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Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
1U. Uwer
4. Neutrino Oscillations
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛⋅⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
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
iiii p
mpmpE2
222 +=+=
4.1 Two-Flavor mixing (for simplicity)
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅⎟⎟⎠
⎞⎜⎜⎝
⎛−
=⎟⎟⎠
⎞⎜⎜⎝
⎛
2
1
cossinsincos
νν
θθθθ
νν
β
α
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
Mixing probability:
⎥⎦⎤
⎢⎣⎡ −−==→ tEEttP
2cos1)sin(cos2)(),( 12222
θθνννν αββα
⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆⋅=⎟⎟
⎠
⎞⎜⎜⎝
⎛ ∆=→ ][
][4][27.1sin2sin
4sin2sin),(
222
222 kmL
GeVEeVmL
EmtP θθνν βα
( ) 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
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
2U. Uwer
Search for Neutrino Oscillations (PDG 1996)
• Disappearance:(I) With known neutrino flux: Measurement of flux at distance L: reactor experiments,
(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.
Exclusion plots
More statistics
excluded
Baseline longer
⎟⎟⎠
⎞⎜⎜⎝
⎛ ∆=→ L
EmtP
4sin2sin),(
222 θνν βα
Observation of Neutrino Oscillations
Oscillation signal(Super)KamiokandeAtmospheric neutrinosMuch disputed signalLSDNAcceleratorClear disappearance signal
K2K
Clear disappearance signal
KamLAND, CHOOZReactor
Ultimate “solar neutrino experiment”: proves the oscillation of solar ν
Water++: SNO
Confirm disappearance of solar neutrinos
Water experiments:(Super)Kamiokande, IMB
First observation of “neutrino disappearance”dates more than 20 years ago: “Solar neutrino problem”
Radio-chemical exp.: Homestake Cl exp., GALLEX, SAGE,
Solar neutrinos
CommentsExperimentNeutrino source
Not confirmed
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
3U. Uwer
4.2 Atmospheric neutrino problem
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)
Neutrino detection with water detectors [Eν~O(GeV)]
Water = “active target”
Elastic scattering
CherenkovLight
Experiments: (Super)-Kamiokande
IMB
Soudan-2
Detection of Cherenkov photons: Photo multiplier
xν xν
−e −e
Z
Xν −X
−e eν
WCharged current Kinematical limit for νµ: Eν>mµ
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
4U. Uwer
Super-Kamiokande
• Largest artificial water detector (50 kt)
• Until the 2001 accident: 11000 PMTs (50 cm tubes!): 40% of surface covered with photo-cathode
• Back in operation since 2003
Stopped Muon
)1(42
1cos
==⇔
=
βθ
βθ
o
n
Cherenkov cone:
Experiment can distinguish electron and muon events, can measure energy
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
5U. Uwer
Ratio of muon to electron neutrinos
• Too few muon neutrinos observed
• Can be explained by oscillation.
Prediction with oscillation
Zenith angle dependence of the neutrino fluxe µ
L~15 km
L~13000 km
w/o oscillationw/ oscillation
Theoretical predicton
νµ deficit depends on angle
νe flux okay
Oscillation: νµ↔ ντ
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
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Oscillation pattern of atmospheric neutrinos
νµ↔ ντ mixing of atmos. neutrinos
..%[email protected])4.04.2(
2
32
LCm
>
×±=∆ −
θ
allowed
Neutrino 2004
4.3 Solar neutrino problemNeutrino production
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
7U. Uwer
Neutrino energy spectrum
2-body decays
Cl2 detectors νe + 37Cl → 37Ar + e, 37Ar → 37Cl (EC) Eν>0.8 MeV
Ga detectors νe + 71Ga → 71Ge + e Eν>0.2 MeV
H2O detectors Elastic scattering: νe + e → νe +e Eν>5 MeV (detection)
Neutrino experiments:
HomestakeSage, Gallex
Radio-chemical experiments: Homestake, SAGE, GALLEX
SSM prediction
• Homestake mine, 1400 m underground
• 615 t of C2Cl4 (perchloroethilene) = 2.2x1030 atoms of 37Cl
• Use 36Ar and 38Ar to carry-out the few atoms of 37Ar (~ 1 atom/day)
• Count radioactive 37Ar decays
Homestake Cl2 experiment
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
8U. Uwer
Solar Neutrino Problem: Experimental summary
Eν>0.8 MeV
Eν>0.2 MeVEν> 5 MeV Eν> 5 MeV
CC CCES ES
Neutrino disappearance
Can one measure the oscillated neutrinos ??
