Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
define approximatively the H-resonance condition:
and the L-resonance condition:
√ 2GF Ne(rH) = ∆m2 13
2E
cos 2θ13
(1.56)
√ 2GF Ne(rL) = ∆m2 12
2E cos 2θ12. (1.57)
These two conditions though not perfect, define quite well the place where the
resonance happens. Besides the description of neutrino propagation in astrophysical
media (Sun, core-collapse supernovae), and the Early Universe, taking into
account matter in 3 flavours may be important in terrestrial experiment if one
wants to measure precisely neutrino parameters like the mixing angles. Indeed
neutrinos going through the Earth can ”feel” the matter which influence the oscillation
probability. For instance, in the future experiments like the Neutrino
Factory (chapter 2), people will use a νµ beam and will look at the appearance
of νe after having traveled inside a part of the Earth. The relevant oscillation
probability in this case will be:
P(νµ → νe) = 4c 2 13s 2 13s 2 23 sin 2 ∆m213 L
× 1 +
4Eν
2a
∆m2 (1 − 2s
13
2
13) (1.58)
+8c 2 13s12s13s23(c12c23cosδ − s12s13s23) cos ∆m223 L
sin
4Eν
∆m213 L
sin
4Eν
∆m212 L
4Eν
−8c 2 13c12c23s12s13s23sin δ sin ∆m223 L
sin
4Eν
∆m213 L
sin
4Eν
∆m212 L
4Eν
+4s 2 12c 2 13(c 2 13c 2 23 + s 2 12s 2 23s 2 13 − 2c12c23s12s23s13 cosδ) sin ∆m212 L
−8c 2 13 s2 13 s2 23 cos ∆m2 23 L
4Eν
sin ∆m2 13 L
4Eν
4Eν
aL
(1 − 2s
4Eν
2 13 ).
which takes into account, not only three flavours but also matter corrections
due to effects represented by a = 2 √ 2GFneEν.
An approximate analytical treatment
If we draw, similarly to the two flavour case, the eigenvalues of the effective
Hamiltonian in matter as a function of density, one can see in 3 flavours 2 crossing
levels, corresponding to the H resonance and to the L-resonance for a higher and
lower density respectively. Following a similar derivation that in the two flavours
case, we can look at the 3 flavour matter eigenstates, namely ν1m, ν2m and ν3m.
As an approximation we can consider that when the neutrinos are emitted the
density is high enough that the matter states coincide with the flavour states. To
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