2/19/01 HEP lunch talk: George Gollin 1 Neutrino mixing Can ν e ν μ ν τ ? ↔ ↔ If this happens: •neutrinos have mass •physics beyond the (perturbative) Standard Model participates Outline: •description/review of mixing phenomenology •possible experimental signatures •short review of existing experimental results
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neutrino oscillation lunchtalk 1 · 2001. 2. 21. · We know K L ≠ K0, etc. Perhaps ν 1 ≠ ν e or ν 2 ≠ ν µ or ν 3 ≠ ν τ? Rewrite the production eigenstates as linear
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2/19/01 HEP lunch talk: George Gollin 1
Neutrino mixing
Can νe νµ ντ ?↔ ↔
If this happens:
•neutrinos have mass
•physics beyond the (perturbative) Standard Model participates
Outline:
•description/review of mixing phenomenology
•possible experimental signatures
•short review of existing experimental results
Analogy with mixing
…but the mass eigenstates are what propagate “sensibly” withoutmixing:
0 0K K↔
ud
dn
Λss
Κ0
strong interaction produces a K0
d
W+uπ+
µ+
νµ
weak interaction produces a νµ
We produce flavor eigenstates...
( ) ( ) ( ) ( )2 2
0 0S S L Lim c im cS S L LK K e e K K e eτ τ τ ττ τ−Γ − −Γ −= =h h
( ) ( ) ( ) ( )2 21 2
1 1 2 20 0im c im ce eτ τν τ ν ν τ ν− −= =h h
( ) ( ) 23
3 3 0 im ce τν τ ν −= h
2/19/01 HEP lunch talk: George Gollin 3
Analogy with mixing0 0K K↔
We know KL ≠ K0, etc. Perhaps ν1 ≠ νe or ν2 ≠ νµ or ν3 ≠ ντ?
Rewrite the production eigenstates as linear combinations ofmass eigenstates:
0
2 20
S
L
K KU
KK×
= ( )
0
2 2 0
S T
L
KKU
K K
∗
×
=
1
2
3
e
Uµ
τ
ν νν νν ν
=
( )1
2
3
eTU µ
τ
ν νν νν ν
∗ =
U is the Maki-Nakagawa-Sakata matrix.
2/19/01 HEP lunch talk: George Gollin 4
12 12sin ...s θ≡12 12cos ,c θ≡ 0 : violationCPδ ≠
Maki-Nakagawa-Sakata mixing matrix
Parameterize mixing with three angles and one phase:
This form is convenient if only two neutrino species mix.(CP violation requires that all three mix.)
13 13 12 12
23 23 12 12
23 23 13 13
1 0 0 0 0
0 0 1 0 00 0 0 0 1
i
i
c s e c s
U c s s cs c s e c
δ
δ
−
+
= −
− −
e τν ν↔µ τν ν↔ e µν ν↔
Analogy with mixing0 0K K↔
d
s
Κ0 Κ0W
s
dW
u,c,t
u,c,t???
Κ0 Κ0 νµ νe
( ) 00 +S LK K K Kτ = = ∼
( ) 2 2
+S S L Lim c im cS LK K e e K e eτ τ τ ττ −Γ − −Γ −= h h
2
~ + ( )S L i mcS L L SK e K e e m m mτ τ τ−Γ −Γ − ∆ ∆ = −h
KL phase rotates (relative to KS phase) ~30° per 10-10 sec.
(maximal mixing!)
Recall: and .0 +S LK K K∼ 0 -S LK K K∼
2/19/01 HEP lunch talk: George Gollin 6
Analogy with mixing0 0K K↔
ν1, ν3 phases rotate relative to ν2 phase if masses are unequal.
( ) 22 231 2
21 1 22 2 23 3im cim c im cU e U e U e ττ τν τ ν ν ν −− −∗ ∗ ∗= + + hh h