Abstract
In the context of a type I seesaw scenario which leads to get light left-handed and heavy right-handed Majorana neutrinos, we obtain expressions for the transition probability densities between two flavor neutrinos in the cases of left-handed and right-handed neutrinos. We obtain these expressions in the context of an approach developed in the canonical formalism of Quantum Field Theory for neutrinos which are considered as superpositions of mass-eigenstate plane waves with specific momenta. The expressions obtained for the left-handed neutrino case after the ultra-relativistic limit is taking lead to the standard probability densities which describe light neutrino oscillations. For the right-handed neutrino case, the expressions describing heavy neutrino oscillations in the non-relativistic limit are different respect to the ones of the standard neutrino oscillations. However, the right-handed neutrino oscillations are phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets.
Highlights
Neutrino physics is a very active area of research which involves some of the most intriguing problems in particle physics
The right-handed neutrino oscillations are phenomenologically restricted as is shown when the propagation of heavy neutrinos is considered as superpositions of mass-eigenstate wave packets [25]
In this work we have studied neutrino oscillations in vacuum between two flavor states considering neutrinos as Majorana fermions
Summary
Neutrino physics is a very active area of research which involves some of the most intriguing problems in particle physics. The content of this work has been organized as follows: In Section 2, after establishing the Majorana condition, we obtain and solve the two-component Majorana equation for a free fermion; in Section 3, we consider a type I seesaw scenario which leads to get light left-handed neutrinos and heavy right-handed neutrinos; in Section 4, we obtain the Majorana neutrino fields with definite masses, we carry out the canonical quantization procedure of these Majorana neutrino fields and we obtain relation between neutrino flavor states and neutrino mass states using operator fields; in Section 5, we determine the probability density of transition between two left-handed neutrino flavor states, we establish normalization and boundary conditions and we obtain left-handed neutrino oscillations for ultra-relativistic light neutrinos; in Section 6, we study the right-handed neutrino oscillations for non-relativistic heavy neutrinos; in Section 7 we present some conclusions
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