Abstract
The neutrino mass term is the central object of the theory of massive and mixed neutrinos. It determines neutrino masses, neutrino mixture and neutrino nature (Dirac and Majorana). The possibility of the existence of so-called sterile neutrinos is also determined by the neutrino mass term.
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Notes
- 1.
We remind that a fermion field \(\psi(x)\) can be presented in the form \(\psi(x)=\psi_{L}(x)+\psi_{R}(x)\), where left-handed \(\psi_{L}(x)\) and right-handed \(\psi_{R}(x)\) components of the field \(\psi(x)\) are determined by the relations \(\psi_{L,R}(x) =\frac{1\mp\gamma_{5}}{2}\,\psi(x).\) From these relations follows that \(\gamma_{5}\,\psi_{L,R}(x)=\mp \psi_{L,R}(x).\)
- 2.
The left-handed flavor fields \(\nu_{l L}\) (\(l=e,\mu,\tau\)) are often called active fields. Right-handed fields are called sterile: they do not enter into the standard charged and neutral currents.
- 3.
Majorana mixing was considered for the first time by Gribov and Pontecorvo. Before this paper there was a belief that in the case of the left-handed neutrino fields neutrino masses are equal to zero. This is correct if the total lepton number L is conserved. As we have shown here, if only left-handed neutrino fields enter into the Lagrangian, neutrinos can have Majorana masses.
- 4.
Majorana mass term is allowed only for particles with equal to zero electric charges such as neutrinos. For charged particles such as quarks and leptons the Majorana mass term is forbidden by the conservation of the electric charge. We also notice that because ν R is \(SU(2)\) singlet with equal to zero hypercharge, there are no constraints on m R . It can be arbitrarily large.
- 5.
CP-violating decays of heavy Majorana particles in the early Universe is widely considered as a possible source of the barion asymmetry of the Universe. We will consider baryogenesis through leptogenesis in Chap. 11.
- 6.
Notice that because the projection of the isotopic spin of the neutrino field is equal to 1/2 a singlet scalar boson cannot be produced in neutrino–neutrino interaction.
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© 2011 Springer-Verlag Berlin Heidelberg
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Bilenky, S. (2011). Neutrino Mass Terms. 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_4
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DOI: https://doi.org/10.1007/978-3-642-14043-3_4
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