Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Chapter 6
Collective neutrino oscillations in
supernovae and CP-violation
Motivated by the important recent developments in the study of neutrino propagation
in dense media, due in particular to the inclusion of the neutrino-neutrino
interaction and the emergence of new collective neutrino flavour conversion phenomena
(described in chapter 4), we have explored the robustness of the analytical
and numerical results found in the standard framework of neutrino propagation
in matter (the MSW effect) when the neutrino self-interactions are present [69].
6.1 Analytical results
Since we are dealing with the neutrino-neutrino interaction, it is more convenient
to write the equation of motion with the density matrix formalism (see appendix
C for details).
Theoretical framework
Considering here the density matrix, the neutrino evolution equation governed
by the Liouville-Von Neumann equation is:
i dρνα(δ)
dt = [UHvacU † + Hm + Hνν(δ), ρνα(δ)], (6.1)
where the neutrino-neutrino interaction term is:
√
2GF
Hνν = D(r/Rν)
2πR 2 ν
with the geometrical factor
α
D(r/Rν) = 1
[1 −
2
[ρνα(q ′ )Lνα(q ′ ) − ρ ∗ ¯να (q′ )L¯να(q ′ )]dq ′
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1 − ( Rν
r )2 ] 2
(6.2)
(6.3)