Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Chapter 5
Neutrino-neutrino interactions
The neutrino-neutrino interactions induce a new paradigm in neutrino physics.
When a medium is teeming with neutrinos, such as the early Universe or during
a Supernova explosion, neutrinos can interact with each other in addition with
the matter present. When the density of neutrinos reach a certain value, the
self interaction can even become dominant in comparison with other interactions
such as with matter. Such interactions create new effects, that turn out to be
collective. These new phenomena have attracted the interest of the world wide
community working on neutrino astrophysics [[105, 101, 108, 64, 44, 62, 101, 32,
24, 64, 95, 61, 54, 72, 104, 103, 42, 51, 94, 53, 52, 55, 59, 60, 58, 69]]. After a
few years of very fast developments, a new picture of neutrino propagation has
emerged, we describe here the present status. However, we might still be far from
a definite comprehension since new ideas and interpretations keep being proposed.
Here we present the current understanding of these collective phenomena. They
depend on the hierarchy, and can be classified as follows: first a synchronization
stage which can occur both in the early Universe environment and in supernovae,
second, bipolar resonances and spectral splits that take place in the supernova
environment. Let us explain when and why such phenomena emerge.
5.1 Theoretical framework
5.1.1 The effective interaction Hamiltonian
We start with the derivation of the effective Hamiltonian which is done just
like the one for the interaction with matter. Neutrinos will interact with other
neutrinos via the neutral current interaction. For neutrino energies much less
than the mass of the Z 0 boson, the effective interaction is
H NC
ν−ν = GF
√2
α=e,µ,τ
¯ναLγ µ (1 − γ5)ναL
89
β=e,µ,τ
¯νβLγµ(1 − γ5)νβL
. (5.1)