Neutrino Oscillations

Transcription

1 Neutrino Oscillations Elisa Bernardini Deutsches Elektronen-Synchrotron DESY (Zeuthen) Suggested reading: C. Giunti and C.W. Kim, Fundamentals of Neutrino Physics and Astrophysics, Oxford University Press (2007; 728 pages)

2 Neutrino oscillations in vacuum Idea: interference of different massive neutrinos The mass differences must be small: ν s are produced and detected coherently Assumptions for the derivation of oscillation probability: Neutrinos are ultra-relativistic Neutrinos are produced in a defined flavor state The experimental resolution in energy-momentum does not allow the determination of the individual masses Neutrino flavor states ν α can then be described by a superposition of mass (Hamiltonian) eigenstates ν k : Eq. 1 2 Bruno Pontecorvo

3 Neutrino propagation The Schroedinger equation implies that they evolve in time as plane waves: The time evolution of a flavor state is then: U U=1 implies that: Eq. 2 Eq. 3 Combining Eq 2 and Eq 3 we obtain that a pure flavor state at t=0 becomes a superposition of different flavors states at t>0 Eq. 4 3

4 Neutrino oscillation probability The coefficient gives the probability of transition as a function of time: For relativistic neutrinos: Eq. 5 4

5 Neutrino oscillations in vacuum The transition probability between two different states is then In experiments, the distance to the source L is measured (not the time t) Neutrino oscillations can shed light on the squared-mass differences and the elements of the mixing matrix Phases of neutrino oscillations: Symmetry transformation of states: CP violated: T violated: CPT conserved: Eq. 6 5

6 Two-neutrino mixing Consider only two massive neutrinos out of three The two flavor states are superposition of the two mass states ν 1 and ν 2 with coefficients given by the elements of the effective mixing matrix: There is one mixing angle 0 θ π/2 and one squaredmass difference Δm 2 The transition probability (α β) is: And its average (in energy and distances): 6

7 Sensitivity to neutrino oscillations Two classes of experiments: Appearance: observe transitions between different flavors Disappearance: measure the survival probability of a flavor According to the ratio L/E: The transition between flavors cannot be observed if Only the average of the transition probability manifests itself if 7

8 Strumia, Vissani 8

9 Sources of neutrinos Reactor/Accelerator Supernova Solar Atmospheric

10 Neutrino fluxes

11 Reactor neutrinos Fission reactors are strong sources of anti-ν e from β- decay of neutron-rich nuclei ( 235 U, 238 U, 239 Pu, 241 Pu) Very intense ~ s -1 per GW th of thermal power Neutrino flux is isotropic Energy ~ few MeV (only ν e disappearance) Anti-ν e detected via inverse β-decay (E th 1.8 MeV) Sensitivity to oscillations: Source-detector distance Neutrino energy (and cross sections) Detector mass Background level (e.g. hadronic component in cosmic rays) 11

12 Reactor experiments Search for disappearance of anti-ν e SBL LBL VLBL important to interpret Atmospheric neutrino data The ratio of observed to measured neutrino flux from reactor experiments as a function of their source distance L important to interpret solar neutrino data 12

13 KamLAND Detect anti-ν e produced by 53 reactors in Japan! Schematics of the KamLAND detector: 1200 m 3 of scintillator in a spherical balloon of 13 m diameter and watched by 1879 PMTs 13

14 Evidence for reactor anti-neutrino disappearance Deficit in the observed flux of electron anti-neutrinos (disappearance) R = ± ± The spectrum shows the signature of neutrino oscillations (L/E dependency) Ratio of the measured to expected anti-neutrino spectrum versus L/E 14

15 Accelerator neutrinos Neutrinos produced by the decay of pions, kaons and muons from a proton beam onto a target Pion decay in flight: mostly muon neutrinos (OR anti-neutrinos) with energies ~ GeV or more; e.g. SBL: CHORUS, NOMAD, CHARM, LSND; LBL: MINOS, OPERA, ICARUS, T2K Muon decay at rest: muon anti-neutrinos of low energy from muon decay, with energy ~ tens MeV; e.g. KARMEN, LSND Beam dump: protons of very high energy are completely stopped by a target; muon and electron neutrinos with energy ~ 100 GeV 15

16 All experiments did not find any indication of oscillations Except LSND: Signal in Weak signal Combined analyses did not exclude this results Three-neutrinos mixing scheme to be extended (sterile neutrinos?) Design dedicated experiment: MiniBooNE LSND Region of squared-mass difference and mixing angle allowed at 90% CL by a combined analysis of LSND and KARMEN (green) and exclusion curves by KARMEN and other experiments 16

