Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
where we can write the last term corresponding to collisions is
⎛
iD(f(y, ξe) − ρνeνe)
C[ρ(x, y)] = ⎝ −iDe−µ,τρνµνe
−iDe−µ,τρντνe
with f(y, ξ) from Eq.(8.4).
−iDe−µ,τρνeνµ
iD(f(y, ξµ) − ρνµνµ)
−iDµ−τρντνµ
⎞
−iDe−µ,τρνeντ
−iDµ−τρνµντ
⎠
iDe−µ,τ(f(y, ξτ) − ρντντ)
(8.32)
8.3 CP-violation: an analytical result
We start from Eq.(8.31), and follow a similar derivation than the one performed
in chapter 6. We therefore rotate in the T23 basis, and factorize the S matrices
from the U matrices to have:
iHx(∂x)S˜ρ(x, y)S † = (8.33)
T 0 13T12M 2T †
12T 0†
13
−
2y
8√2GFy 3m2 S
W
˜ ES †
+ √ 2GF(S˜ρS † − S˜ρS † ), S˜ρ(x, y)S †
+ C[S˜ρ(x, y)S † ],
We study all terms in the r.h.s. of Eq.(8.33) at initial time to see if they contain
the phase δ.
As we can see from Eq.(8.32), since initially the terms ρνiνi are equal to f(y, ξi)
and the terms ρνiνj = 0 for i = j, in any basis the term C[ρ(p, t)] is zero. The
matter related term in Eq.(8.33) is in this basis:
⎛
S ˜ ES † = ⎝
Eee 0 0
0 −s 2 23Eµµ c23s23Eµµe iδ
0 c23s23Eµµe −iδ −c 2 23 Eµµ
⎞
⎠ (8.34)
Therefore, if the presence of muons and anti-muons is not neglected during the
studied epoch, then it will introduce a source of CP-violation effects. Indeed, in
this case, one cannot factorized the Hamiltonian which implies a δ dependence on
ρνeνe The more the temperature goes down, the less the term Eµµ is important.
Let us now take a look at the neutrino-neutrino interaction term ρ − ¯ρ. Initially,
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