Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Flux Ratio
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
20 40 60 80 100
Neutrino Energy (MeV)
Flux Ratio
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
20 40 60 80 100
Neutrino Energy (MeV)
Figure 4.2: Same as Fig.4.1 for νµ (left) and ντ (right) fluxes.
curves show results for the two hierarchies and the two values of θ13. Similarly to
the case where Tνµ = Tντ, while for the N-L case the first resonance is adiabatic
and the electron neutrinos get a hotter spectrum, for all other cases the spectra
keep very close to the Fermi-Dirac distributions (Figure 3.3). The situation is
obviously reversed for the muon neutrino flux. Figures 4.5, 4.6 and 4.7 show the
ratios of the νe and νµ fluxes for a non-zero over a zero delta phase, as a function
of neutrino energy, at different distances from the neutron star surface. One can
see that effects up to a factor of 2-4 on the νe and up to 10 % on νµ are present.
A similar behavior is found for the ¯νe and ντ fluxes.
The behavior of the flux ratios shown in Figure 4.6 is easy to understand.
From Eqs. (4.26) and (4.27) one can write
φνe(δ) = φνe(δ = 0) + sin 2θ23 sin δ
2 (Lντ − Lνµ) (4.39)
× sin 2θ23 sin δ
2 (|Bµe| 2 − |Bτe| 2
) + cos 2θ23 sin δ
δ
− i cos (BµeB
2 2
∗
τe ) + h.c.
Clearly the ratios calculated in these figures would be identity at the value of the
energy where νµ and ντ spectra would cross (i.e., Lντ = Lνµ). Away from this
energy one expects an oscillatory behavior due to the additional terms in Eq.
(4.39) as the figure indicates. Note that even for δ = 0 the neutrino fluxes could
also exhibit an oscillatory behavior. Concerning Fig. 4.7, one can see that the
effects due to δ = 0 and induced by taking different temperatures or luminosities
are small, compared to the case with δ = 0 only (Figure 4.3).
Effects on the electron fraction Ye
Figure 4.8 shows results on the electron fraction Ye. As previously discussed,
if δ = 0 there are no CP violation effects on Ye since this quantity depends on
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