17 MiniBooNE Concept of sterile neutrino: non-interacting light particle Singlet in the SU(3)xSU(2)xU(1) group It is mixed with active neutrinos Test LSND studying Changes: Higher energy (500 MeV compared to 30 MeV Longer baseline (500 m compared to 30 m) The MiniBooNE excluded region compared with LSND results The MiniBooNE detector 17

18 LBL accelerator experiments K2K designed to test atmospheric neutrino oscillations based on observation of muon neutrino disappearance. Beam: almost pure ν µ with mean energy 1.3 GeV Other LBL: MINOS, ICARUS, OPERA K2K observed muon neutrino disappearance No oscillations Best-fit with oscillations Energy spectrum of the muonneutrino events observed in the K2K experiment important to interpret Atmospheric neutrino data 18

19 Atmospheric neutrinos Generated in the interaction of primary cosmic rays with the Earth s atmosphere Secondaries are generated which include all the hadrons and their decay products Energy spectrum is peaked at ~ GeV and extends to higher energies with a power-law Cosmic Ray e + µ + π + ν e ν µ ν µ 15 Km 19

20 The up-down symmetry/asymmetry 1. The production of high energy atmospheric neutrinos is uniform around the globe 2. A neutrino passing at point A with angle θ, reaches B at an angle π θ A ν α θ The fluxes of neutrinos of a given flavor from opposite directions are the same at any location B Up/down symmetry expected π θ 20

21 Atmospheric neutrinos Mostly pions are produced, which decay into muons and neutrinos In the 1960s (neutrino induced) muon tracks detected deep underground (~ 8000 mwe) The Kamiokande and IMB detectors: detect charged particles via Cherenkov radiation in water Observed less muon than expected Atmospheric neutrino anomaly To detect charged particles, the KAMIOKANDE detector utilizes Cherenkov radiation in the water. 21

22 (Super-)kamiokande Underground detector with arrays of PMTs: IMB, (Super-)Kamiokande, SNO The inside of the Superkamiokande detector 22

23 Wave front Charged Particle v > c / n 23

24 How to tell a ν µ from a ν e 24

25 The up-down asymmetry Asymmetry observed: a model independent proof of neutrino oscillations Up/down asymmetry of the neutrino flux as a function of the neutrino energy for the Kamioka and Sudan sites. Right: muon neutrinos. Left: electron neutrinos 25

26 The atmospheric neutrino anomaly First indication: the number of Sub-GeV muon-like events was less than expected, while the number of electron-like events was compatible to the prediction Deficit of muon-like events Data from Kamiokande alone cannot separate between ν µ ν e and ν µ ν τ but results from CHOOZ excluded ν µ ν e Zenith angle distribution of the through-going muon flux observed in Kamiokande 26

27 Solution of the atm. anomaly: flavor The results of CHOOZ and Paolo Verde disfavor ν µ ν e The results of Superkamiokande favor ν µ ν τ and disfavor ν µ ν s (s=sterile neutrino) Confirmed by K2K (extremely important since rather different concepts and systematic uncertainties) 27

28 Solar neutrinos Powerful source of electron neutrinos Neutrino produced in two groups of reactions: pp chain CNO cycle Energy ~ 1 MeV 28

29 The pp chain of stellar thermonuclear reactions 29

30 Standard Solar Model (SSM) Rate of radio-chemical detectors is measured in Solar Neutrino Units (SNU) = events atom -1 s -1 Predicted energy spectra of neutrino fluxes 30

31 Detection Energy ~ MeV σ = cm 2 Interaction probability ~ Detection of solar neutrinos First Homestake in 1970 Gallex/GNO in the 90s Super-Kamiokande and SNO later Proof of the theory of thermonuclear energy generation is stars! Discovery of the solar neutrino problem in favor of neutrino oscillations Pauli: I have done a very bad thing today by proposing a particle that cannot be detected: it is something no theorist should ever do 31

32 Detection of Solar Neutrinos The Homestake experiment: detect the radioactive Ar nucleus produced by interaction of a solar neutrino with the nucleus of a Cl atom (E th =814 KeV): Expected 1.5 ± 0.6 atoms/day) Found fewer (~ 1/3) neutrinos than expected from the SSM. Deficit confirmed by other experiments and at other energies The solar neutrino problem The Homestake solar neutrino detector (1,500 m underground to filter out cosmic particles, 615 ton of C 2 Cl 4 ) 32

