Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
we have to take them all into account. Let’s make explicit Nνe for instance :
Nνe(q ′ )dq ′ =
⎛
⎜
⎜
⎝
Lνe(q ′ )ψe,eψ∗ e,e − Lνe(q ′ )ψ ∗
e,eψe,e Lνe(q ′ )ψµ,eψ∗ e,e − Lνe(q ′ )ψ ∗
µ,eψe,e Lνe(q ′ )ψτ,eψ∗ e,e − Lνe(q ′ )ψ ∗
τ,eψe,e
Lνe(q ′ )ψe,eψ∗ µ,e − Lνe(q ′ )ψ ∗
e,eψ µ,e
Lνe(q ′ )ψµ,eψ∗ µ,e − Lνe(q ′ )ψ ∗
µ,eψ µ,e
Lνe(q ′ )ψτ,eψ∗ µ,e − Lνe(q ′ )ψ ∗
τ,eψ µ,e
Lνe(q ′ )ψe,eψ∗ τ,e − Lνe(q ′ )ψ ∗
e,eψτ,e Lνe(q ′ )ψµ,eψ∗ τ,e − Lνe(q ′ )ψ ∗
µ,eψτ,e
Lνe(q ′ )ψτ,eψ∗ τ,e − Lνe(q ′ )ψ ∗
τ,eψτ,e
dq ′
dq ′
dq ′
dq ′
dq ′
dq ′
dq ′
dq ′
dq ′
⎞
⎟
⎠ (6.16)
The subscript for the wave functions means respectively, the neutrino flavour
considered, and the initial neutrino flavour at the neutrinosphere.
The input parameters
The numerical results we present are obtained by solving the three flavour evolution
equation of Eq.(6.1) with a supernova density profile for which the region of
the first 100 km, where the neutrino self-interaction dominates, is well separated
from the one of the MSW (high and low) resonances, produced by the interaction
with ordinary matter. The oscillation parameters and the neutrino fluxes at the
neutrinosphere are the same as the one used in chapter 4. We take the neutrino
luminosity L 0 να = 1051 erg · s −1 . To include the neutrino-neutrino interaction we
use the single-angle approximation of Eqs.(5.15-5.16) with Rν = 10 km, considering
that all neutrinos are emitted radially.
Our numerical results in three flavours present the collective oscillations induced
by the neutrino-neutrino interaction, already discussed in the literature (see e.g.
[105, 108, 95, 54, 72, 104, 103, 61]) and in the previous chapter.
Let us now discuss the CP violation effects in presence of the neutrino-neutrino
interaction 2 and of the loop corrections to the neutrino refractive index, with
the condition that the muon and tau fluxes at the neutrinosphere are equal
(Lνµ = Lντ).
2 Note that a comment is made in [53, 55] on the δ effects on the neutrino fluxes in the
presence of the neutrino self-interaction in a core-collapse supernova.
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