Etude et impact du bruit de fond corrélé pour la mesure de l'angle ...

2.4 Measuring neutrino oscillation parameters 23
tel-00821629, version 1 - 11 May 2013
three matrices M 2,3 ⇥ M 1,3 ⇥ M 1,2 :
0
U = @
1
1 0 0
0 c 23 s 23
A
0 s 23 c 23
0
@
c 13 0 s 13 e i 1 0
0 1 0 A @
c 12 s 12
1
0
s 12 c 12 0 A
0 0 1
(2.16)
M 2,3 is parametrized in terms of ✓ 23 which is the mixing angle dominating
the ⌫ µ ! ⌫ ⌧ , related to the oscillation of atmospheric neutrino. M 1,2 is
parametrized in terms of ✓ 12 dominating the transition ⌫ e ! ⌫ µ,⌧ , related
to the oscillation of neutrino coming from the sun. Finally, M 13 depends
on ✓ 13 which is the mixing matrix dominating the oscillation ⌫ µ ! ⌫ e .The
CP phase always appears multiplied by the terms sin ✓ 13 , so it would be
measurable only if ✓ 13 is di↵erent than zero.
To conclude, the observation of the neutrino oscillations has two main consequences:
neutrinos have a non-zero mass and the lepton flavour is not
conserved.
2.4 Measuring neutrino oscillation parameters
To easily understand neutrino oscillation experimental results, the simpler
case with only two active neutrino is considered. The mixing among two
neutrino families can be described by a real and orthogonal 2 ⇥ 2 matrix
with one mixing parameter, the rotation angle ✓ between the flavour and
the mass eigenstates:
✓
⌫↵
⌫
◆ ✓ cos ✓ sin ✓
=
sin ✓ cos ✓
The oscillation probability take the form:
P (⌫ ↵ ! ⌫ )=sin 2 (2✓)sin 2 ✓
◆✓
⌫1
⌫ 2
◆
m 2 ◆
L
4E
(2.17)
(2.18)
the amplitude of the oscillation, sin 2 2✓, is determined by the mixing angle
✓ and does not allow to distinguish between ✓ and ⇡/2 ✓, which are not
physically equivalent.
Restoring the physics units, the oscillation phase becomes:
✓
=1.27
m 2 (eV 2 ◆
)L(km)
E(GeV )
(2.19)
In the limit where ⌧ 1, P (⌫ ↵ ! ⌫ ) ' sin 2 2✓( m 2 L/(4E)) 2 ,sothe
measurement of the oscillation probability would determine information only
on the product sin 2 (2✓)⇥ m 2 . The oscillation would not have enough time
to develop and the number of neutrino oscillation events measured in the