Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
one has:
S(˜ρ − ¯˜ρ)S † (xini) =
⎛
⎝
dyy 2 (f(y, ξe) − f(y, −ξe))
⎛
= nγ ⎝
0
0
0
dyy 2 [c 2 23 (f(y, ξµ) − f(y, −ξµ)) + s 2 23 (f(y, ξτ) − f(y, −ξτ))]
dyy 2 c23s23 [(f(y, ξµ) − f(y, −ξµ)) − (f(y, ξτ) − f(y, −ξτ))]e iδ
0
dyy 2 c23s23 [(f(y, ξµ) − f(y, −ξµ)) − (f(y, ξτ) − f(y, −ξτ))]e −iδ
dyy 2 [s 2 23 (f(y, ξµ) − f(y, −ξµ)) + c 2 23 (f(y, ξτ) − f(y, −ξτ))]
Lνe 0 0
0 c 2 23Lνµ + s 2 23Lντ c23s23(Lνµ − Lντ)e iδ
0 c23s23(Lνµ − Lντ)e −iδ s 2 23 Lνµ + c 2 23 Lντ
where Lνi is the i flavour lepton asymmetry and nγ the density number of photons.
Following the derivation in chapter 6, if the neutrino asymmetry of νµ and ντ are
equal, then by recurrence S(˜ρ−¯˜ρ)S † (x) won’t depend on δ at any time. Therefore,
the Hamiltonian in Eq.(8.33) can be factorized as usual. Consequently, ρνeνe and
ρ¯νe¯νe won’t depend on δ, neither the degeneracy parameter ξe. Indeed, the lepton
asymmetry is given by the relation:
Lνe = nνα − n¯νe
nγ
= π2
ξe +
12ζ(3)
ξ3 e
π2
⎞
⎞
⎠
⎠ (8.35)
(8.36)
Therefore one can give the value of ξe at a given time considering that the density
number of species is described by a Fermi-Dirac with a chemical potential. On
the contrary, if the degeneracy parameter of νµ and ντ are different then it will
influence ξe and possibly the neutrino cosmic radiation contribution and also the
neutron to proton ratio. In conclusion, we have demonstrated that there could
be CP-violating effects on the neutrino degeneracy parameter, the source of such
effects being the presence of muon-antimuons pairs and any possible difference
between the degeneracy parameter of νµ and ντ. To quantify such effect we now
need to perform numerical calculations of three flavour neutrino oscillation in the
Early Universe.
8.4 Numerical results
To measure the effects on ξe that CP-violation could induce, we have to write
a new three flavour code using density matrices. We have first written a two
flavour code and reproduced the numerical results of [48] (Fig. 1, 2 and 3 of that
paper.) We are currently finishing the 3 flavour generalization. This work will
be in a paper to come soon.
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