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Neutrinos
Overview
Overview
Pauli postulates Neutrino
Discovery of neutrino flavours
Electron, muon and tau neutrinos
Neutrino Interactions
Cross sections
Neutrino mass
Direct measurement
Neutrino oscillations
Lepton flavour violation
Formalism
Solar neutrinos
Homestake, Super-K and SNO
Atmospheric neutrinos
Super-K
Discovery of Neutrino Mass
neutrino oscillations
Cosmology
Nuclear and Particle Physics
Franz Muheim
1
Pauli’s Letter
Particle Physics in 1930
Only 3 knowns fundamental particles: e-, p, γ
Continuous energy spectrum of e- in beta decay
A
Z
X → Z +1AX + e − + ν e
Pauli postulates Neutrino
Pauli
Dear radioactive Ladies and Gentleman
“ … desperate remedy to save … the law of
conservation of energy”
“ … that there could exist … neutrons”
“in beta decay a neutron is emitted in addition to
the electron“
1934 name - “neutrino” coined by Fermi
1932 neutron discovered by Chadwick
Nuclear and Particle Physics
Franz Muheim
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Neutrino Interactions
Neutrinos
point-like leptons
do not interact strongly, no colour charge
charge Q = 0 → no electromagnetic interactions
Only weak interactions by coupling to W± and Z0
Expect very small detection rates
“ I have done a terrible thing. I have postulated a
particle that cannot be detected.” Pauli
Inverse Beta Decay
ν e + n → p + e−
ν e + p → n + e+
Cross section
σ (ν e + p → n + e ) ≈ 5 ⋅ 10
+
2
− 44
⎛ Eν ⎞
2
⎜
⎟ cm
⎝ MeV ⎠
Mean Free Path
60 light years of water for 1 MeV anti-neutrino
λ=
1
≈ 6 ⋅ 1019 cm ≈ 60 light years
nσ
n= Z
NA
= 3.34 ⋅ 10 23 cm - 3
A
1 ν in 1011 interacts when crossing the earth
Require huge rates as neutrino sources
Nuclear and Particle Physics
Franz Muheim
3
Discovery of Neutrinos
Electron Neutrino νe
discovered 1956 by
Anti-neutrino source
Reines and Cowan
Nuclear reactor --- anti-ν flux 6·1020 s-1
Target and Detector --- 400 l liquid scintillator
Water and Cadmium Chloride
Detection of anti-neutrino ν e + p → n + e +
e + e − → γγ
e+ annihilates with atomic enCd → Cd * → γ Cd
n Cd reaction delayed by 20 µs
Delayed coincidences only produced by signal
Muon Neutrino νµ
1962 at Brookhaven by
Pion beam
Ledermann, Steinberger, Schwartz
Iron absorber --- only muons survive
π - beam
π + → µ +ν µ
π − → µ −ν µ
observe ν µ + n → µ − + p
νµ + p → µ+ + n
don' t see ν µ + n → e − + p
ν µ + p → e+ + n
Î νµ and νe are different
Tau Neutrino ντ
2000 at Fermilab - Donut
p on tungsten target
produce Ds mesons
Ds+ → τ + + ν τ
ντ + N → τ − + X
τ − → µ − +ντ +ν µ
Nuclear and Particle Physics
Franz Muheim
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Neutrino Physics
Neutrino Sources
Natural radioactivity – e.g. rocks
Cosmic rays hitting the atmosphere
Nuclear reactors
Particle accelerators
Sun - nuclear fusion reactor
4 p→ 4He + 2e + + 2ν e + 26.7 MeV
Flux on earth ~1011 cm-2s-1
100 billions/sec through your finger nail
Neutrino Mass
No apparent “reason” for neutrino to be massless
all other fermions have mass
Direct mass measurements
Beta decay energy spectrum
3
H → 3He + e − + ν e
dΓ GF2
(E0 − Ee )2 Ee2
=
3
dE 2π
dΓ 1
∝ E0 − Ee
dE E e2
Kurie plot
linear
Endpoint modified by resolution
and non-zero νe mass
Tritium Beta Decay Mass m(νe) < 3 eV
Neutrino Oscillations
No apparent “reason” for neutrinos not to oscillate
into each other
Nuclear and Particle Physics
Franz Muheim
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Neutrino Oscillations
Lepton flavour conservation
Le, Lµ, Lτ are conserved separately
Neutrinos with mass can mix – weak eigenstates
are linear superpositions of mass eigenstates
Î Le, Lµ, Lτ not absolutely conserved
Le, Lµ, Lτ Violation too small to observe BF < 10-40
2 Neutrino flavours
Easy to understand, can be expanded to 3 generations
⎛ν e ⎞ ⎛ cos θ
⎜ ⎟ = ⎜⎜
⎜ν ⎟
⎝ µ ⎠ ⎝ − sin θ
⎛ν 1 ⎞
⎜⎜ ⎟⎟
⎝ν 2 ⎠
sin θ ⎞
⎟
cos θ ⎟⎠
Time evolution ν 1 ( t ) = ν 1 (0) exp(− iE1t )
ν 2 ( t ) = ν 2 (0) exp(− iE 2 t )
Intensity I(t) for initial νe beam
⎛
Iν e ( t ) = Iν e (0)⎜⎜ cos 2 θ + sin 2 θ
