E - Carleton University
E - Carleton University
E - Carleton University
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Neutrino Oscillations<br />
Neutrino States<br />
Mass States states<br />
Weak States states<br />
First Second First Second<br />
ν 1<br />
ν 2<br />
ν e<br />
ν μ<br />
ν μ<br />
ν 2<br />
ν 1<br />
sinθ<br />
θ<br />
cosθ<br />
θ<br />
ν e<br />
⎛ν<br />
e ν e cosθ (<br />
⎞<br />
ν<br />
) ⎛=( cosθ<br />
sinθ<br />
ν<br />
μ<br />
2sinθ cosθ<br />
)( ⎞ ⎛ 1<br />
ν<br />
ν<br />
) 1 ⎞<br />
⎜ ⎟<br />
= ⎜<br />
⎟<br />
⎜ 2<br />
⎟<br />
⎝ν<br />
μ ⎠ ⎝−<br />
sinθ<br />
cosθ<br />
⎠ ⎝ν<br />
2 ⎠<br />
Time Evolution<br />
Pure ν μ<br />
Pure ν μ<br />
Pure ν μ<br />
i<br />
d<br />
dt<br />
⎛ν<br />
e ⎞<br />
⎜ ⎟<br />
=<br />
⎝ν<br />
⎠<br />
1<br />
2<br />
⎛ν<br />
e ⎞<br />
T ⎜ ⎟<br />
⎝ ⎠<br />
μ<br />
ν μ<br />
ν 2<br />
2<br />
⎛ Δm<br />
Δm<br />
⎜−<br />
cos 2θ<br />
T = ⎜ 2E<br />
2E<br />
⎜ 2<br />
2<br />
Δm<br />
2 Δm<br />
⎜ sin θ<br />
⎝ 2E<br />
2E<br />
2<br />
2<br />
2<br />
⎞<br />
sin θ ⎟<br />
⎟<br />
⎟<br />
cos 2θ<br />
⎟<br />
⎠<br />
0<br />
ν 1<br />
Time, t<br />
FAAQ2006 Alain Bellerive 39
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