Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Figure 5.7: Relative fluxes of νe (blue/dotted) and ¯νe (red/solid) in a toy supernova
model with 20% fewer antineutrinos than neutrinos and sin 2 ˜ θV = 0.001.
Taken from [72]
H = ±ωB + µD in opposite direction because of the sign in front of ωB. Consequently,
the vector D = P − ¯P develops components on the x- and y-axis and
therefore evolve in time because of the rotation of P and ¯ P. Because of the nonlinearity,
the movement of D will in return influence the movements of P and ¯P,
creating wiggles as in Fig.(5.8). In addition, the fact µ decreases in intensity with
time will make P and ¯P to move aside developping bigger components on the xand
y-axis. The norm of P and ¯P being constant, their z component (related to
the flavour), will decrease in time in oscillating. This explains the behaviours of
P and ¯P on Fig.(5.7).
5.2.3 The spectral splits
We follow the analytical derivations given in [104, 103].
The theoretical framework
Concerning the formalism we define the total polarization vectors as P = ∞
dω Pω 0
and ¯ P = ∞
0 dω ¯ Pω and introduce D ≡ P−¯ P, representing the net lepton number.
With the same notations than the ones used previously we write the equations
of motion (EOMs) for neutrinos:
∂tPω = (ωB + λL + µD) × Pω. (5.49)
In vacuum antineutrinos oscillate ”the other way round” and consequently the
EOM is the same for ¯ Pω but with ω → −ω. Therefore, instead of using ¯ Pω we
104