The Nobel Prize in Physics 2002
Riccardo GiaconiMasatoshi KoshibaRaymond Davis Jr.
"for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos"
"for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources"
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
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Sudbury Neutrino Observatory
• 6 m radius transparent acrylic vessel
• 1000 t of heavy water (D2O)
• 9456 inward looking photo multipliers
• Add 2 t of NaCl to detect neutrons
Neutrino detection with SNO
)()()(154.0
τµ νσνσνσ=
=⋅ e
Charged current
xν xν
−e −e
Z
eν e
−e eν
W
eν −e
pn
W
eν eν
nn
Z
Elastic scattering
Neutral current
CherenkovLight
CherenkovLight
Neutron)()()( τµ νσνσνσ ==e
0)()( == τµ νσνσ
Cl),(Cl 3635 γn
eνν φφ =
6/)(τµ νννν φφφφ ++=
e
τµ νννν φφφφ ++=e
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
10U. Uwer
SNO Evidence for Neutrino Oscillation
Electron neutrino flux is too low:
Total flux of neutrinos is correct. Interpreted as νe ↔ νµ or ντ oscillation
)%235( ±=eeP νν
But in case of simple “vacuum oszillation”: %502sin211 2 =−≥ θνν eeP ?
Neutrino oscillations in matter: MSW-effect
Neutrino oscillation in vacuum:
Mikhaev, Smirnov (1986), Wolfenstein (1976)
time development of mass eigenstates ⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
2
122
21
2
1
00
21
νν
νν
mm
pdtdi
With unitary transformation U one obtains for the flavor oscillationin vaccum:
⎟⎟⎠
⎞⎜⎜⎝
⎛−
=θθθθ
θ cossinsincos
U
⎟⎟⎠
⎞⎜⎜⎝
⎛=
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
µ
µµ
νν
νν
νν
e
ee
p
dtdi
2
2
T
M
UMU ⎟⎟⎠
⎞⎜⎜⎝
⎛−∆=
θθθθ
2cos2sin2sin2cos
4
2
pmTUMU
p2
2M
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
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Neutrinos in matter:
xν xν
−e −e
Z
Electron neutrinos suffer an additional potential Ve affecting the forward scattering amplitude which leads to change in the effective mass for νe:
ENGm
EVmpVEpEm
eFM
ee
22
2)(2
222222
=∆
+≈−+→−=
eν e
−e eν
W
Ne=electron densityeFe NGV 2=
222 mNEGa eF ∆=
Neutrino oscillation in matter:
⎟⎟⎠
⎞⎜⎜⎝
⎛
∆−∆
+⎟⎟⎠
⎞⎜⎜⎝
⎛−∆=→ 2
22
00
2cos2sin2sin2cos
2 M
M
mmm
θθθθ2
M2 MM
one define the matter mass eigenstates which one obtains by diagonalizing 2MM
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
ανν
νν e
m
m Tθm
U2
1
Go the opposite direction…
⎟⎟⎠
⎞⎜⎜⎝
⎛∆
∆−+=
m
mmm0
0)(
21 2
121mm θ
2Tθ UMU
θθ 2sin)2cos( 222 +−∆=∆ amm
ENGm eFM 222 =∆
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
12U. Uwer
2/22 mNEGa eF ∆=
22 1042sin −⋅=θ22 1012sin −⋅=θ32 1042sin −⋅=θ
⎟⎟⎠
⎞⎜⎜⎝
⎛−
=mm
mmm θθ
θθθ cossin
sincosU with
θθθθ
2sin)2(cos2sin2sin 22
22
+−=
am
Matter mixing angle can go through a resonance:
Fe EG
mNa22
2cos i.e.02cos 2 θθ ∆==−
As in the core of the sun, Ne is larger than the critical density the resonance condition will always be fulfilled: oscillation largely modified by matter.
