Étude des invariants de rephasage en passant par la transformée de Mellin
|Advisor:||Marleau, Luc; Fortin, Jean-François|
|Abstract:||From the first mention of massive neutrinos by Pontecorvo in 1957 to recent experiments with neutrinos, the demonstration of their oscillatory behavior indicates the need for a physics beyond the standard model. One way to solve neutrinos oscillation is by adding a mass to these particles. Fortunately, this deviation from the physics of the Standard Model is the solution to another problem, CP violation. Assuming massive neutrinos, one can add phases to the mixing matrix and then explain CP violation in the same way as for quarks. Those phases cannot inform about the amplitude of the CP violation since they depend on the chosen parametrization for the PMNS matrix, and they are not invariant under change of basis. That is why in 1985, Jarlskog developed a new formalism based on basis invariant quantity namely the rephasing invariants. This memoir aims to study those phases in the context of the anarchy principle. In this theoretical framework, the elements of the PMNS matrix are studied without any constraints being imposed on them so that they appear random in the low energy limit. It is possible to conclude that the Haar measure, which follows naturally from the anarchy principle, is likely to reproduce the PMNS matrix at low energies. A formalism is therefore developed to study the rephasing invariants under this measure. Moreover, we show that all the rephasing invariants of the same type have the same probability density function under the Haar measure for a fixed number of neutrinos. From these results, the probability density functions for all types of rephasing invariants under the Haar measure are easily obtained for an arbitrary number of neutrinos. Finally, the physical implications of our analytical results in terms of neutrino generation number are discussed.|
|Document Type:||Mémoire de maîtrise|
|Open Access Date:||11 October 2021|
|Collection:||Thèses et mémoires|
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