Neutrino Oscillations in vacuum

Student Seminar on Subatomic PhysicsFundamentals of Neutrino Physics

Dennis Visser15-10-2010

Outline

1. Plane wave derivation of neutrino oscillation probabilities

2. Wave packet treatment3. Averaged oscillation probabilities

4. The KamLAND experiment5. Additional topics (given time)

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

Plane wave derivation

7.23

Consider two-neutrino mixing

7.67

Oscillation term because of the mass difference

Amount of mixing

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 ?

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 ?

Wave packet treatment

When different masssive neutrinos in general not detected coherently

Fig. 8.2

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

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

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:

Averaged oscillation probabilities

7.94

7.95

7.93

7.96

Averaged oscillation probabilities

7.93

7.96

Let’s consider the case

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

Averaged oscillation probabilities

Fig 7.2

Averaged oscillation probabilities

Fig 7.3

Assume that from an experiment we have an upper limit for the transition probability:

Then:

→ EXCLUSION PLOT

Averaged oscillation probabilities

Exclusion plot for a disappearance experiment

EXCLUDED REGION

7.109

Fig. 7.4 b

(lower bound)

Averaged oscillation probabilities

Fig 7.5 a

EXCLUDED REGION

EXCLUDED REGION

(bounds)

Averaged oscillation probabilities

Fig 7.5 b

(measured)

(measured)

Averaged oscillation probabilities

Fig 12.3

Dotted curve:

best fit values:

The KamLAND experiment

Ref.[3]

The KamLAND experiment

Ref.[3]

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]

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

7.38

7.30

Antineutrino oscillation probabilities

7.49

7.50

7.51

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

Mass spectrum

13.5

13.6

Fig 13.1

Mass spectrum

Assume that

Then:

13.13

13.14

13.15

13.16

Mass spectrum

Now assume that

Then:

13.18

13.19

13.20

13.21

Mass spectrum

13.8

13.22