E - Carleton University
E - Carleton University
E - Carleton University
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Neutrino Mixing (detail)<br />
As in the quark sector<br />
one defines a neutrino<br />
mixing matrix which<br />
relates the mass and<br />
weak eigenstates<br />
⎛<br />
⎜<br />
⎜<br />
⎝<br />
ν e<br />
ν μ<br />
ν τ<br />
Mixing Matrix<br />
⎞ ⎛ U e1<br />
U e2<br />
U e 3<br />
⎟<br />
⎟ = ⎜<br />
U μ1<br />
U μ2<br />
U μ 3<br />
⎜<br />
⎠ ⎝ U τ1<br />
U τ 2<br />
U τ 3<br />
⎞<br />
⎟<br />
⎟<br />
⎠<br />
⎛<br />
⎜<br />
⎜<br />
⎝<br />
ν 1<br />
ν 2<br />
ν 3<br />
⎞<br />
⎟<br />
⎟<br />
⎠<br />
Quark:<br />
Neutrino:<br />
θ12 ≈ π /14 θ<br />
23<br />
≈ π / 76 yes θ13 ≈ π / 870<br />
θ ≈ / 6 θ ≈ / 4 ??? θ < / 20<br />
12<br />
π<br />
23<br />
π<br />
13<br />
π<br />
solar atmospheric CP violation short-baseline<br />
⎛ c<br />
⎜<br />
Uα<br />
i<br />
= ⎜−<br />
s<br />
⎜<br />
⎝ 0<br />
where c<br />
ij<br />
12<br />
12<br />
s<br />
c<br />
12<br />
12<br />
0<br />
= cosθ<br />
,<br />
ij<br />
0⎞<br />
⎛1<br />
⎟ ⎜<br />
0⎟⋅⎜0<br />
1⎟<br />
⎜<br />
⎠ ⎝0<br />
and s =<br />
ij<br />
c<br />
0<br />
23<br />
− s<br />
23<br />
sinθ<br />
ij<br />
s<br />
c<br />
0<br />
23<br />
23<br />
⎞ ⎛1<br />
⎟ ⎜<br />
⎟⋅⎜0<br />
⎟ ⎜<br />
⎠ ⎝0<br />
0<br />
1<br />
0<br />
0 ⎞ ⎛ c<br />
⎟ ⎜<br />
0 ⎟⋅⎜<br />
0<br />
e<br />
− iδ ⎟ ⎜<br />
⎠ ⎝−<br />
s<br />
13<br />
13<br />
0<br />
1<br />
0<br />
s<br />
c<br />
13<br />
0<br />
13<br />
⎞<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
FAAQ2006 Alain Bellerive 71
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