Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Implications on the fluxes in the supernova environment
According to supernova simulations, the neutrino fluxes at the neutrino sphere
are quite well described by Fermi-Dirac distributions or power-law spectra [78].
Neutrino masses and mixings modify this simple pattern by mixing the spectra
during neutrino evolution. We recall that a neutrino hierarchy of temperatures
at the neutrino sphere exists Eq.(3.21). The (differential) neutrino fluxes of type
i (mass or flavour) are given logically by this formula:
φνi (δ) = Lνi P(νi → νi) + Lνj P(νj → νi) + Lνk P(νk → νi) (4.31)
where the luminosities are defined by the following relation:
Lνi (r, Eν) =
L 0 νi
4πr 2 (Tνi )3
1 E
〈Eν〉F2(η)
2 ν
1 + exp (Eν/Tν − ηνi )
(4.32)
as seen in chapter 3.
Since here we consider interactions between neutrinos and matter only at tree
level, the interactions via neutral current for νµ and ντ will be the same before
being emitted at the neutrino-sphere. Their respective last scattering surface will
also be superimposed with such assumptions. Consequently, for νµ and ντ we have
the same L0 , the same temperature Tνi (therefore the same average energy) and
νi
finally the same pinched factor ηνi . All these equalities on the different parameters
of a flux (Eq.(4.32)) imply the equality of the two fluxes:
Lνµ = Lντ
(4.33)
Using this relation on the flux expression of Eq.(4.31) for electron neutrinos, we
have:
φνe(δ) = Lνi P(νe → νe) + Lνµ (P(νµ → νe) + P(ντ → νe)) (4.34)
As seen previously, the electron neutrino survival probability P(νe → νe) does
not depend on δ (Eq.(4.25)), neither the sum of P(νµ → νe) + P(ντ → νe)
(Eq.(4.29)). Consequently, the electron neutrino flux does not depend on δ, the
Dirac CP-violating phase 2 . The reason we are mainly interested in such a flux
is simple. Recalling that the electron neutrino and anti-neutrinos are the only
fluxes that interact with matter via charged-current, they are the only one to
have an influence inside the supernova, like on the electron fraction, or leave a
specific imprint on an observatory on Earth. Indeed, only these fluxes can be
detected independently because they can interact via charged-current, contrary
to the νµ and ντ fluxes since the neutrino energy are too low in comparison with
the muon mass (and even more the tau mass) for such particles to be created. If
one starts with identical spectra with tau and mu neutrinos, one gets the same
electron neutrino spectra no matter what the value of the CP-violating phase is.
2 A remark on this aspect is also made in [120] where such relation was only numerically
observed.
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