Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
MASS
ν
3
ν 2
ν 1
NORMAL
ν 2
ν 1
ν 3
INVERTED
Figure 2.6: Possible neutrino mass hierarchies. Normal or inverted. Next generation
experiments or a SN explosion will be able to solve the so-called hierarchy problem.
Taken from [109].
2.4.1 What about ∆m 2 31 ?
Supposing there exists only three flavours for neutrinos one would have the following
relation among their squared mass:
m 2 1 − m2 1 + m2 2 − m2 2 + m2 3 − m2 3
= 0
∆m 2 21 + ∆m 2 32 = ∆m 2 31. (2.12)
Therefore, knowing the value and the sign of ∆m2 21
∆m2 23 will yield the possible values of ∆m231 , depending on the sign of ∆m2 23 .
The problem of the ∆m2 23 sign is known as the hierarchy problem. For the moment,
the hierarchy of these masses is unknown (see Fig.2.12). Thanks to the
solar experiments, we know that electron neutrinos undergo an MSW resonance
in the Sun which implies a positive sign for ∆m2 21 . This means that m2 > m1.
Unfortunately, all previous experiments on Earth were unable to tell whether the
ν e
νµ
ν τ
and the absolute value of
mass m3 is heavier than m2 or lighter than m1. Note that depending on the
hierarchy, the absolute value of ∆m2 13 varies: in Normal Hierarchy (NH)(while
in Inverted Hierarchy (IH)) ∆m2 32 ≷ 0 which gives for ∆m213 = ∆m221 ± ∆m232 .
Knowing the hierarchy is a crux for neutrinos physics and beyond. To discriminate
between the normal or the inverted hierarchy should be possible in the
future, with long-baseline experiments, or with a (long time expected) supernova
explosion in our galaxy.
2.5 Current and future neutrino experiments
The goal of reactor/accelerator neutrino experiments nowadays are: to find the
value of θ13, to know the mass hierarchy, and to look for the value of δ, the Dirac
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