Neutrino Oscillations and the Matter Effect
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1 Master of Science Examination Neutrino Oscillations and the Matter Effect RAJARSHI DAS Committee Walter Toki, Robert Wilson, Carmen Menoni
2 Overview Introduction to Neutrinos Two Generation Mixing and Oscillation Long Baseline Accelerator Neutrino Experiments Setting an Upper limit on θ µe mixing angle: Improved Search for ν μ ν e Oscillation in a Long-Baseline Accelerator Experiment, S. Yamamoto, J. Zalipska, et. al. (K2K Collaboration), Phys. Rev. Lett. 96, (2006) Matter Effect and its application to a Long Baseline Experiment: "Possible Explanation of the Solar-Neutrino Puzzle,"Bethe, H. A., Phys. Rev. Lett. 56 (12), 1305 (1986) Multi-Generation Mixing, Oscillation and three generation to two generation approximation: Neutrino Mass, Mixing, and Flavor Change, Kayser, B., Review of Particle Physics, in C. Amsler et. al. (Particle Data Group), Physics Letters B, 667, 1 (2008) 8/3/2010 2
3 Introduction to Neutrinos Small, nearly mass-less, weakly interacting particles Spin ½, Neutral charge fermions Part of the lepton sector Left-handed chirality only (spin opposite to momentum) They can change flavor! 8/3/2010 3
4 Flavor States Neutrinos are produced in flavor states Interacts with matter and is detected in flavor states NOT eigenstates of vacuum Hamiltonian Assume, for now, that only 2 flavors exist: 8/3/2010 4
5 Two Generation Mixing Mass Basis Hamiltonian Eigenstates Flavor Basis Orthonormal 8/3/2010 5
6 Two Generation Mixing In terms of an Unitary Rotation Matrix 8/3/2010 6
7 Neutrino Oscillation Approximations Time Evolution of Mu Neutrino State 8/3/2010 7
8 Neutrino Oscillation Appearance Amplitude Appearance Probability for Vacuum 8/3/2010 8
9 Mass Splitting Appearance Probability (with units) Mass Squared Splitting We have not yet determined the exact masses of each eigenstate. But the splittings have been observed experimentally. For the above expression: 8/3/2010 9
10 Long Baseline Neutrino Experiments T2K Examples: KEK to Kamioka (K2K) and Tokai to Kamioka (T2K) Pure mu-neutrino beam created at Linear Accelerator with energy ~1.3 GeV/.6 GeV (K2K/T2K) Near Detector placed at 300 m/280 m from beam source 250 km/295 km to Super-KamiokaNDE Water Cherenkov Detector 8/3/
11 T2K and K2K The Beam Super-K Protons accelerated into graphite (aluminum) target Pions and Kaons produced Focused by electromagnetic horns Decay into muons and mu neutrinos mainly Lorentz-boosted beam in direction of Super-K 22.5 kt Cylindrical Fiducial Volume (FV) Water Cherenkov Detector Lined with 11,200 Photomultiplier Tubes (PMT) Reconstruct energy and momentum from Cherenkov rings Detect electrons/muons from neutrino interactions in FV 8/3/
12 K2K and T2K Parameters Experiment Parameters Experiment: K2K T2K Beam Energy: Baseline: Mass Splitting: Ratio to Oscillation Maxima T2K K2K K2K T2K 8/3/
13 Measuring Mixing Angle The sin 2 θ µe from the ν µ ν e probability expression is small, and thus, difficult to measure We start with a pure ν µ beam and look for ν e signal at our detector some distance away In the detector, the signal is identified by the following reaction with a water nucleus: In Super KamiokaNDE, the product electron causes electromagnetic shower identifiable Cherenkov ring pattern K2K set an upper limit despite challenges: Low to negligible signal Background on the order of or above signal Absolutely essential to understand and reduce background 8/3/
14 Event Selection Electron event at Super K (Dots correspond to detected photon energy). Electron neutrino scatters water electron causing an electromagnetic shower (note indistinct edges of Cherenkov ring) 112 fully contained events in fiducial volume of Super-K (K2K I + K2K II) Electron Ring ID via Cherenkov ring pattern and opening angle Electron-equivalent energy (>100 MeV) No subsequent muon decay 8/3/
