Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
νe νe
p p ′
k
e −
Figure 1.4: Neutral-current interactions between fermions and all type of neutrinos.
can be calculated in a similar way. Starting from the effective low-energy neutralcurrent
weak interaction Hamiltonian corresponding to the diagram in Fig.(1.4)
we have:
H CC
eff(x) = GF
√2
α=e,µ,τ
Z 0
e −
k ′
[¯να(x)γ µ (1 − γ5)να(x)]
[ ¯ f(x)γµ(1 − γ5)f(x)]. (1.36)
Comparing with the effective CC Hamiltonian which generates the potential
in Eq.(1.35) one can see that the neutral-current potential of any flavor neutrino
να due to coherent interaction with fermions f is:
For electrons we have:
V f
NC
g e V
=
f
f
√
2GFNf g f
V . (1.37)
= −1
2 + 2 sin2 θW
Since p = uud and n = udd, we have for protons:
and for neutrons:
(1.38)
g p
V = 2gu V + g d V = 1
2 − 2 sin2 θW, (1.39)
g n V = gu V + 2gd V
= −1.
(1.40)
2
For the astrophysical environments we are interested in, such as the Sun or a
supernova, locally matter is composed of neutrons, protons, and electrons. Since
electrical neutrality implies an equal number density of protons and electrons,
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