Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
Consequently, using Eqs. (1.61) and (1.62), the total ν1 flux at the surface of the
star equals the sum of the three contributions:
F1 = PHPLF 0 e + (1 − PHPL)F 0 x
. (1.64)
Similarly, the fluxes of neutrino mass eigenstates ν2 and ν3 arriving at the surface
of the star are
F2 = PH(1 − PL)F 0 e + (1 + PH(PL − 1)F 0 x ,
F3 = (1 − PH)F 0 e + PHF 0 x . (1.65)
The interest of looking at the fluxes of mass eigenstates is because these are
eigenstates of the vacuum Hamiltonian. Each state evolves independently in
vacuum and acquires a phase. Therefore, from the stars to Earth, a spread
will occur for the wave packets, any coherence between the mass eigenstates
will be lost on the way to Earth. The neutrinos arriving at the surface of the
Earth as incoherent fluxes of the mass eigenstates, we have to perform another
transformation to obtain flavour fluxes to which experiments are sensitive. To
calculate the νe flux on Earth 12 , one has to multiply the flux associated to each
mass eigenstate by the probability to get a νe from a mass eigenstate i:
Fe = F1P(ν1 → νe) + F2P(ν2 → νe) + F3P(ν3 → νe) (1.66)
where the decoherence among the mass eigenstates is explicit. The P(νi → νe)
probabilities are nothing but the squared modulus of the corresponding elements
of the MNSP matrix (given by Eq.()):
Fe = |Ue1| 2 F1 + |Ue2| 2 F2 + |Ue3| 2 F3 (1.67)
Taking into account the unitarity condition |Uei| 2 = 1, we can write the final
electron neutrino flux reaching the Earth:
where
Fe = pF 0 e + (1 − p)F 0 x , (1.68)
p = |Ue1| 2 PHPL + |Ue2| 2 (1 − PL)PH + |Ue3| 2 (1 − PH) . (1.69)
According to (1.68), p may be interpreted as the total survival probability of electron
neutrinos. Note that the final fluxes of the flavor states at the Earth like in
Eq.(1.68) can be written only in terms of the survival probability p. In conclusion,
what occurs in a medium like supernovae, depends on the hopping probability of
the H- and the L-resonances and the associated adiabaticity (PH,L = 0) or nonadiabaticity
(PH,L = 1) of the transition. In the Landau-Zener approximation,
the hopping probability has an explicit dependence upon θ, ∆m 2 and dNe/dr. In
12 Up to an implicit geometrical factor of 1/(4πL 2 ) in the fluxes on Earth
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