Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Flux Ratio
4
3
2
1
0
0 20 40 60 80 100 120
Neutrino Energy (MeV)
Flux Ratio
1.1
1.05
1
0.95
0 20 40 60 80 100 120
Neutrino Energy (MeV)
Figure 4.5: Ratios of the νe flux δ = 180 ◦ over for δ = 0 ◦ at 200 km from the
neutron star surface, obtained by taking L 0 ντ = 1.1 L0 νµ (right) or Tντ= 8.06 MeV
and Tνµ= 7.06 MeV (left) (see text). The curves correspond to N-L (solid), N-S
(dashed), I-L (dot-dashed), I-S (dotted).
4.2 CP effects including one loop corrections
4.2.1 Theoretical framework
The refraction index
Matter interactions with neutrinos, in addition with the traditional approach
studied in the chapter 4, can also be seen, by analogy with photons going through
matter in optics, as an index of refraction. We can think of a low energy neutrino
passing through matter as a wave with wavelength λ = h/p. For a typical neutrino
(from nuclear reactors, the Sun, a Supernova, etc...), we take p = 1 MeV, which
yields: λ ≃ 1 pm. Since λ is small compared to the size of the scatterer, diffraction
can be ignored, and one can describe the propagation of a neutrino ”ray” though
matter by geometrical optics. The index of refraction for ν(ν) is given (for small
n − 1) by:
nν, ν = 1 + 2π
p 2
f
Nfs f
ν,ν (0) (4.40)
where Nf is the number density of scatterers of type f and sf ν (0) (resp.(sfν
(0)))
is the forward scattering amplitude for νf (resp.νf) elastic scattering. sf can be
computed to give (for a target at rest):
s f GFE
ν, ν (0) = ∓1 √ K(p, mν)(C
π 2 f
V
79
+ Cf
A σf.p) (4.41)