Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
5.2.1 The synchronized regime
During the investigation on the neutrino-neutrino interaction that can occur in
media such as a supernova or the early Universe, people have found that a particular
phenomenon can occur when the interactions between neutrinos overcome
the other interactions. Usually, the flavor oscillation of neutrinos depends on
the energy of a given mode, but self-interactions can induce a strong coupling
between neutrinos in such a way that their flavour oscillations are synchronized.
Let us discuss its physical interpretation. In this subsection, concerning the synchronized
regime, we do not take into account the interactions between neutrinos
and matter.
The equation of motion
We use here the formalism of the polarization vectors (appendix C) where the
equation of motion for a single mode j is
˙Pj = ∆m2
√
2GF
B × Pj + J × Pj, (5.18)
2pj V
The vector B = (sin 2θV , 0, − cos 2θV ), with the mixing angle θ, can be seen as
an effective ”magnetic field” around which P precesses. The total polarization
vector J which represents an ensemble of neutrinos is defined by
Nν
J ≡ Pj, (5.19)
j=1
where we considered a large volume V filled homogeneously with Nν neutrinos.
The first term in the r.h.s of (5.18) shows that P plays the role of an angular
momentum vector and ω is the precession frequency in vacuum of P around B.
The second term represents the self interactions. Taken alone on the r.h.s, it
means that the neutrino j precesses around the total polarization vector J.
The synchronized oscillations
Let us put ourselves in the case where the neutrino density is sufficiently large
so that the vacuum term can be neglected. We follow the analytical derivations
given in [95]. Equation (5.18) becomes
√
2GF ˙Pj = J × Pj, (5.20)
V
From this equation, it is clear that every individual modes precesses around the
direction J. Considering that the density of neutrinos is very large, even by
switching on the vacuum term, the evolution of a given mode remains dominated
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