1. Solar Neutrino Problem
where astrophysics and fundamental physics meet

2. Neutrinos  Neutron  neutrino Weakly interacting light particles
Produced by nuclear interaction when weak force is involved

4. CNO not important

5. Photons vs. Neutrinos   Photons mean free path 1cm at core
nuclear reactions cannot be observed directly with EM radiation
Diffuse to surface >105 year
 mean free path 1010R*
leaves the star freely  

6. Why Important? Direct evidence of nuclear reaction
“Real time” energy production in the Sun
Compare with photon flux, thermodynamic equilibrium > 105yr
Test the Standard Solar Model

7. CNO not important

8. Solar Neutrinos Interaction Energy (MeV) Flux at Earth (m-2s-1)
𝑝+𝑝⟶ 2 D + 𝑒 + +𝜈
≤0.42
6.0×1014
7 B e+ 𝑒 − ⟶ 7 L i+𝜈
0.86 (90%) 0.38 (10%)
4.9×1013
7 B ⟶ 7 B e+ 𝑒 + +𝜈
≤15
5.7×1010
billion of photons passing us every s

9. Solar Neutrinos

10. How to detect ?

11. Neutrino Detection 1 event per day needs 1030 atoms ktons of targets
Interaction cross-section 10-46cm2
 solar  flux 1010cm-2s-1
1 event per day needs 1030 atoms
ktons of targets
Common detectors:
Water, chlorine, gallium, scintillation

12. Neutrino Detection
scintillator
gallium
chlorine
water

13. Radiochemical Chlorine 𝜈+ 37 C l⟶ 𝑒 − + 37 A r Gallium
𝜈+ 71 G a⟶ 𝑒 − G e

14. Chlorine 𝜈+ 37 C l⟶ 𝑒 − + 37 A r (=35days) Energy threshold: 0.8MeV
e.g. Homestake (1960s)
600 tons C2Cl4 (dry clean liquid)

15. Homestake Experiment
Raymond Davis, Jr. & John N. Bahcall in late 1960s
Homestake Gold Mine in South Dakota, USA 1,500m deep (why underground?)
𝜈+ 37 CL ⟶ 𝑒 − +37Ar energy threshold 0.8MeV
Half-life of 37Ar = 35 days
400,000L = 600 tons C2Cl4 ∼2× Cl atoms (Perchloroethylene C2Cl4 -- dry clean liquid)
Only tens of 37Ar atoms are found by a Geiger counter
⅓  ½ of prediction!

18. Gallium 𝜈+ 71 G a⟶ 𝑒 − + 71 G e 𝜏=11.4d 71 G a+𝛾
0.23MeV, can detect p-p 
e.g. GALLEX ( ) 30 tons of Ga SAGE ( ) 60 tons of metallic Ga (> annual world production!).

19. GALLEX and SAGE Neutrino-electron scattering: 𝜈+ 71 Ga ⟶ 𝑒 − +71Ge
Ge  Ga+ , half-life 11.4day
Much lower detection threshold energy: 0.23MeV, can detect major reaction in the p-p chain
: GALLEX experiment in Russia by T. Kirsten, 30 tons of Ga in aqueous solution.
SAGE experiment in Italy by V. Garvin, 60 tons of metallic Ga (more than annual world production!).
 flux only 60% of prediction

20. Water Cerenkov Electron scattering 𝜈+ 𝑒 − ⟶𝜈+ 𝑒 −
Superluminal e- ⟶ Cerenkov radiation
5MeV threshold, only sensitive to 8B
e.g. Super-Kamiokande, Sudbury Neutrino Observatory (SNO)
SNO: Heavy water

21. Kamiokande Experiments
Kamioka Mozumi Mine in Japan, >1000m deep
Neutrino-electron scattering: 𝜈+ 𝑒 − ⟶ 𝑣 ′ + 𝑒 − ′
Kamiokande II: M. Koshiba & Y. Totsuka in 1980s
Super-Kamiokande: Y. Totsuka & Y. Suzuki in 2000s
Huge water tank: 40m diameter x 40m height = 50,000m3 pure water
11,000 light detectors to detect Cherenkov (radiation from particles faster than speed of light)
 >7MeV, fewer than 20 events per day!

24. Solar Neutrino Problem
Solar model wrong? But all other observations match theory, e.g., sound speed from helioseismology agrees with prediction.
Measurement error? But similar results from different experiments.
Standard model wrong? New physics is needed.

