Neutrino Oscillations - ·...

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

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  • Neutrino Oscillations

    Suggested reading:

    C. Giunti and C.W. Kim, Fundamentals of Neutrino Physics and Astrophysics, Oxford University Press (2007; 728 pages)

    Elisa BernardiniDeutsches Elektronen-Synchrotron DESY (Zeuthen)

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    Neutrino oscillations in vacuum Idea: interference of different massive neutrinos

    The mass differences must be small: 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 can then be described by

    a superposition of mass (Hamiltonian) eigenstates k: Eq. 1

    Bruno Pontecorvo

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    Neutrino propagation The Schroedinger equation implies that they evolve in

    time as plane waves:

    The time evolution of a flavor state is then:

    UU=1 implies that:

    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. 3

    Eq. 2

    Eq. 4

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    Neutrino oscillation probability The coefficient

    gives the probability of transition as a function of time:

    For relativistic neutrinos:

    Eq. 5

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    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

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    Two-neutrino mixing Consider only two massive neutrinos out of three The two flavor states are superposition of the two mass

    states 1 and 2 with coefficients given by the elements of the effective mixing matrix:

    There is one mixing angle 0 /2 and one squared-mass difference m2

    The transition probability () is:

    And its average (in energy and distances):

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    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

    Sensitivity to neutrino oscillations

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    Strumia, Vissani

  • Sources of neutrinos

    Reactor/Accelerator Supernova Solar Atmospheric

  • Neutrino fluxes

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    Reactor neutrinos Fission reactors are strong sources of anti-e from -

    decay of neutron-rich nuclei (235U, 238U, 239Pu, 241Pu)

    Very intense ~ 1020 s-1 per GWth of thermal power

    Neutrino flux is isotropic

    Energy ~ few MeV (only e disappearance)

    Anti-e detected via inverse -decay (Eth 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)

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    Reactor experiments Search for disappearance of anti-e

    The ratio of observed to measured neutrino flux from reactor experiments as a function of their source distance L


    important to interpret Atmospheric neutrino data

    important to interpret solar neutrino data

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    KamLAND Detect anti-e produced by 53 reactors in Japan!

    Schematics of the KamLAND detector: 1200 m3 of scintillator in a spherical balloon of 13 m

    diameter and watched by 1879 PMTs

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    Evidence for reactor anti-neutrino disappearance

    Ratio of the measured to expected anti-neutrino spectrum versus L/E

    Deficit in the observed flux of electron anti-neutrinos (disappearance)R = 0.658 0.044 0.047

    The spectrum shows the signature of neutrino oscillations (L/E dependency)

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    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

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    LSND 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

    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

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    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

    The MiniBooNE detector

    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

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    LBL accelerator experiments K2K designed to test atmospheric

    neutrino oscillations based on observation of muon neutrino disappearance. Beam: almost pure

    with mean energy 1.3 GeV Other LBL: MINOS, ICARUS, OPERA

    K2K observed muon neutrino disappearance

    Energy spectrum of the muon-neutrino events observed in the

    K2K experiment

    Best-fit with oscillations

    No oscillations

    important to interpret Atmospheric neutrino data

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    Atmospheric neutrinos Generated in the interaction of primary cosmic rays with the Earths


    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

    15 Km

    Cosmic Ray

    + +



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    The up-down symmetry/asymmetry1. The production of high energy atmospheric neutrinos is uniform

    around the globe

    2. A neutrino passing at point A with angle , reaches B at an angle



    The fluxes of neutrinos of a given flavor from opposite directions are the same at any location

    Up/down symmetry expected

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    Atmospheric neutrinos Mostly pions are produced, which decay into muons and


    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.

