Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2011-03-14
Physics
High Energy Physics
High Energy Physics - Phenomenology
21 pages, some type corrections, some references added
Scientific paper
The main goal of this work is to perform an introduction to the Majorana's formalism of neutrino oscillations and to study its physical consequences. To do it we calculate the probability amplitude of transition in vacuum between two neutrino flavor states by considering neutrinos as Majorana fermions. We perform this calculation in the context of an approach developed in the canonical formalism of Quantum Field Theory for the case of the propagation of neutrinos which are considered as superpositions of mass-eigenstate plane waves with specific momenta. First we obtain and solve the two-component Majorana equation and then we develop the canonical quantization procedure for the Majorana field. Next we calculate the probability amplitude of transition between two different neutrino flavor states. In the same approach and by establishing normalization and boundary conditions we can obtain the Majorana neutrino oscillations for two cases: the ultra-relativistic and non-relativistic limits. While the first case for neutrino oscillations is well known in the literature, the second one is phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets.
Pérez Y. F.
Quimbay C. J.
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