Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
x
B
2 ˜ θV
z
P
¯P
D
y
Figure 5.8: Left figure: schematic view of the initial condition of the system.
Right: schematic picture of the evolution. Black ellipse represents the precession
of P and ¯ P around the Hamiltonian. Black wiggles represent the nutation created
by the vector D. Violet arc represents the diminution of µ which in addition to
the variations of D will lead to a global simultaneous decrease of Pz, ¯Pz and Dz
may extend Pω to negative frequencies such that ¯ Pω = P−ω (ω > 0) and use
only Pω with −∞ < ω < +∞. In these terms, D = +∞
−∞ dω sω Pω, where sω ≡
sign(ω) = ω/|ω|. To comprehend analytically the spectral split phenomenon, we
have to use several approximations. To do so, let us state first that we work in
the flavour basis. In this basis we have for the vacuum term10 :
⎛ ⎞
and for the matter term:
B = ⎝
sin 2 ˜ θV
0
cos 2 ˜ θV
⎛
λL = ⎝
0
0
λ
⎞
x
¯P
H
z
P
⎠ . (5.50)
⎠ . (5.51)
10 We use the relation ˜ θV = π/2 − θV with θV is the vacuum mixing angle, having ˜ θV close
to π/2 means we work in the inverted hierarchy.
105
y