Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Ye
0.7
0.6
0.5
0.4
0.3
theta13=9° NH
theta13=0.5° NH
theta13=9° IH
theta13=0.5° IH
2 4 6 8 10
distance from NSS (in units of 100 Km)
Ye
1,001
1.0005
1
0.9995
2 4 6 8 10
distance from NSS (in units of 100 Km)
Figure 4.8: Electron fraction for δ = 0 (left) and ratios of the electron fraction
(right) for δ = 180 ◦ compared to δ = 0 ◦ , as a function of the distance from the
neutron-star surface. The initial νµ, ντ fluxes have temperatures which differs by
1 MeV (see text). The results correspond to the normal hierarchy and sin 2 2θ13 =
0.19.
unpolarized medium of normal matter density one finds for neutrinos3 :
pν(nνl − 1) = −√2GF
C V νlfNf f=e,u,d
In the standard electroweak model SU(2)L × U(1), one finds, at tree level,
C V νℓf = T3(fL) − 2Qfs 2 W + δℓf
(4.45)
(4.44)
with s2 W ≡ sin2 θW, T3(fL) the third component of isospin of fL and Qf its
charge. The evolution equation for neutrino in matter with the index of refraction
formalism is:
i d
dt
⎛
⎝
νe
νµ
ντ
⎞
⎠ =
⎡
⎣ 1
U
2pν
⎛
⎝
∆m 2 12 0 0
0 0 0
0 0 ∆m 2 32
⎞
⎠ U † − pν
⎛
⎝
∆neµ 0 0
0 0 0
0 0 ∆nτµ
⎞⎤
⎛
⎠⎦
⎝
(4.46)
where U is the unitary MNSP matrix relating the neutrino flavour (να, with
α = e, µ, τ) and mass (νi, with i = 1, 2, 3) eigenstates. Also ∆m2 ij ≡ m2νi −
m2 νj and ∆nαβ ≡ nνα − nνβ . Note here that we removed a term proportional
to the identity matrix nνµ, therefore we display only differences of refraction
indices. This equation is absolutely general in matter. If consider only treelevel
interactions with matter then the term ∆neµ is strictly equal to −Ve =
− √ 2GF Ne and the term ∆nτµ becomes zero. Going to the one-loop corrections
will not give the same relations.
3 neglecting the neutrino mass.
81
νe
νµ
ντ
⎞
⎠ ,