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Neutrino Physics. Neutrino mass and mixing No neutrinoless double beta decay. Nishikawa @ XXXIV International Meeting on Fundamental Physics April 3-7,2006. Neutrinos are Everywhere. Big Bang: They are still left over: ~300 neutrinos per cm 3 Natural sources

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Neutrino Physics

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Neutrino physics

Neutrino Physics

Neutrino mass and mixing

No neutrinoless double beta decay

  • Nishikawa

  • @XXXIV International Meeting

  • on Fundamental Physics

  • April 3-7,2006

Neutrinos are everywhere

Neutrinos are Everywhere

  • Big Bang:

    • They are still left over: ~300 neutrinos per cm3

  • Natural sources

    • Sun : 1012 of neutrinos /sec /cm2

    • Atmosphere : 103 high energy neutrinos /sec/m2

    • Reactor : 1020 neutrinos/GWth

  • Weak:

    • Need to stack up lead shield up to three light-years to stop them

  • Light

    • Twelve orders of magnitudes below Mt or weak scale10

Neutrino physics

Brief history

  • 1930 Pauli’s neutrino hypothesis

  • 1934 Fermi theory of weak interaction

  • 1956 Neutrino observation by Reines and Cowan

  • Neutrinos are left handed

    q-t puzzle and parity

    • 1957 Parity violation by Wu

      Helicity of neutrino measured by M.Goldhaber

    • 1958 V-A (Sudarshan & Marshak, Feynman & Gell-Mann) Current-current formulation

  • Intermediate Vector Boson (W) hypothesis

    • 1960 Two neutrino hypothesis (Lee, Yang)

    • 1968 Solar neutrino problem (Ray Davis)

  • Electro-weak unification

    • 1967 Weinberg, Salam, Glashow

    • ‘t Hooft’s proof

    • 1973 Discovery of Weak Neutral Current (Gargamelle)

    • 1983 Observation of Z,W

  • Conclusion of this series of talks

    Conclusion of this series of talks

    Experimental evidences for the following summary

    Neutrino physics

    • Two mass eigen-states haveDm2~8x10-5 eV2

    • Define n1, n2 such that

    • mn2 > mn1

    • Solarn MSW in neutrino (not anti-neutrino)

    • n1 is the largest component inne

    • Third mass eigen-sate (n3) isseparated byDm2~ ±3x10-3 eV2

    • Smallne component inn3 (n3 consists ofnm, nt, almost 50;50)which is larger in nt ? (q23<p/4 ?)

    • neutrino mass and charged lepton mass ordering

    • same or inverted




    Issues about neutrinos for coming years

    Issues about neutrinos for coming years?


    • What is Neutrino?Tiny mass (~x 10-10 ) of q,l±

      • Majorana : Majorana and Dirac masses co-exist

        • See Saw mn~ m2/M (M~coupling unification scale)

        • neutrino = antineutrino DL= 2 units

      • Dirac : ~ quarks, charged leptons

        • very very weakly coupled RH

    • Different patterns of mixings in quarks and in leptons

      • Masses and interactions (transitions among elementary particles)

      • Particle and anti-particle distinction, especially in pure leptonic process

    • Baryon- Anti-Baryon asymmetry in Universe ?


    Contents 1


    • Experimental achievements

    • What are neutrinos?

    • Their interactions?

    • Imaging type water Cherenkov detector (Super-Kamiokande)

    Helicity of neutrino v a

    Helicity of neutrino (V-A)

    • Parity



    direction of motion

    direction of motion


    Maximum parity violation means a possibility

    where only one of those state exist in nature

    direction of spin = direction of advancement of right handed screw

    Neutrino physics

    Only left handed component exists

    Neutrinos must be massless

    Neutrinos must be Massless

    • All neutrinos left-handed  massless

    • If they have mass, can’t go at speed of light.

    • Now neutrino right-handed??

       contradiction  can’t be massive

    Anti neutrinos are right handed


    Anti-Neutrinos are Right-handed

    • CPT theorem in quantum field theory

      • C: interchange particles & anti-particles

      • P: parity (r → -r)

      • T: time-reversal (t → -t)

    • State obtained by CPT from nL must exist: nCR

    • Lorenz transformed state

      nR (Lorenz)

    nCR = nR ?

