\beta\)-decay of \(^{76} \mathrm{Ge}\) with the following 3 σ range for the half-life of \(^{76}\mathrm{Ge}\): \(0.69\cdot 10^{25}\leq T^{0\,\nu}_{1/2}(^{76} {\mathrm{Ge}})\leq 4.18\cdot 10^{25}\,\mathrm{y}\). This claim is going to be checked by the GERDA collaboration.
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© 2011 Springer-Verlag Berlin Heidelberg
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Bilenky, S. (2011). Neutrinoless Double Beta-Decay. In: Introduction to the Physics of Massive and Mixed Neutrinos. Lecture Notes in Physics, vol 817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14043-3_8
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DOI: https://doi.org/10.1007/978-3-642-14043-3_8
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