Neutrino Oscillations in vacuum Student Seminar on Subatomic Physics Fundamentals of Neutrino Physics Dennis Visser

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 We have assumed that all neutrinos have equal momenta and we define: We also assume that neutrinos propagate with the speed of light: 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 Whendifferent masssive neutrinos in general not detected coherently Fig. 8.2

Wave packet treatment Fig. 8.3 Whendifferent masssive neutrinos in general not detected coherently

Wave packet treatment Natural Linewidth: Particle decaying at rest: Particle decaying in flight:

Wave packet treatment For reactor neutrinos: [5] L coh >> baseline L, implying that one can neglect the wave packet effects for reactor neutrinos (for supernova neutrinos this is not true, L coh << baseline L) Due to the velocity difference between the two massive neutrinos

Averaged oscillation probabilities 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

Averaged oscillation probabilities 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 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 Fig. 7.4 b (lower bound)

Averaged oscillation probabilities Fig 7.5 a EXCLUDED REGION (bounds)

Averaged oscillation probabilities Fig 7.5 b (measured)

Averaged oscillation probabilities Fig 12.3 Dotted curve: best fit values:

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 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, [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/ , 1996 [6] The KamLAND Collaboration, Precision Measurement of Neutrino Oscillation Parameters with KamLAND, hep-ex/ , 2008

Additional topics

Oscillation probabilities

Antineutrino oscillation probabilities

CPT & CP transformations CPT is assumed to be conserved in SM

Mass spectrum Fig 13.1

Mass spectrum Assume that Then:

Mass spectrum Now assume that Then:

Mass spectrum