Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Number of Events
100
1
0.01
50 100 150
Neutrino Energy (MeV)
Number of Events Ratio
1.04
1.02
1
0.98
0.96
NEvents( δ =135°)/NEvents(δ = 0°)
NEvents(δ =180°)/NEvents(δ =0°)
NEvents ( δ =45°)/NEvents( δ =0°)
50 100 150
Neutrino Energy (MeV)
Figure 4.9: Number of events associated to ¯νe+p → n+e + from a possible future
supernova explosion at 10 kpc in a detector like Super-Kamiokande (22.5 ktons).
These results are obtained for inverted hierarchy and large third mixing angle.
The one-loop corrections
To parametrise the effects of the radiative corrections we use:
C V νℓf = ρ νℓf T3(fL) − 2Qfλ νℓf s 2 W + δℓf
(4.47)
where ρνℓf νℓf and λ are the coefficients that represent the corrections. The complete
O(α) electroweak corrections to CV νℓf can be obtained from []. The decomposition
of the O(α) corrections in Eq.(4.47) between ρνℓf νℓf and λ is quite arbitrary
though possible and furthermore convenient. It is such that the ρνℓf depend on
f but not on the νl while the λνℓf depend on the νl but are independent of the
f. For an electrically neutral medium with Ne = Np (such as supernovae), one
finds for the difference of refraction indices:
pν(nνℓ − nνℓ ′) = − √
2GF
C V νℓf Nf − C V ν ℓ ′f Nf
f=e,u,d
= − √ 2GF[ (ρ νℓe ν
− ρ ℓ ′e
)T3e − 2Qe(λ νℓe
ν
− λ ℓ ′e 2
) sin θW Ne
+ (ρ νℓu − ρ ν ℓ ′u )T3u − 2Qu(λ νℓu − λ ν ℓ ′u ) sin 2 θW
+ (ρ νℓd − ρ ν ℓ ′d )T3u − 2Qd(λ νℓd − λ ν ℓ ′d ) sin 2 θW
(2Ne + Nn)
(Ne + 2Nn)]
= √ 2GF[2(λ νℓf ν
− λ ℓ ′f 2
) sin θW
× (−Ne + 2
3 (2Ne + Nn) − 1
3 (Ne + 2Nn)]
= 0 (4.48)
Consequently, the leading corrections to those differences are terms of O(αm2 τ/m2 W )
which were neglected so far. For nνe − nνµ, such O(αm2 µ /m2W ) corrections to the
tree level are negligible in addition with the fact that the presence of electrons
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