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Neutrino Oscillations

​
initial flavor
electron
muon
tau
mass hierarchy
indicated flavors
electron
muon
tau
all
mixing parameters
θ
23
0.79
θ
13
-0.2
θ
12
0.59
δ
0
mass parameters
2
Δm
21
0.00008
2
Δm
31
0.0024
Experiments show that neutrinos initially created with a definite flavor (electron, muon, or tau) can be found with a different flavor after they travel far from the source. This is caused by neutrino oscillation. In the language of quantum physics, the states representing the three types of flavor do not have definite mass. Each of the mass eigenstates is a linear combination of the flavor states. The oscillation phenomenon depends on the parameters of the model, namely the mass differences of the mass eigenstates and the mixing parameters, from which the coefficients of the linear combination can be calculated. The plots show the probability of finding a 1 GeV neutrino in the different flavors as a function of the distance between the source and the detector. The fourth figure demonstrates the hierarchy of the neutrino masses and the flavor coefficients in each eigenstate.

Details

In particle physics three types of neutrinos (electron, muon, tau) are known. They can be described mathematically in a vector space in which the three flavor states (
|e>
,
|μ>
,
|τ>
) define a basis. However, these states are not eigenvectors of the Hamiltonian of that three-dimensional system, so they do not have definite masses. The mass states are linear combinations of the flavor states:
f≥
3
∑
i=1
U
f,i
m
i
>
.
U
, the mixing matrix, is unitary. If the initial state is a flavor state, then after time
t
it will evolve into
Ψ(t)≥
3
∑
i=1
U
f,i
m
i
>
-i
E
i
t
e
(in units with
ℏ=1
,
c=1
), where
E
i
are the energies of the three neutrinos. We know that neutrinos are extremely light objects so that they travel approximately at the speed of light. Thus
L≈t
and their energies are
E
i
=
p
i
+
2
m
i
(2p)
. We want to know the probability of finding a neutrino initially created with flavor
f
in
f'
:
P
ff'
=
2
〈f'|Ψ(L)〉
=
2
3
∑
i=1
U
f'i
U
f,i
-i
E
i
L
E
. This formula depends only on the energy differences
Δ
E
i
=Δ
2
m
i
(2p)
.
The first two parameters of the model are the mass-square differences. It can be shown that there are four other relevant parameters contained in
U
: three real angle parameters (if
U
is real this is just a rotation) and one complex phase factor. Some of these parameters are already known from experiments. In this Demonstration the default setting of that parameter is the measured value.
More details about experiments and theory are found in the references:
Wikipedia, "Neutrino Oscillation."

External Links

Permanent Citation

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