    Standard model

    Standard Model

    Finite mass of neutrinos imply the Standard Model is incomplete!

    • Not just incomplete but probably a lot more profound

      • New kind of field (Majorana : nCR=nR)

      • Very small RH interaction (Cannot produced by interaction)

    Number of neutrino species

    Number of neutrino species

    Intermediate vector boson and m decay

    Intermediate Vector Boson and m-decay

    • Feinberg’s argument (1958)

    • V-A current-current formulation suggest W± analog to g

    • Pontecorvo (1959) Schwartz (1960) idea of high energy neutrino beam

    nm = ne ?

    Neutrino physics


    FNAL E872 Beam dump beam


    406 neutrino interaction analyzed.

    7 ntCCevent detected

    On-going :

    Component analysis of the prompt neutrino beam


    Interaction Point


    Decay Point of t


    Vertex detection :

    Neutrino interaction and decay of short lived particles

    Reject Low momentum tracks

    (114 tracks remained)

    Reject passing

    through tracks

    (420 tracks remained)

    All tracks in the Scanning region (4179 tracks)

    Detection of ντCCin DONUT

    The number of neutrinos collider experiments

    N = 2.984 0.008

    The Number of Neutrinoscollider experiments

    • most precise measurements come from Z e + e

    • invisible partial width, inv, determined by subtracting measured visible partial widths (Z decays to quarks and charged leptons) from the Z width

    • invisible width assumed to be due to N

    • Standard Model value (  l)SM = 1.991  0.001 (using ratio reduces model dependence)

    Neutrinos how they interact

    Neutrinos How they interact

    Charged current interaction


    Charged current interaction

    Transformation between pair of particles, differ by unit charge

    neL nmL ntL uL cL tL


    (nR nR nR)

    uR cR tR

    eR mR tR

    dR sR bR

    eL mL tL dL sL bL


    mixing exist (CKM)

    • Coupling constant(GF) is universal for all particles

    • Left-handed particles form weak isospin-doublets

    • All right-handed particles have no charged current interaction

    • (even if they exist in nature) iso-singlets

    • Interaction is mediated by W intermediate vector boson

    GF =

    Neutrino physics






    nl + n→ l(-) + p

    nl + p → l(+) +n

    GF : Fermi coupling constant

    isotropic in cms



    nl+e → ne+l


    l:Forward peak

    qn-e small


    ~10-38・En cm2

    Complication by free, almost free nucleons

    form factors, Nuclear effect(Pauli blocking) H2O D2O CH

    Quasi elastic scattering cross sections

    Quasi-elastic scattering cross-sections





    Cross-section (nm)


    magenta Old MC

    red new MC

    • Two form factors

      • MV fixed by e.m. (CVC)

      • Axial V form factor


    s/En (10-38cm2/GeV)

    1 10 100 GeV

    Data on charged current processes

    Data on charged current processes

    • Not well known

    • Especially 2~3 GeV

    • must be determined internally

    Neutral current interaction

    neL nmL ntL eL mL tL

    uL cL tL dL sL bL

    (nR nR nR)

    eR mR tR

    uR cR tR

    dR sR bR



    Neutral current interaction






    g=T3 - sin2qW·Q

    Neutrino mass and oscillation

    Neutrino mass and oscillation

    Neutrino oscillation

    Neutrino oscillation





    • Inteferometry (i.e., Michaelson-Morley)

      • Coherent source

      • Interference (i.e., large mixing angles)

      • Need long baseline for small Dm2

    • Neutrino mass must be non-zero, if oscillation occurs

    The hamiltonian

    The Hamiltonian

    • The Hamiltonian of a freely-propagating massive neutrino

    • But in quantum mechanics, mass is a matrix in general. 22 case:

    Two neutrino oscillation

    Two-Neutrino Oscillation

    • When produced (e.g., p+m+nm), neutrino is of a particular type

    • At time t

    • No longer 100% nm, partly nt!

