Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
the neutral-current potentials of protons and electrons cancel each other and
only neutrons contribute, yielding
VNC = − 1√
2GFNn
2
Together with Eq.(1.35) we can write the effective matter Hamiltonian:
⎛
⎞
Hm = ⎝
Ve + Vn 0 0
0 Vn 0
0 0 Vn
(1.41)
⎠ . (1.42)
Since one cannot observe wave functions of neutrinos but only the oscillation
probabilities, every term proportional to the identity matrix gives a common
phase that we can get rid of. The effective Hamiltonian is finally:
⎛
Hm = ⎝
Ve 0 0
0 0 0
0 0 0
⎞
⎠ . (1.43)
Note that for antineutrinos, one has to replace Va → −Va. It is Wolfenstein
that discovered in 1978, that neutrinos propagating in matter are subject to a
potential due to the coherent forward elastic scattering with the particles in the
medium (electrons and nucleons)[117]. This potential, which is equivalent to an
refraction index, modifies the mixing of neutrinos.
1.2.1 The Mikheyev-Smirnov-Wolfenstein (MSW) effect
Following the work of Wolfenstein, Mikheyev and Smirnov in 1986 show the
possibility of a resonant conversion in a non-constant matter density profile [89,
90]. It is natural to write the neutrino evolution equation in matter in the flavour
basis since they interact with matter via the electroweak bosons.
i d
νe
dt νµ
=
− ∆m2
4E cos 2θV + √ 2
2 GFNe
∆m2 sin 2θV 4E
∆m 2
4E
sin 2θV
∆m 2
4E cos 2θV − √ 2
2 GFNe
νe
(1.44)
where θV is the vacuum mixing angle. From this equation we can think of new
neutrino states, the matter states, related to the flavour states by:
νm1
= U † m (t)
νe
cosθm(t) − sin θm(t) νe
=
sin θm(t) cosθm(t)
νm2
νµ
νµ
νµ
,
, (1.45)
where Um(t) is the matter mixing matrix with θm(t) the associated matter mixing
angle associated. These two quantities depend on time (or distance) because of
the matter density profile which varies with time (or distance). Actually, these
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