⎝
(
)
2
⎛ ( E − E1 )t ⎞ ⎞
− 4 sin 2 θ cos 2 θ sin 2 ⎜ 2
⎟ ⎟⎟
2
⎝
⎠⎠
Neutrino energy E and mass difference ∆m122
E i2 = pi2 + m i2
E i >> m i
∆m122 ≡ m 22 − m12
⇒ ∆E ≡ E 2 − E1 ≈ ∆m122 / 2 E
m i2
⇒ E i ≈ pi +
2 pi
Neutrino Oscillation Probabilities
⎛ 1.27∆m122 [eV ]L[m] ⎞
⎟⎟
P (v e → v e ) = 1 − sin 2θ sin ⎜⎜
E
[
MeV
]
⎠
⎝
2
(
P ve → v µ
)
2
⎛ 1.27∆m122 [eV ]L[m] ⎞
⎟⎟
= sin 2θ sin ⎜⎜
E
[
MeV
]
⎠
⎝
2
2
Distance from source L [m], E[MeV] and ∆m122 [eV2]
Nuclear and Particle Physics
Franz Muheim
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Solar Neutrinos
Standard Solar Model (SSM)
Bahcall
Predicts rates and solar neutrino energy spectra
pp flux below 0.42 MeV
8B ν up to 14 MeV
e
pp cycle
Homestake Experiment
First observed solar neutrinos in 1970s
100,000 gallons of
cleaning fluid C2Cl4
Davies
Measurement
ν e + 37Cl → e − + 37Ar
0.5 Ar atoms/day
2.56±0.23 SNU
SSM prediction
1.5 Ar atoms/day
7.7±1.3 SNU
Puzzle - What is wrong?
1 SNU = 1 interaction
Experiment, SSM, Neutrinos 1036 target atoms/sec
Nuclear and Particle Physics
Franz Muheim
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Solar Neutrinos II
Super-Kamiokande
50,000 tons of water, 11,000 phototubes
underground inside a mine in Japan, started 1997
νe Detection
Elastic scattering
ν e + e− → ν e + e−
Directional
sensitivity
Measurements
(0.465 ± 0.005
+ 0.016 -0.015) x SSM
νe definitely from sun
Signal from centre of sun
Puzzle - What is wrong?
Homestake experiment
confirmed
Experiment, SSM, Neutrinos
Nuclear and Particle Physics
Franz Muheim
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Solar Neutrinos III
SNO --- Sudbury Neutrino Observatory
1000 tons of heavy water (D2O)
10,000 photo multipliers tubes
Sensitivity
SNO is able to measure νe
- Charged Current
- Neutral Current
but also νµ and ντ (νi=e,µ,τ )
Charged current (CC)
ν e + D → p + p + e−
Elastic scattering (ES) ν i + e − → ν i + e −
Neutral current (NC)
ν i + D → n + p +ν i
Measurements
2003 results
31% of SSM
100% of SSM
31 % of solar ν’s arrive as νe at earth
100% of solar ν’s detected if νµ and ντ are included
Puzzle - What is wrong?
Experiment, SSM,
Neutrinos
Neutrino
Neutrino Oscillations
Oscillations
νe change to νµ in flight
Nuclear and Particle Physics
Franz Muheim
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Atmospheric Neutrinos
Cosmic Rays
Protons hit nuclei in upper part of atmosphere
Producing chain of particles
copious source of neutrinos
Main decay sequence
π + → µ +ν µ and π − → µ −ν µ
µ + → e +ν eν µ
µ − → e −ν eν µ
Expect 2 νµ for each νe
~1990 1st indications for ”too few νµ”
Super-Kamiokande
Can discriminate νµ from νe
ν µ + N → µ− + X
ν e + N → e− + X
Recoil muon produces clean ring
Recoil e- produces fuzzy ring
ν e + N → e− + X
ν µ + N → µ− + X
Nuclear and Particle Physics
Franz Muheim
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Atmospheric Neutrinos II
Measurements
1998 Super-Kamiokande
Observe significant deficit of νµ
and agreement for νe
Neutrino Disappearance
νµ traversing the earth
i.e arriving at the detector
from below disappear
Neutrino
Neutrino Oscillations
Oscillations
Atmospheric neutrinos
νµ change to ντ in flight
Nuclear and Particle Physics
First Evidence for
Neutrino Oscillations
Franz Muheim
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Discovery of Neutrino Mass
Atmospheric Neutrino Oscillations
Atmospheric νµ change into ντ
2
⎛ 1.27 ∆m µτ
[eV ]L[m] ⎞
Oscillation
2
2⎜
⎟
P (v µ → vτ ) = sin (2θ µτ )sin ⎜
⎟
[
MeV
]
E
probability
⎝
⎠
Fit data for best values
of mass difference ∆m232
and mixing angle θµτ
Find θµτ ≈ 450 and
∆m232 ≈ 2.4·10-3 eV2
Î Neutrinos have Mass
Solar Neutrino Oscillations
Super-Kamiokande, SNO
Kamland – reactor anti-νe
Find θeµ ≈ 330 and
∆m122 ≈ 8.0·10-5 eV2
Neutrino mass
Minimum mν ~ 0.05 eV
2 scenarios
Cosmology
Big Bang large nr. of neutrinos
Neutrinos are
hot dark matter candidates
Supernova 1987A
Kamiokande and IMB
Observed ~ 10 neutrinos
Nuclear and Particle Physics
Franz Muheim
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