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    The inside of the Superkamiokande detector

    Underground detector with arrays of PMTs: IMB, (Super-)Kamiokande, SNO

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    Wave front

    Charged Particle v > c / n

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    How to tell a from a e

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    The up-down asymmetry Asymmetry observed: a model independent proof of neutrino


    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

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    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

    Zenith angle distribution of the through-going muon flux observed in Kamiokande

    Data from Kamiokande alone cannot separate between e and but results from CHOOZ excluded e

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    Solution of the atm. anomaly: flavor The results of CHOOZ and Paolo Verde disfavor e

    The results of Superkamiokande favor and disfavor s (s=sterile neutrino)

    Confirmed by K2K (extremely important since rather different concepts and systematic uncertainties)

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    Solar neutrinos Powerful source of electron

    neutrinos Neutrino produced in two

    groups of reactions: pp chain CNO cycle

    Energy ~ 1 MeV

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    The pp chain of stellar thermonuclear reactions

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    Standard Solar Model (SSM) Rate of radio-chemical detectors is measured in Solar Neutrino Units (SNU) =

    10-36 events atom-1s-1

    Predicted energy spectra of neutrino fluxes

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    Detection Energy ~ MeV = 10-44 cm2

    Interaction probability ~ 10-12

    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

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    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 (Eth=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 problemThe Homestake solar neutrino detector

    (1,500 m underground to filter out cosmic particles, 615 ton of C2Cl4)

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    Other radiochemical experiments

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    GALLEX/SAGE results

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    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

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    Solar neutrino anomaly

    Angular distribution of solar neutrino event candidates of SuperKamiokande (SK, 50

    kton water tank)

    elastic scattering peak

    background events

    Recoil electron have a sharp forward peak

    Flux measured ~ 1/2 of expected

    22400 230 solar neutrino events

    SuperKamiokande image of the Sun

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    Vacuum Oscillations of Solar s Pontecorvo & Gribov 1969 1968, the Homestake experiment detects less neutrinos

    than expected: the solar neutrino problem Survival probability of solar neutrinos in case of two-s

    mixing (L distance Sun-Earth, L0=1 a.u., e eccentricity of Earths 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

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    Modulation of solar neutrinos The only periodic variation in the rate of solar neutrinos agrees

    with what expected due to the eccentricity of the Earths orbit. No indication of other modulations due to neutrino oscillations

    Seasonal variation of the solar flux measured in Superkamiokande

    Solar neutrino flux as a function of time measured in Superkamiokande

    Prediction based on the eccentricity of the Earths orbit

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    The Sudbury Neutrino Observatory (SNO) SNO detect solar neutrinos through

    CC: NC: ES:

    They provide a handle on CC: energy spectrum of e NC: total neutrino flux ES: equivalent (independent) to SK,

    measure the angular distribution of the events

    Measure (e) and i(i)

    The flux of non-electron neutrinos (oscillated) is then: (none) = i(i) - (e)

    The SNO detector: one kiloton pure D2O in a spherical acrylic vessel

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    Neutrino reactions in SNO

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    Phys. Rev. C 75 045502 (2007)

    Model prediction (no oscillations)

    Flux of and as a function of

    SNO results: solar 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 8B:

    They largely disagree: proof that e do change during propagation

    Good agreement between the NC SNO flux and what expected by the SSM


    Total flux

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    Neutrino oscillations in vacuum The flavor states do not coincide with the mass

    eigenstates k

    The flavor states are combinations of the eigenstates k:

    The mass states k are eigenstates of the Hamiltonian: Admixture of mass eigenstates in a given neutrino state do not

    change (there is no 1 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

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    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 (VCC, left) and the NC potential (VNC, right). GF Fermi coupling

    constant and Ne (Nn) number density of electrons (neutrons)

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    Propagation in matter In the presence of matter the Hamiltonian changes

    Ho H = Ho + V (Ho 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

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    Matter effects in a medium with changing density

    If the density changes during propagation: The mixing angle changes

    The instantaneous eigenstates of the Hamitonian 1m and 2m are no longer eigenstates of propagation

    Transitions 1m 2m can take place

    If the density changes slowly (adiabatic condition) the transitions 1m 2m can be neglected

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    Global fit of solar neutrino data Large mixing angle solution of the solar neutrino

    problem: The mixing angle is large but not maximal

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    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


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