1. Neutrino Physics II Hitoshi Murayama University of Pisa February 25, 2003

2. 2 Outline Solar Neutrinos Solar Neutrino Oscillations –Vacuum Oscillation –Matter Effect in the Sun –Matter Effect in the Earth –Seasonal Effect Future of Solar Neutrinos –Reactor neutrino –Day/Night Effect –Seasonal Variation

3. Solar Neutrinos

4. 4 How the Sun burns The Sun emits light because nuclear fusion produces a lot of energy

5. 5

6. 6 SuperK sees the Sun

7. 7 Solar Neutrino Spectrum

8. 8 We don’t get enough

9. 9 Why? 1.Astrophysics is wrong –pp neutrino flux tied to solar luminosity –Change 7 Be, 8 B arbitrarily  can’t fit the data 2.Some of the data are wrong –Even if only one experiment correct, the puzzle remains –Need both 1. & 2. to explain the situation 3.Something is wrong with neutrinos

10. 10 Astrophysics wrong? Fit data with arbitrary 7 Be, 8 B Best fit needs negative 7 Be Remember 8 B is a product of 7 Be!

11. 11 Astrophysics wrong? Helioseismology data agree well with the SSM

12. 12 Josh Klein, Lepton Photon 2001

13. 13 SNO comes to the rescue Charged Current: e Neutral Current: e +  +  5.3  difference   are coming from the Sun!

14. 14 Wrong Neutrinos Only e produced in the Sun Wrong Neutrinos   are coming from the Sun! Somehow some of e were converted to  on their way from the Sun’s core to the detector  neutrino oscillation!

15. 15 SNO CC run SNO first ran in the “CC mode” Studied CC, ES, and NC with neutron capture on deuterium No sign of spectrum distortion Saw discrepancy between ES and CC at 3.3  ES has ~1/7 of   

16. 16 SNO NC run Added salt (NaCl) Greater efficiency and gamma energies from neutron capture on 37 Cl than on d Cannot separate NC, CC, ES on event-by-event basis Subtract CC from CC run Other handles

17. Solar Neutrino Oscillation

18. 18 Neutrino Rates We need survival probabilities of 8 B: ~1/3 7 Be: ~1/3 pp: ~2/3 Can we get three numbers correctly with two parameters?

19. 19 Dark Side of Neutrino Oscillation Traditional parameterization of neutrino oscillation in terms of (  m 2, sin 2 2  ) covers only a half of the parameter space (de Gouvêa, Friedland, HM) Convention: 2 heavier than 1 –Vary  from 0˚ to 90˚ –sin 2 2  covers 0˚ to 45˚ –Light side (0 to 45˚) and Dark Side (45˚ to 90˚ )

20. 20 Dark Side of Neutrino Oscillation To cover the whole parameter space, can’t use (  m 2, sin 2 2  ) but (  m 2, tan 2  ) instead. (Fogli, Lisi, Montanino; de Gouvêa, Friedland, HM) In vacuum, oscillation probability depends only on sin 2 2 , i.e., invariant under  90  Seen as a reflection symmetry on the log scale tan 2  cot 2  Or use sin 2  on the linear scale sin 2  cos 2 

21. 21 Fit to the rates of solar neutrino events from all experiments (Fogli et al) How do we understand this plot?

22. 22 Vacuum Oscillation Ga~1/2, Cl~1/3, water~1/3 One possible explanation is that neutrinos oscillate in the vaccum just like in atmospheric neutrinos But oscillation is more prominent for lower energies while Ga retains the half The oscillation length needs to be “just right” so that 8 B, 7 Be are depleted more than average 7 Be:

23. 23

24. 24 Matter Effect CC interaction in the presence of non- relativistic electron Neutrino Hamiltonian Electron neutrino higher energy in the Sun

25. 25 Electron Number Density Nearly exponential for most of the Sun’s interior  oscillation probability can be solved analytically with Whittaker function

26. 26 Propagation of e Use “instantaneous” eigenstates + and – L

27. 27 Survival Probability Decoheres upon Averaging over Production region Hopping probability

28. 28 Survival Probability cont. Thermal effects   E~kT~1keV The last term averages out if Now we need P c

29. 29 Level Crossing For small angles and  <45 , e is higher at the core while lower outside, and hence two levels cross  >>1P c  0adiabatic limit  1P c  cos 2  non-adiabatic limit

30. 30 Survival Probability “MSW triangle” 100% lost at the center of the triangle, possible even for small angles Dark side always bigger than 50% Scales with energy because of  m 2 /p dependence No level crossing Non-adiabatic