    • “Survival probability” for nm after t

    Three flavor mixing in lepton sector




    Three Flavor Mixing in Lepton Sector

    mass eigenstates

    Weak eigenstates




    cij = cosqij, sij=sinqij

    q12, q23, q13

    + d (+2 Majorana phase)

    Dm122, Dm232, Dm132

    Matter effect msw effect

    Matter effect MSW effect

    • Neutrinos propagate in matter receive a refractive effect due to their interaction (extra energy V, the energy E, momentum k’) with matter

    The refractive index n is defined by

    E2=k2+m2the dispersion relation in vacuum and k’=nk


    ne electron density

    Msw effect ii

    MSW effect (II)

    - for anti-neutrino

    Dn=1-n ~7.6 x 10-19 (r/100g cm-3)(E/10MeV)-1 for ne small for nm,t

    velocity changes == effective mass changes in matter

    (r=100g/cc at the center of Sun)

    Active neutrinos by interaction with p,n

    Can distinguish ‘active’ and ‘sterile’ neutrinos

    Effective mass in matter

    effective mass in matter

    Schrodinger eq.


    Effective mass difference of ne and nm,tin matter by Ve

    Mass difference and mixing angle in matter

    Mass difference and mixing angle in matter

    A change sign for anti-neutrinos

    Ne= 6x1025 /cc = 6 x 10-14 /fm3 for r=100g/cc

    GF~10-5 GeV-2 (0.2GeV·fm)3 =8 x 10-8 GeV fm3

    A =10-2 En (GeV) eV2

    Neutrino physics

    MSW in the Solar neutrinos





    Also Day Night!

    Msw for sterile

    ‘MSW’ for sterile

    Large Dm2 →(E >10 GeV in earth) Dm2~A

    Matter effect in the earth for sterile neutrinos

    matter effect in the earth for sterile neutrinos

    PC, Evis>5GeV


    up/down ratio










    up through going μ


    vertical/horizontal ratio

    Detectors for neutrino oscillation experiments

    Detectors for Neutrino Oscillation Experiments

    • Massive

    • Neutrino oscillation is the oscillation between different flavors

      • e, μ, τidentification by charged current interactions

      • target and sensor must be combined

    • Only Flux(En) x s(En) will be measured

      • En, L must be known event-by event to get Dm2

      • Two distances if possible

    Particle identification

    Particle identification

    • m-ID

      • minimum ionizing particle with long range R500g/cm2/GeV

    • e-ID

      • showering particle, large g (TRD), E/p1(with magnet)

    • t-ID

      • short decay length

      • isolated hadronic activity (charm)

      • t→enn t→mnn, t→nt +hadrons

    Super kamikande

    Super Kamikande

    Inside super k

    Inside Super-K


    Super kamiokande 1996



    Super-Kamiokande (1996)

    • 1996-

    • 50000ton water

    • 11146 50cmf PMT (40% photo coverage)

    • 1000m underground

    • Min det. energy ~ 5 MeV

    • Inner and outer

    Principle of the technique


    dN 2pasin2qc

    dxdl l2


    Principle of the technique

    • Cherenkov radiation: electromagnetic radiation in a medium with refractive index n if nb>1 (b=v/c)

      • cosqc = 1/nb,

      • where N is the number of emitted Cherenkov photons with wavelength l, dx is the particle’s path length, and a =1/137

      • Cherenkov photons are detected with a large number of photomultiplier tubes (PMT)

    • For Super-K, qC = 42deg (b = 1), good at simple geom.

    • N(photo e.) ~ 6 / Mev e- : about 1/1000 of scintillator

    • Attenuation length can be attained upto ~100m

    • P(threshold)~1.2 GeV/c for protons

    Neutrino physics

    Cherenkov light

    Charged particle

    Electron like and muon like events

    Electron-like and muon-like events





    Particle id e m in single ring events

    Particle ID (e & m)(in single ring events)

    • An experiment with test beams confirmed the particle ID

      capability (PL B374(1996)238)

    K2K 98% nm beam

    near detector





    Atm. data

    Excellent for low multiplicity

    Low energy

    Particle id in multi ring events p 0 selection

    Particle ID in multi ring events (p0 selection)


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