Etudes des proprietes des neutrinos dans les contextes ...

tel-00450051, version 1 - 25 Jan 2010
by J. The precession around B, the external magnetic field is slow while the fast
precession around J implies that the transverse component of the Pj averages
to zero and only the projection on J is conserved. The individual modes are
coupled to each other by their strong internal magnetic fields represented by J
in Eq.(5.20) forming a compound system with one large magnetic moment that
precesses around B:
˙J = ωsynch B × J. (5.21)
To identify what is this synchronization frequency, we start from the equation
(5.18) and we sum over the different neutrinos to obtain:
˙J =
Nν
j=1
∆m2 B × Pj
2pj
(5.22)
Realizing that only the projections of the Pj along J are not averaging out, we
have:
˙J =
Nν
∆m
j=1
2
B × (Pj.ˆJ)ˆJ
2pj
= 1
Nν ∆m
|J|
2
(Pj.ˆJ) B × J (5.23)
2pj
j=1
where ˆJ = J/|J| is a unit vector in the direction of J. Consequently, from
Eq.(5.21) and Eq.(5.23), we obtain
ωsynch = 1
|J|
Nν
j=1
∆m2 ˆJ · Pj. (5.24)
2pj
In particular, if all modes started aligned (coherent flavor state) then |J| = Nν
and ˆJ · Pj = 1 so that
2 ∆m
ωsynch =
2p
= 1
Nν
Nν
j=1
∆m2 . (5.25)
2pj
To observe the consequence of such a synchronization one can consider the parameter
κ ≡ 2√2GFnνp0 ∆m2 = 2µp0
∆m2 (5.26)
which measures the comparative strength of the neutrino-neutrino interaction
µ = √ 2GFnν (where nν represents the neutrino density) with respect to the
vacuum oscillation ∆m2 /2p. For a given momentum p0, varying the value of κ
will give different oscillation frequencies for the νe survival probability, like in
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