Neutrino Oscillations in vacuum
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Neutrino Oscillations in vacuum
Student Seminar on Subatomic PhysicsFundamentals of Neutrino Physics
Dennis Visser15-10-2010
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Outline
1. Plane wave derivation of neutrino oscillation probabilities
2. Wave packet treatment3. Averaged oscillation probabilities
4. The KamLAND experiment5. Additional topics (given time)
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Plane wave derivation7.4 7.10
7.17
7.8 7.19
7.20
7.21
7.23
We have assumed that all neutrinos have equal momenta and we define:
We also assume that neutrinos propagate with the speed of light:
def
def
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Plane wave derivation
7.23
Consider two-neutrino mixing
7.67
Oscillation term because of the mass difference
Amount of mixing
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Wave packet treatment
Consider the decay process
In principle it is possible to know the energy and momentum of the neutrino from experiment, but even when we know them exactly …
Heisenberg uncertainty relation:
WHY ?
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Wave packet treatment
1. Heisenberg uncertainty relation:
2. Different massive neutrinos have different velocities
→ Neutrinos described by wave packets
→ Different massive neutrino wave packets only detected coherently when the baseline is small enough
WHY ?
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Wave packet treatment
When different masssive neutrinos in general not detected coherently
Fig. 8.2
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Wave packet treatment
Fig. 8.3
When different masssive neutrinos in general not detected coherently
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Wave packet treatment
Natural Linewidth:
Particle decaying at rest: 8.128
Particle decaying in flight: 8.129
8.130
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Wave packet treatment
For reactor neutrinos:[5]
Lcoh >> baseline L, implying that one can neglect the wave packet effects for reactor neutrinos
(for supernova neutrinos this is not true, Lcoh << baseline L)
Due to the velocity difference between the two massive neutrinos
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Averaged oscillation probabilities
7.93
- Energy resolution of the detector is finite
- Propagation distance not exactly known
Beside the averaging of the oscillation probabilities because of the wavepacket nature of neutrinos, there is also need for averaging the oscillation probabilities because for example:
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Averaged oscillation probabilities
7.94
7.95
7.93
7.96
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Averaged oscillation probabilities
7.93
7.96
Let’s consider the case
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Averaged oscillation probabilities1. Averaged oscillation probabilities because of the wave packet nature of neutrinos:
2. Averaged oscillation probabilities because of experimental uncertainties:
Note that we have assumed
For reactor neutrinos only experimental uncertainties important
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Averaged oscillation probabilities
Fig 7.2
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Averaged oscillation probabilities
Fig 7.3
Assume that from an experiment we have an upper limit for the transition probability:
Then:
→ EXCLUSION PLOT
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Averaged oscillation probabilities
Exclusion plot for a disappearance experiment
EXCLUDED REGION
7.109
Fig. 7.4 b
(lower bound)
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Averaged oscillation probabilities
Fig 7.5 a
EXCLUDED REGION
EXCLUDED REGION
(bounds)
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Averaged oscillation probabilities
Fig 7.5 b
(measured)
(measured)
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Averaged oscillation probabilities
Fig 12.3
Dotted curve:
best fit values:
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The KamLAND experiment
Ref.[3]
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The KamLAND experiment
Ref.[3]
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The KamLAND experimentBalloon filled with 1000 tons of liquid scintillator, acting as both the target and detection volume
Surrounded by 1879 PMTs mounted on a steel
sphere
Volume between balloon and steel spere filled with non-scintillating mineral oil acting as a shield from external neutron and gamma radiation
Volume between the steel sphere and the rock has a third layer, filled with water with PMTs mounted on the cylindrical surface on the outside KamLAND. This final layer uses Cherenkov radiation to detect muons passing through the detector. The muons can interact with the material in the central detector producing background radiation. By knowing exactly when a muon passes through KamLAND, the detector volume can be vetoed, to avoid detecting the background.
20 m
Ref.[2]
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The KamLAND experiment
Ref.[6]
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The KamLAND experiment
Ref.[4]
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The KamLAND experiment
Ref.[4]
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Summary• Neutrino flavor eigenstates not equal to neutrino mass eigenstates,
this implies that neutrinos oscillate• Neutrinos described by wave packets, wave packet description is
important when the baseline is large• Plane wave derivation valid for small L/E ratio• To explain results for large L/E ratio we need to average over an
appropriate distribution of L/E, because of experimental uncertainties and/or wave packet effects. For large L/E ratio neutrinos are detected incoherently
• Neutrino experiments give exclusion plots in the plane
• Neutrino experiments are not that easy• From the KamLand experiment + solar experiment we have
obtained precise values for one of the oscillation angles and one of the mass differences
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References
[1] Carlo Giunti and Chung W. Kim, Fundamentals of Neutrino Physics and Astrophysics, Oxford University Press, 2007
[2] KamLAND website, http://kamland.lbl.gov
[3] Koichi Ichimura, Recent Result from KamLAND, presentation given at ICHEP08
[4] Patrick Decowski, KamLAND Neutrino Oscillation Results and Solar Future, presentation given at Neutrino 2008
[5] C.W. Kim, Neutrino Physics: Fundamentals of Neutrino Oscillations, hep-ph/9607391, 1996
[6] The KamLAND Collaboration, Precision Measurement of Neutrino Oscillation Parameters with KamLAND, hep-ex/0801.4589, 2008
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Additional topics
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Oscillation probabilities
7.23
7.38
7.30
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Antineutrino oscillation probabilities
7.49
7.50
7.51
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CPT & CP transformations
CPT is assumed to be conserved in SM
7.53
7.56
7.57
7.59
7.61
7.62
7.63
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Mass spectrum
13.5
13.6
Fig 13.1
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Mass spectrum
Assume that
Then:
13.13
13.14
13.15
13.16
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Mass spectrum
Now assume that
Then:
13.18
13.19
13.20
13.21
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Mass spectrum
13.8
13.22