Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
then ∆m 2 < 0 since one gets an opposite matter potential sign in the effective
Hamiltonian. 9 Therefore, for a given sign of ∆m 2 , either neutrinos or antineutrinos
(but not both) can experience the resonantly enhanced oscillations in matter.
This is how we deduced that ∆ 2 m21 > 0: electron neutrinos undergo a MSW resonance
in the Sun as we will discuss more in the next chapter.
Finally, in a more realistic case where matter density varies, like the Sun where
neutrinos are produced with a certain spectrum in energy, one can realize that the
resonance condition does not involve any fine tuning: if ∆m 2 is of the right order
of magnitude, then for any value of the matter density there is a value of neutrino
energy for which the resonance condition (1.55) is satisfied and vice-versa. This
is tru only if the condition of adiabaticity is fulfilled (See appendix B).
1.2.2 3 flavours in matter
In Nature, neutrinos exist in 3 flavours mixed by the MNSP matrix and can interact
coherently with matter giving rise to a matter potential in the Hamiltonian.
When one takes into account 3 flavours neutrinos in matter, at the tree level,
two resonances might occur, one called the high resonance (H-resonance) which
requires a high density and a low resonance (L-resonance) which happen at lower
density 10 . Such phenomena can occur if the matter density if sufficiently high,
like in the supernova environment. Approximations can be made to handle the
problem analytically, but a numerical calculation is required if one wants to keep
all the physical information encoded in the neutrino fluxes while propagating
through matter.
MSW resonances in 3 flavours
Contrary to the 2 flavour case, it is difficult to define an MSW resonance condition
in 2 flavours. In fact, different ways used previously, like for instance the
maximization of the amplitude of the oscillation probability, or minimization of
the difference between the eigenvalues of the effective Hamiltonian in matter, lead
to different results. Following the derivation of the MSW in section 1.2.1, we can
9 One can also considers that ∆m 2 is always postive. If the angle is between 0 ◦ and 45 ◦ it
corresponds to the normal hierarchy, if the range is 45 ◦ to 90 ◦ then it is inverted hierachy.
10 Actually, when one considers one loop corrections for neutrino interacting with matter,
a supplementary potential appears, named Vµτ which can be seen as an effective presence
of τ in the medium. Its inclusion introduces an extra resonance, deep inside the supernova.
Nevertheless, such resonance depends on the hierarchy, the mixing angles, and if θ23 is larger
or smaller than 45 ◦ . A detailed study has been recently performed in [80]. The hypothesis
usually made is that Vµτ engenders no change of the fluxes at the resonance but just a mixing
between the concerned states. This assumption is valid only if one considers that the νµ flux is
equal to the ντ flux.
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