15 Sources of Background We want: Vµ-CC / Vµ-NC Pi-0 Decay Originated from ν e : Beam ν e : 13% (after event selection) Originated from ν µ (87%): Charged current (CC) ν µ interactions Neutral current (NC) interactions of ν µ and ν τ Dominated by NC π 0 production Can be misclassified as a single ring shower-like event 8/3/
16 Reduction of Events at SK K2K I and K2K II (two separate periods of running) data. After all cuts have been applied, the number of observed events are on the order of expected background. 1 observed event and 1.7 event background 8/3/
17 Setting Upper Bound to Probability Averaged over L/E Distribution Background Expectation: Confidence Level Limits Observed Events: At 90% Confidence Level, the background and observed events corresponds to an upper limit P max, which lets us set: For a L/E distribution being approximately gaussian we get: 8/3/
18 Upper Bound on Data from K2K Using an expected 1.7 ( ) events from no oscillation and an observed 1 event, we get an upper bound on the mixing angle At 90% CL limit, we can exclude sin 2 (2θ µe ) >.13 for mass squared splitting ~2.7E-3 ev 2 Search for θ µe continues! T2K will use a more optimized setup with higher statistics to boost the signal 8/3/
19 Neutrinos in Matter So far we have used a vacuum treatment of neutrino oscillation However, neutrinos in K2K and T2K are passing through several hundred kilometers of rock! Neutrinos behave differently when traveling through matter Deficiency in detected solar neutrino flux (known as the Solar Neutrino Problem) Ultimately explained by neutrino mixing and MSW Effect (Mikheyev, Smirnov, Wolfenstein) MSW Effect originates from electron neutrinos having an extra mode of interaction in matter 8/3/
20 Matter Effect (2 Gen.) Vacuum Hamiltonian Effect in Matter time Charged Current coherent forward elastic scattering : Fermi Constant : Electron Density 8/3/
21 Matter Hamiltonian Characterize Matter Hamiltonian with New Parameters Where we ignore any additional multiples of the Identity matrix. They are irrelevant to the calculation of effective mass splitting and mixing angle Compare to Vacuum Hamiltonian case for easy solution 8/3/
22 Oscillation with Matter Effect Neutrinos oscillate with different parameters in matter where For a time independent matter Hamiltonian only! Time dependent Hamiltonian would result in evolving mass eigenstates. Time independent Hamiltonian corresponds to uniform matter density along baseline 8/3/
23 Matter Effect in T2K Mass Splitting: Beam Energy: Using Rock Density of 2.8 gm/cm^3 we calculate A: 8/3/
24 Appearance in Matter Assuming we were at vacuum oscillation maxima Using 90% CL limit from K2K and Averaging over given interval We have a chance of observing 10% more oscillated events than in the strictly vacuum case! Considering the difficulty of attaining a signal, this boost helps. 8/3/
25 Multi-Generation Neutrinos Three Known Neutrino Flavors Why can we use a 2 Generation treatment to determine mixing parameters? Known neutrinos actually occur in 3 flavors, 3 generation treatment is necessary Unknown if even more than 3 generations of neutrinos exist Severely complicates calculations First we develop formalism for arbitrary number of generations 8/3/
26 Multi-Generation Mixing Assume several mass eigenstates Where: :Mass States :Flavor States are elements of the Unitary transformation matrix Time Evolution 8/3/
27 Multi-Generation Mixing Amplitude Oscillation Probability 8/3/
28 Dominant Mass Splitting Neutrino Mass Eigenvalues Group 2 Mass Where the sums are over Group 1 OR Group 2 only! So what are the elements of U? Group 1 8/3/
29 Three Generation Mixing Rotation of rigid body in 3-dimensions requires 3 rotation angles Rotation around X-axis Rotation around Y-axis and CP Violating Phase Rotation around Z-axis 8/3/