33 Other radiochemical experiments 33

34 GALLEX/SAGE results 34

35 Electron scattering Mostly electron neutrinos contribute to the process The cross section (T kinetic energy of the final electron) Strongly peaked for electron emission in the neutrino direction 35

36 Solar neutrino anomaly Recoil electron have a sharp forward peak Flux measured ~ 1/2 of expected ± 230 solar neutrino events elastic scattering peak background events SuperKamiokande image of the Sun Angular distribution of solar neutrino event candidates of SuperKamiokande (SK, 50 kton water tank) 36

37 Vacuum Oscillations of Solar ν s Pontecorvo & Gribov , the Homestake experiment detects less neutrinos than expected: the solar neutrino problem Survival probability of solar neutrinos in case of two-ν s mixing (L distance Sun-Earth, L 0 =1 a.u., e eccentricity of Earth s orbit): But from the analysis of solar neutrino data: No significant seasonal variation observed Energy spectra not compatible with the distortion expected due to the transition probability Vacuum oscillation are disfavored 37

38 Modulation of solar neutrinos The only periodic variation in the rate of solar neutrinos agrees with what expected due to the eccentricity of the Earth s orbit. No indication of other modulations due to neutrino oscillations Prediction based on the eccentricity of the Earth s orbit Solar neutrino flux as a function of time measured in Superkamiokande Seasonal variation of the solar ν flux measured in Superkamiokande 38

39 The Sudbury Neutrino Observatory (SNO) SNO detect solar neutrinos through CC: NC: ES: They provide a handle on CC: energy spectrum of ν e NC: total neutrino flux ES: equivalent (independent) to SK, measure the angular distribution of the events Measure Φ(ν e ) and Σ i Φ(ν i ) The flux of non-electron neutrinos (oscillated) is then: Φ(non ν e ) = Σ i Φ(ν i ) - Φ(ν e ) The SNO detector: one kiloton pure D2O in a spherical acrylic vessel 39

40 Neutrino reactions in SNO 40

41 SNO results: solar ν e deficit confirmed The NC measurement of the total neutrino flux demonstrates that about two electron neutrinos out of three change their flavor Fluxes needed to explain SNO data, assuming the energy spectrum of 8 B: Phys. Rev. C (2007) Model prediction (no oscillations) They largely disagree: proof that ν e do change during propagation Good agreement between the NC SNO flux and what expected by the SSM ν e Flux of ν µ and ν τ as a function of ν ε Total ν flux 41

42 Neutrino oscillations in vacuum The flavor states ν α do not coincide with the mass eigenstates ν k The flavor states are combinations of the eigenstates ν k : The mass states ν k are eigenstates of the Hamiltonian: Admixture of mass eigenstates in a given neutrino state do not change (there is no ν 1 ν 2 transition) The phase difference between eigenstates increases monotonously The process is periodic. The oscillation length is the distance at which the system returns to its original state 42

43 Resonant flavor transition in matter Neutrinos in matter are subject to a potential due to elastic scattering with the medium (electrons and nucleons), equivalent to an index of refraction Feymann diagrams for the elastic scattering processes that generate the CC potential (V CC, left) and the NC potential (V NC, right). G F Fermi coupling constant and N e (N n ) number density of electrons (neutrons) 43

44 Propagation in matter In the presence of matter the Hamiltonian changes H o H = H o + V (H o Hamiltonian in vacuum) The Schroedinger equation can be written in terms of matter mixing angle and effective squared-mass difference The eigenstates and the eigenvalues (and therefore the mixing angle) depend on the matter density and on the neutrino energy 44

45 Matter effects in a medium with changing density If the density changes during propagation: The mixing angle changes The instantaneous eigenstates of the Hamitonian ν 1m and ν 2m are no longer eigenstates of propagation Transitions ν 1m ν 2m can take place If the density changes slowly ( adiabatic condition ) the transitions ν 1m ν 2m can be neglected 45

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47 Global fit of solar neutrino data Large mixing angle solution of the solar neutrino problem: The mixing angle is large but not maximal 47

48 Three neutrino mixing The solar and atmospheric neutrino data provide evidence of at least two squared-mass differences Presence of sterile neutrinos disfavored in both cases Three neutrino mixing: two independent squared mass differences 48

49 49