Abstract
Discovery of neutrino oscillations, driven by neutrino mass-squared differences and neutrino mixing, is one of the most important discovery in the particle physics. It is unlikely that small neutrino masses are of the standard Brout-Englert-Higgs mechanism origin. A new, beyond the Standard Model mechanism of the generation of neutrino masses is required.
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Notes
- 1.
Notice that in the case of the Dirac neutrinos \(\langle 0|\nu _{eL}(x_{1}) \nu ^{T}_{eL}(x_{2})|0\rangle =\frac {1-\gamma _{5}}{2}~\sum _{k} U^{2}_{ek}~\langle 0|\nu _{k}(x_{1}) \nu ^{T}_{k}(x_{2})|0\rangle \frac {1-\gamma ^{T}_{5}}{2}=0\). The neutrinoless double β-decay is obviously forbidden in the Dirac case.
- 2.
We took into account that in the propagator \(m^{2}_{k}\to m^{2}_{k}-i\epsilon \).
- 3.
An additional factor 1/2 is due to the fact that in the final state there are two identical electrons.
- 4.
In fact, from CP invariance follows that \(U_{ei}=U^{*}_{ei}\eta _{i}\), where η i = ±i is the CP parity of the Majorana neutrino with mass m i . From this condition we find \(e^{2i\bar {\alpha _{i}}}=\eta _{i}\). Thus, we have \(e^{2i(\bar {\alpha _{2}}-\bar {\alpha _{1}})}=e^{2i\alpha }=\eta _{2}\eta ^{*}_{1}\). If η 2 = η 1 we have α = 0, π (the upper bound in Eq. (9.69)), and if η 2 = −η 1 we have α = ±π/2 (the lower bound in Eq. (9.69)).
- 5.
If \(|m_{\beta \beta }|\simeq \sqrt {\varDelta m^{2}_{A}}\simeq 5\cdot 10^{-2}~\mathrm {eV}\) (inverted hierarchy) in one ton of isotopically enriched detector about one 0νββ-decay event per year is expected.
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Bilenky, S. (2018). Neutrinoless Double Beta-Decay. In: Introduction to the Physics of Massive and Mixed Neutrinos. Lecture Notes in Physics, vol 947. Springer, Cham. https://doi.org/10.1007/978-3-319-74802-3_9
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