30 Three Generation Mixing U Matrix for 3 Mixing Angles and 1 Phase Where: and Mass Hierarchy (3 Gen) Mass Hierarchy remains unknown Mass Normal Inverted 2 possible types: Normal and Inverted Dominant mass splitting: 8/3/
31 Appearance (3 Gen) Using normal mass hierarchy, we only need to sum over top group, namely i=3 where Despite the presence of a third generation, given a dominant mass splitting approximation, the 2 neutrino treatment is valid! 8/3/
32 Conclusion Flavor states are not Energy eigenstates, which leads to flavor oscillation over time Sin 2 (2θ µe ) is small. K2K set its upper limit at 0.13 at 90% Confidence Level limit for the best fit value of m 2 Long Baseline Neutrino Oscillation Experiments (such as T2K) are continuing the ν µ to ν e search The presence of matter changes neutrino oscillation parameters and boosts the oscillation probability in T2K by ~10% Multi-generation neutrino mixing is the correct approach to neutrino oscillations, but the mass hierarchy still allows for a valid 2 neutrino approximation in some cases 8/3/
33 References 1. Improved Search for ν µ ν e Oscillation in a Long-Baseline Accelerator Experiment, S. Yamamoto, J. Zalipska, et. al. Collaboration), Phys. Rev. Lett. 96, (2006) (K2K 2. "Possible Explanation of the Solar-Neutrino Puzzle," Bethe, H. A., Phys. Rev. Lett. 56 (12), 1305 (1986) 3. Neutrino Mass, Mixing, and Flavor Change, Kayser, B., Review of Particle Physics, in C. Amsler et. al. (Particle Data Group), Physics Letters B, 667, 1 (2008) 4. Letter of Intent: Neutrino Oscillation Experiment at JHF, (T2K Collaboration) 5. The T2K Long-Baseline Neutrino Experiment, Ichikawa, A. K., Lect. Notes Phys. 781, 17 (2009) 6. Limits on neutrino oscillations from the CHOOZ experiment, Appolonio, M. et. al., Phys. Lett. B 466, 415 (1999) 7. Fundamentals of Neutrino Physics and Astrophysics, Giunti, C., Kim W. C., Oxford University Press (2007) 8/3/
34 8/3/
35 Questions, Comments, Concerns?
36 Backup Slides
37 T2K and K2K: Beam Protons accelerated into graphite (aluminum) target Pions and Kaons produced Focused by electromagnetic horns Decay into muons and mu neutrinos mainly Lorentz-boosted beam in direction of Super-K 8/3/
38 T2K and K2K: Detector 22.5 kt Cylindrical Fiducial Volume (FV) Water Cherenkov Detector Lined with 11,200 Photomultiplier Tubes (PMT) Reconstruct energy and momentum from Cherenkov rings Detect electrons/muons from neutrino interactions in FV 8/3/
39 Gaussian L/E Distribution Analytically Solve for Gaussian L/E We take the sigma to be a multiple of <L/E>. L and E have independent distributions The relative energy spread is much greater than the relative distance spread 8/3/
40 Systematic Uncertainties 8/3/
41 T2K and K2K Beam T2K Beam contamination 0.4% (~1% K2K) 3 Electromagnetic Horns for T2K, 2 for K2K 8/3/
42 Off-Axis Energy Spectrum Choose off axis angle that corresponds to an Energy distribution peak at oscillation maxima 8/3/
43 Expected Theta-13 Limit (T2K) 5x10^21 POT exposure Maximum theta23 mixing 90% CL 8/3/
44 Cherenkov Radiation and SuperK 8/3/
45 CHOOZ Limit A better limit is given by CHOOZ, a reactor neutrino experiment that sets sin 2 2θ < 0.1 8/3/
46 Event Selection (detail) Electron Ring ID via Cherenkov ring pattern and opening angle Fuzzy rings caused by electromagnetic showering. Also can be caused by photons Electron-equivalent energy (>100 MeV) Remove misidentified charged pions and electrons from muon decay for muons below cherenkov threshold No subsequent muon decay Resonant nucleon states decay to pions which may decay to leptonic products or gammas. Signals from these decays are background and can be identified if the muon also decays after a certain amount of time 8/3/
47 Parametrizing 3 Gen Matrix 8/3/
48 Matter Effect in T2K (plots) 8/3/
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