)%235( ±=eeP ννExplains observed with SNO
Status of oscillation measurements
Atmosνµ→νx
Solar+KamLANDνe→νx
LMA = large mixing angle: MSW effect
necessary
..%[email protected])4.04.2(
2
32
LCm
>
×±=∆ −
θ
83.02sineV10)6.02.8(
2
52
≈
×±=∆ −
θ
m
Long baseline “many”reactors experiment
Different oscillation pattern for different neutrinos – what can we learn about the masses ??
allowed
allowed
excluded
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
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4.4 Neutrino masses
25eV102.8~ −⋅
23eV104.2~ −⋅
25eV102.8~ −⋅
23eV104.2~ −⋅
Absolute neutrino masses are not known !
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−−−−−−=
132313231223121323122312
132313231223121323122312
1313121312
ccscsscsccsscssssccssccs
scsccU
ijijijij sc θθ sin,cos where ==
solθθ ≡12 atmθθ ≡23 013 ≈θ
Neutrino masses in the Standard Model
Lν
• Neutrino Mass term: the same as for charged leptons:
Rν
Higgsh0 Masses of neutrinos through Yukawacoupling to Higgs:
2υλν
ν =m
From the vacuum expectation value of the Higgs, υ≈246 GeV, follows that the Yukawacoupling must be extremely small (<10-11) to generate the small neutrino masses.
• Lepton numbers: Le Lµ and Lτ are not conserved. L is conserved !!
• But why are the neutrino masses so small ?
• Dirac mass terms imply existence of right (left) -handed (anti) neutrinos.Minimal extension of the Standard Model:
Introduce singlets of right (left)-handed (anti)neutrinos which do not couple to charged and neutral currents.
Dirac mass term
LRm ψψ~
→ unnatural)( νννν LRRLmm D +=
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
14U. Uwer
Majorana Neutrinos• Unlike the charged leptons, neutrinos
could be their own anti-particles: ⎩⎨⎧
==
=RR
LL
νννν
νν
Majorana Neutrinos
Lν Rν
Higgsh0
Majorana mass term
Mass term violates Lepton flavor conservation: ∆L = ± 2
• Majorana character can be checked in neutrinoless double beta decay (0ν2β):
• Majorana-mass terms in addition to Dirac mass terms possible:
• Can we prove that neutrino is a Dirac particle
( ) ..0
0,
,
, ccRR
mm
LLmRM
LM +⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
ν
ννν
Search for 0ν2βGermanium decay (example)
2β energy spectrum
0ν2β
?Klapdor-Kleingrothaus
2004
Advanced Particle Physics: IX. Flavor Oscillation and CP Violation
15U. Uwer
Seesaw mechanism to generate light neutrinos• If neutrinos are Majorana particles:
Introduce in addition to the Dirac mass term also a Majorana mass term for the right-handed neutrino singlet:
Seesaw Model: Assume Majorana mass MR of the right-handed neutrino very heavy, Majorana mass ML of left handed neutrino =0.
Solving the mass matrix one obtains a small mass mν for LH neutrinos
R
D
Mmm
2
=νLν Rν
0h 0h=Rν
0h 0hx
RM1
Lν Rν Lν
Seesaw mass term for light neutrino
• Small neutrino masses can be explained … but how large is MR (1010…1015 GeV) ?
( ) ..,,
, ccRR
mmmm
LLmRMD
DLM +⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
ν
ννν
The End