Neutrino Physics

1. Neutrino Physics Neutrino mass and mixing No neutrinoless double beta decay • Nishikawa • ＠XXXIV International Meeting • on Fundamental Physics • April 3-7,2006

2. 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

3. 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 et.al. Helicity of neutrino measured by M.Goldhaber et.al. • 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

4. Conclusion of this series of talks Experimental evidences for the following summary

5. 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 8 atm. 3x10-3eV2

6. Issues about neutrinos for coming years? Neutrino-lessbb • 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 ? NeutrinoOscillation

7. Contents-1 • Experimental achievements • What are neutrinos? • Their interactions? • Imaging type water Cherenkov detector (Super-Kamiokande)

8. Helicity of neutrino (V-A) • Parity LH RH direction of motion direction of motion P 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

9. Only left handed component exists

10. 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

11. nCR 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 ?

12. 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)

13. Number of neutrino species

14. 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 ?

15. DONUT FNAL E872 Beam dump beam Status: 406 neutrino interaction analyzed. 7 ntCCevent detected On-going　： Component analysis of the prompt neutrino beam νe：νμ：ντ Interaction Point t Decay Point of t neutrino 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

16. 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)

17. Neutrinos How they interact

18. W Charged current interaction Transformation between pair of particles, differ by unit charge neL nmL ntL uL cL tL t3=1/2 (nR nR nR) uR cR tR eR mR tR dR sR bR eL mL tL dL sL bL t3=-1/2 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 =

19. l nl W e ne nl + n→ l(-) + p nl + p → l(+) +n GF : Fermi coupling constant isotropic in cms ~10-41・Encm2 Enth~10GeVform nl+e → ne+l g ｌ：Forward peak qn-e small g ~10-38・En cm2 Complication by free, almost free nucleons form factors, Nuclear effect(Pauli blocking) H2O D2O CH

20. Quasi-elastic scattering cross-sections m- nm W p Cross-section (nm) 10-38cm2 magenta Old MC red new MC • Two form factors • MV fixed by e.m. (CVC) • Axial V form factor n s/En (10-38cm2/GeV) 1 10 100 GeV

21. Data on charged current processes • Not well known • Especially 2~3 GeV • must be determined internally

22. neL nmL ntL eL mL tL uL cL tL dL sL bL (nR nR nR) eR mR tR uR cR tR dR sR bR gL,R nl Neutral current interaction nl Z e(N) e(N) gL,R g=T3 - sin2qW·Q

23. Neutrino mass and oscillation

24. Neutrino oscillation n1 n2 nt nm • 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

25. The Hamiltonian • The Hamiltonian of a freely-propagating massive neutrino • But in quantum mechanics, mass is a matrix in general. 22 case:

26. 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

27. ne nm nt Three Flavor Mixing in Lepton Sector mass eigenstates Weak eigenstates m1 m2 m3 cij = cosqij, sij=sinqij q12, q23, q13 + d (+2 Majorana phase) Dm122, Dm232, Dm132

28. 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 n=1-EV/k2 ne electron density

29. 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

30. effective mass in matter Schrodinger eq. Hamiltonian Effective mass difference of ne and nm,tin matter by Ve

31. 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

32. MSW in the Solar neutrinos In(Dm2) m2 m1 In(sin2q) Also Day Night!

33. ‘MSW’ for sterile Large Dm2 →(E >10 GeV in earth) Dm2~A

34. matter effect in the earth for sterile neutrinos PC, Evis>5GeV <Eν>～25GeV up/down ratio ns ns Z νμーνs νμーνs n νμーντ νμーντ n up through going μ <Eν>～100GeV vertical/horizontal ratio

35. 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

36. 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

37. Super Kamikande

38. Inside Super-K Kamiokande

39. ４１．４ｍ ４０ｍ Super-Kamiokande (1996) • 1996- • 50000ton water • 11146 50cmf PMT (40% photo coverage) • 1000m underground • Min det. energy ~ 5 MeV • Inner and outer

40. qc 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

42. Cherenkov light Charged particle

43. Electron-like and muon-like events e-like m-like m e

44. 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 m e m e Atm. data Excellent for low multiplicity Low energy

45. Particle ID in multi ring events (p0 selection) π0←