Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
ν e ) [%]
∆P = P(ν µ ν e ) - (ν µ
20
15
10
5
0
-5
-10
-15
-20
sin 2 2θ 13 = 0.05 E = 1 GeV
δ = 0, π
δ = π/2
δ=3π/2
1000 2000 3000 4000 5000
Distance (km)
Figure 1.2: Examples of ∆Pν¯ν ≡ P(νµ → νe) − P(¯νµ → ¯νe) in vacuum as a function
of distance for fixed value of energy, E = 1 GeV and sin 2 2θ13 = 0.05. Taken from [92]
An visual example of such formula can be seen on Fig.(1.2). In vacuum the
only thing that distinguishes the evolution of a neutrino and an antineutrino is
the CP-violation phase δ. From this formula, one can see the consistency of the
statements above: ∆Pab vanishes in the limit 5 δ = 0 ◦ and/or θ13 = 0 ◦ . From the
formula linking the mass squared differences 6 , the CP asymmetry (1.22) vanishes
if even one of ∆m 2 ij = 0.
The CP asymmetry is delicate to observe, because contrary to vacuum probabilities,
the average in time or energy of ∆Pab gives a zero value. Therefore, to
detect CP-violation neutrinos must not oscillate over long distance. Thus, the
experimental observation of CP violation effects in neutrino oscillations is a very
difficult task, even more if the mixing angle θ13 is small. In addition, matter
effects on neutrino oscillations may mimic CP violation and so make the searches
of the genuine CP violation even more difficult (see chapter 2 for a discussion of
future reactor and accelerator experiments).
1.2 Oscillations in matter
Incoherent scattering with matter
At first glance, considering that neutrinos are only sensitive to electroweak interactions.
Those with matter are doubtlessly very small and one could think that
5 This term also cancels if any of the mixing angle is zero or 90 ◦ . But experimentally we
know that the angles θ12 and θ23 are non zero. We only have an upper limit for θ13 which
allows it to be zero. See next chapter for the experimental results.
6 2 m1 − m2 1 + m2 2 − m22 + m23 − m2 3 = 0
15