Neutrino Oscillations in
vacuum
Student Seminar on Subatomic Physics
Fundamentals of Neutrino Physics
Dennis Visser
15-10-2010
Outline
1. Plane wave derivation of neutrino
oscillation probabilities
2. Wave packet treatment
3. Averaged oscillation probabilities
4. The KamLAND experiment
5. Additional topics (given time)
Plane wave derivation
7.4
We have assumed that all neutrinos have equal momenta and we define:
7.10
def
7.21
7.17
7.8
7.19
7.20
We also assume that neutrinos propagate with the speed of light:
def
7.23
Plane wave derivation
7.23
Consider two-neutrino mixing
7.67
Amount
of mixing
Oscillation term because of
the mass difference
Wave packet treatment
WHY ?
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:
Wave packet treatment
WHY ?
1. Heisenberg uncertainty relation:
→ Neutrinos described by wave packets
2. Different massive neutrinos have different
velocities
→ Different massive neutrino wave packets only
detected coherently when the baseline is small enough
Wave packet treatment
Fig. 8.2
When
different masssive neutrinos in general not detected coherently
Wave packet treatment
Fig. 8.3
When
different masssive neutrinos in general not detected coherently
Wave packet treatment
Natural Linewidth:
Particle decaying at rest:
8.128
Particle decaying in flight:
8.129
8.130
Wave packet treatment
Due to the velocity
difference between the
two massive neutrinos
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)
Averaged oscillation probabilities
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:
- Energy resolution of the detector is finite
- Propagation distance not exactly known
7.93
Averaged oscillation probabilities
7.93
7.94
7.95
7.96
Averaged oscillation probabilities
7.93
7.96
Let’s consider the case
Averaged oscillation probabilities
1. 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
Averaged oscillation probabilities
Fig 7.2
Averaged oscillation probabilities
Assume that from an experiment we have an
upper limit for the transition probability:
Then:
→ EXCLUSION
PLOT
Fig 7.3
Averaged oscillation probabilities
Exclusion plot for a disappearance experiment
7.109
EXCLUDED
REGION
(lower bound)
Fig. 7.4 b
Averaged oscillation probabilities
(bounds)
EXCLUDED
REGION
EXCLUDED
REGION
Fig 7.5 a
Averaged oscillation probabilities
(measured)
(measured)
Fig 7.5 b
Averaged oscillation probabilities
Dotted curve:
best fit values:
Fig 12.3
The KamLAND experiment
Ref.[3]
The KamLAND experiment
Ref.[3]
The KamLAND experiment
Balloon filled with 1000 tons of liquid scintillator,
acting as both the target and detection volume
Surrounded by 1879 PMTs mounted on a steel
sphere
20 m
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.
Ref.[2]
The KamLAND experiment
Ref.[6]
The KamLAND experiment
Ref.[4]
The KamLAND experiment
Ref.[4]
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
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
Additional topics
Oscillation probabilities
7.23
7.30
7.38
Antineutrino oscillation probabilities
7.49
7.50
7.51
CPT & CP transformations
7.53
7.56
CPT is assumed to be conserved in SM
7.57
7.59
7.61
7.62
7.63
Mass spectrum
Fig 13.1
13.5
13.6
Mass spectrum
Assume that
13.13
Then:
13.14
13.15
13.16
Mass spectrum
Now assume that
13.18
Then:
13.19
13.20
13.21
Mass spectrum
13.22
13.8