Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Figure 1.1: Two-flavor neutrino oscillations pattern as a function of distance. From
[102].
The two-flavors oscillation probability
The probability of neutrino oscillations of Eq.(1.12) consists of two terms.
1. The first term sin 2 2θV is the amplitude of the neutrino oscillations, and does
not depend on the distance traveled by neutrinos. When the mixing angle is
θV = 45 ◦ the amplitude is maximal. When θV is close to zero or 90 ◦ , flavour
eigenstates are nearly aligned with mass eigenstates, which corresponds to
small mixing. A vanishing mixing angle implies no oscillations at all.
2. The second term oscillates with time or distance L traveled by neutrinos.
The oscillation phase is proportional to the energy difference of the mass
eigenstates i.e ∆m 2 /2E and to the distance L.
It is interesting to notice that if the masses are equal, the oscillation length
is infinite which means that there is no oscillation. Therefore, oscillations
require neutrinos to have both non-degenerate masses and non-trivial mixing.
Moreover, in order to have an appreciable transition probability, it is
not enough to have large mixing, in addition, the oscillation phase should
not be too small.
When the oscillation phase is very large, the transition probability undergoes
fast oscillations. Averaging over small energy intervals (corresponding
to the finite energy resolution of the detector), or over small variations of
the distance between the neutrino production and detection points (corresponding
to the finite sizes of the neutrino source and detector), results
then in averaging out the neutrino oscillations. The observed transition
probability in this case is
P(νe → νµ) = P(νµ → νe) = 1
2 sin2 2θV . (1.13)
12