Particle Physics / Standard Model: Neutrino Mixing & SUSY 1 J. Pawlowski / U. Uwer 1 Physics beyond the Standard Model 1. Neutrino Mixing 2. Supersymmetry 3. Extra Dimensions 2 1. Neutrino Oscillation ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⋅ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ 3 2 1 3 2 1 3 3 1 3 2 1 ν ν ν ν ν ν τ τ τ µ µ µ τ µ U U U U U U U U U e e e e For massive neutrinos one could introduce in analogy to the quark mixing a mixing matrix describing the relation between mass and flavor states: 3 3 2 2 1 1 ν ν ν ν e e e e U U U + + = Constant for massless ν: mixing is question of convention β β β α α α ν ν ν t iE i i i i t iE i i i i e U U e U t − − ∑ ∑ = = * , ) 0 ( ) ( → there will be a mixing of the flavor states with time. Massive neutrinos develop differently in time. ) 2 ( 2 ) 0 ( ) 0 ( ) ( i i i i p m p i i t iE i i e e t + − − = = ν ν ν for masses m i <<E i : i i i i i i p m p m p E 2 2 2 2 + = + =
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Particle Physics / Standard Model: Neutrino Mixing & SUSY
1J. Pawlowski / U. Uwer
1
Physics beyond the Standard Model
1.Neutrino Mixing
2.Supersymmetry
3.Extra Dimensions
2
1. Neutrino Oscillation
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛⋅⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
3
2
1
321
331
321
ννν
ννν
τττ
µµµ
τ
µ
UUUUUUUUU eeee
For massive neutrinos one could introduce in analogy to the quark mixing a mixing matrix describing the relation between mass and flavor states:
332211 νννν eeee UUU ++=
Constant for massless ν: mixing is question of convention
βββ
αααννν tiE
ii
iitiE
ii
ii eUUeUt −− ∑∑ == *
,)0()(
→ there will be a mixing of the flavor states with time.
Massive neutrinos develop differently in time.
)2
(2
)0()0()( i
ii
i pmpi
itiE
ii eet+−
− == νννfor masses mi<<Ei:
i
iiiii p
mpmpE2
222 +=+=
Particle Physics / Standard Model: Neutrino Mixing & SUSY
2J. Pawlowski / U. Uwer
3
Mixing probability:
⎥⎦⎤
⎢⎣⎡ −−==→ tEEttP
2cos1)sin(cos2)(),( 12222
θθνννν αββα
⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆⋅=⎟⎟
⎠
⎞⎜⎜⎝
⎛ ∆=→ ][
][4][27.1sin2sin
4sin2sin),(
222
222 kmL
GeVEeVmL
EmtP θθνν βα
1.1 Mixing in the 2 neutrino case
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⎟⎟⎠
⎞⎜⎜⎝
⎛−
=⎟⎟⎠
⎞⎜⎜⎝
⎛
2
1
cossinsincos
νν
θθθθ
νν
β
α
( ) LEmtEE
Em
pmmEE
pmpmpE i
ii
2
:1w/L/tsame) the is p (assuming
22
2
2
12
i
222
21
12
222
∆=−
≈=
∆≈
−=−
+=+=
ββ
Definite momentum p; same for all mass eigenstate components
Time development for an initially pure |να> beam:
[ ][ ] β
α
α
νθθ
νθθ
νθνθν
⋅−+
⋅+=
+=
−−
−−
−−
)(sincos
sincos
sincos)(
21
21
21
22
21
tiEtiE
tiEtiE
tiEtiE
ee
ee
eet
4
• Disappearance:(I) With known neutrino flux: Measurement of flux at distance L: reactor experiments (sun).
(II) Measure neutrino flux at position 1 and verify flux after distance L.
• Appearance:Use neutrino beam of type A and search at distance L for neutrinos of type B.
⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆=→ L
EmtP
4sin2sin),(
222 θνν βα
How to search for neutrino oscillation ?
Solar neutrinos, atmospheric neutrinos
Reactor neutrinos
Particle Physics / Standard Model: Neutrino Mixing & SUSY
3J. Pawlowski / U. Uwer
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1.2 Atmospheric neutrinos
Cosmic radiation: Air shower
)()(
)(,,
µµ
µµ
ννννµ
ννµππ
++→
+→
→+
±±
±±±
±±
eee
KKNp
2=++
=ee
Rνννν µµ
Exact calculation: R=2.1 (Eν<1GeV)
(For larger energies R>2.1)
6
Neutrino detection with water detectors [Eν~O(GeV)]Water = “active target” (Cherenkov effect)
Elastic scattering ES
CherenkovLight
Experiments: (Super)-Kamiokande
Detection of Cherenkov photons: Photo multiplier
xν xν
−e −e
Z
Charged current CCKinematical limit for νµ: Eν>mµµν ,e
−− µ,e
pn
W
eν e
−e eν
W
Particle Physics / Standard Model: Neutrino Mixing & SUSY
4J. Pawlowski / U. Uwer
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Super-Kamiokande
• Largest artificial water detector (50 kt)
• 11000 PMTs (50 cm tubes!): 40% of surface covered with photo-cathode
8
Stopped Muon
)1(42
1cos
==⇔
=
βθ
βθ
o
n
Cherenkov cone:
Experiment can distinguish electron and muon events, can measure energy
stoppedµνµ →
Particle Physics / Standard Model: Neutrino Mixing & SUSY