Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
7.2 A signature for small θ13 in inverted hierarchy
Our main goal is to explore the neutrino time signal in an observatory, depending
on the yet unknown neutrino parameters, and see if we can exploit a combination
of the neutrino-neutrino interaction and shock wave effects to get clues on
important open issues.
Theoretical framework
We calculate the three flavor neutrino evolution in matter in two steps. First, we
determine the neutrino wavefunctions up to some radius using supernova density
profiles at different times during the supernova explosion, as done in chapter 3,
4 and 6 for one static density profile. This calculation includes the neutrino coupling
both to matter with loop corrections (i.e. Vµτ) and to neutrino themselves.
For the latter we use the single-angle approximation, i.e. we assume that neutrinos
are essentially emitted with one angle (see chapter 5). Such an assumption
accounts rather well both qualitatively and quantitatively for the neutrino collective
effects [51, 64], even though in some cases decoherence in a full multi-angle
description might appear (see e.g. [60]). The density profile used is a dynamic
inverse power-law.
The second step is to determine the exact neutrino evolution through the rest
of the supernova mantle by solving the evolution operator equations as described
in [81] which is a 3 flavor generalization of [79]. The 1D density profiles used
are taken from [81] and include both the front and reverse shock. These profiles
are matched to the dynamic inverse power-laws used in the first step. The full
results are then spliced together using the evolution operators rather than probabilities
c.f. [81, 85]. Finally, the flux on Earth is calculated taking into account
decoherence [47] but not Earth matter [43] which might occur if the supernova
were shadowed. Indeed, we do not consider them here since their presence (or
absence) in the neutrino signal is a function of the position of the supernova with
respect to the detector when the event occurs, and knowing this position their
addition is easy.
Input parameters
We take as an example the electron anti-neutrino scattering on protons which
is the dominant channel in Cerenkov and scintillator detectors. The results
we present are obtained with the best fit oscillation parameters, i.e. ∆m 2 12 =
8 × 10 −5 eV 2 , sin 2 2θ12 = 0.83 and |∆m 2 23 | = 3 × 10−3 eV 2 , sin 2 2θ23 = 1 for the
solar and atmospheric differences of the mass squares and mixings, respectively
[9]. The Dirac CP violating phase is taken to be zero since no effects show up
when the muon and tau luminosities are taken equal [26] (see chapter 4); while a
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