31. 31 SMA LMA LOW

32. 32 March 2002 Preferred Regions

33. 33 Matter Effect in the Earth

34. 34 Matter Effect in the Earth When neutrino mass eigenstates go through the Earth, some of lost e state may be regenerated Sun may be brighter in the night Day-night asymmetry: 7 Be

35. 35 Day/Night Spectra at SuperK

36. 36 Absence of day/night effect cuts into LMA 7 Be

37. 37 No D/N effect yet at SNO

38. 38 Spectrum Distortion Survival probability may be energy- dependent Knowing 8 B spectrum measured in the laboratory, one can look for spectrum distortion in data

39. 39 No spectrum distortion yet at SuperK

40. 40 No spectrum distortion yet at SNO

41. 41 Absence of spectrum distortion removes SMA

42. 42 Seasonal Effect Earth’s orbit is slightly eccentric The Earth-Sun distance changes 3.5% from max to min 1/r 2 law says 7% change in neutrino flux from max (summer) to min (winter)

43. 43 So far no seasonal effect in 8 B

44. 44 Vacuum Oscillation again

45. 45 Quasi-Vacuum oscillation Vacuum region actually reached slowly as  m 2 decreased Transition region between “MSW” and “vacuum” region: quasi-vacuum Both matter effect and oscillatory term need to be kept

46. 46 LOW extends down to VAC, especially in the dark side!

47. 47 March 2002 April 2002 with SNO Progress in 2002 on the Solar Neutrino Problem

48. 48 Terrestrial “Solar Neutrino” Can we convincingly verify oscillation with man-made neutrinos? Hard for low  m 2 Need low E, high  To probe LMA, need L~100km, 1kt Use neutrinos from nuclear reactors à la CHOOZ

49. 49 KAMioka Liquid scintillator ANti-Neutrino Detector KamLAND Detectors electron anti-neutrinos from nuclear power plants by inverse beta decay 1kt KamLAND

50. 50 Location, Location, Location

51. 51 KamLAND sensitivity on LMA First terrestrial expt relevant to solar neutrino problem KamLAND will exclude or verify LMA definitively Data taking since Feb 2002

52. 52 KamLAND first neutrino event

53. 53 Reactor Neutrino Data Very clean No distortion yet

54. 54 KamLAND result Expected #events:86.8±5.6 Background #events: 0.95±0.99 Observed #events:54 No oscillation hypothesis Excluded at 99.95%

55. 55 Oscillation Parameters

56. 56 March 2002 April 2002 with SNO Dec 2002 with KamLAND Progress in 2002 on the Solar Neutrino Problem

57. Future of Solar Neutrinos

58. 58 More from SNO NC/CC  confirmation of neutrino conversion  sterile neutrino? Day/night effect  LMA CC spectrum  SMA, VAC Seasonal effect  VAC

59. 59 Measurements at KamLAND Can see the dip when  m 2 >2  10 –5 eV 2 (Pierce, HM) Can measure mass & mixing parameters Data/theory

60. 60 If LMA confirmed... Dream case for neutrino oscillation physics!  m 2 solar within reach of long-baseline expts Even CP violation may be probable –neutrino superbeam –muon-storage ring neutrino factory If LMA excluded by KamLAND, study of lower energy solar neutrinos crucial

61. 61 CP Violation Possible only if: –  m 12 2, s 12 large enough (LMA) –  13 large enough

62. 62 VAC by seasonal variation 7 Be neutrino monochromatic seasonal effect probes VAC region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too!

63. 63 VAC by seasonal variation Fit to seasonal variation to measure parameters Can pep resolve degeneracy?

64. 64 LOW by day/night effect 7 Be neutrino monochromatic Day/night effect probes LOW region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too!

65. 65 LOW by zenith angle dependence More information in zenith angle depend. (de Gouvêa, Friedland, HM)

66. 66 Flavor Content Small difference in recoil spectrum NC: e –   e –  NC+CC: e – e  e – e Can in principle be used to discriminate flavor of solar neutrinos model- independently (de Gouvêa, HM) 7 Be SMA KamLAND 600t*3yrs

67. 67 SMA by pp neutrinos SMA: Sharp falloff in probability in the pp neutrino region the survival Because of the condition for the level crossing Measure the falloff   m 2 measurement

68. 68 Can pp neutrinos be studied? CC+NC (electron recoil) –gaseous He TPC –HERON: superfluid He (phonon & roton) –liquid Xe –GENIUS: Ge CC ( e capture) –LENS: Yb or In –MOON: Mo LENS-Yb