25. Sudbury Neutrino Observatory
SNO: Creighton Mine in Ontario, Canada, 2,000m underground
Led by A. McDonald in the 2000s
1,000 tons of salt heavy water
10,000 PMT to detect Cherenkov radiation
Sensitive to all flavors of neutrinos: e, , 

26. Electron scattering channel:
𝜈 𝑒 + 𝑒 − ⟶ 𝜈 𝑒 ′ + 𝑒 − ′
Charged Current channel:
𝜈 𝑒 +𝑑⟶𝑝+𝑝+ 𝑒 −
Neutral Current channel:
𝜈+𝑑⟶𝑛+𝑝+𝜈

28. Sudbury Neutrino Observatory
SNO: Creighton Mine in Ontario, Canada, 2,000m underground
Led by A. McDonald in the 2000s
1,000 tons of salt heavy water
10,000 PMT to detect Cherenkov radiation
Sensitive to all flavors of neutrinos: e, , 
Total  flux consistent with theory!

30. What was wrong before?
Neutrino oscillation, only e were detected in previous experiments except SNO.
100% e produced in the Sun, but some converted to other spices (, ) on the way to the Earth.
Only 35%  arrived on Earth are e. (This is energy dependent)

31. Neutrino Oscillation
Why? Because flavour eigenstates  mass (i.e. energy) eigenstates

32. Nature, 512, 383 (2014)

33. Solar Neutrinos
86%

34. Liquid Scintillator Elastic scattering 𝜈+ 𝑒 − ⟶𝜈+ 𝑒 −
More photons than Cherenkov
can detect single event
Real-time, good energy resolution
threshold limited by background
No directional information
e.g., KamLAND, Borexino

35. Neutrino Detection
scintillator
gallium
chlorine
water

36. Borexino Borex: Boron Solar Neutrino Experiment
2000t TMB i.e. B(OCH3)3
BOREX  Borexino (cf. neutron neutrino)
2000t300t
Main goal: detect neutrinos from 7Be

37. Borexino Gran Sasso in Italy, 2007-
280 tons liquid scintillator, 2200 PMTs
1,2,4-Trimethyl-benzene C6H3(CH3)3
from crude oil to reduce 14C
Real-time detection
Single event down to 150keV, good energy spectrum by photon counting

41. 18m

42. Background

43. Results
144±13/day/100t

44. Results

45. Results 144±13(stat)±10(sys) cts/day/100t Accounted for oscillation:
(6.6±0.7) x1010cm-2s-1
Predicted flux
5.98x(1±0.006) x1010cm-2s-1 (high metallicity)
6.03x(1±0.006) x1010cm-2s-1 (low metallicity)

46. Survival Probability
𝑃 𝜈 𝑒 → 𝜈 𝑒 =0.64±0.12

47. Summary Solar p-p neutrinos first time directly detected:
(6.6±0.7) x1010cm-2s-1
P 𝜈 𝑒 → 𝜈 𝑒 = 0.61±0.12
Agree with Standard Solar Model
Thermodynamic equilibrium > 100,000yr
Precise test of solar model and oscillation need 1% level measurements

48. Neutrino Oscillation

49. Neutrino Oscillation
Flavour eigenstates  mass (i.e. energy) eigenstates
Simple example: two-flavour oscillation
𝜈 𝑒 𝜈 𝜇 = cos 𝜃 sin 𝜃 − sin 𝜃 cos 𝜃 𝜈 1 𝜈 2 , 𝜈 1 , 𝜈 2 are mass (energy) eigenstates,  is called the mixing angle

50. Time Evolution of 𝜈 𝑒
𝜈 𝑒 𝑡 = cos 𝜃 𝑒 −𝑖 𝑝 2 + 𝑚 1 2 | 𝜈 1 ⟩ +sin 𝜃 𝑒 −𝑖 𝑝 2 + 𝑚 2 2 | ν 2 ⟩ ≈ 𝑒 −𝑖𝑧 𝑐𝑜𝑠 𝜃 | 𝜈 1 ⟩+ sin 𝜃 𝑒 𝑖𝛥 𝑚 2 𝑥/𝑝 | 𝜈 2 ⟩ , where 𝑐=1, 𝑧= 𝑝+ 𝑚 1 2 2𝑝 𝑡 and 𝛥 𝑚 2 = 𝑚 1 2 − 𝑚 2 2 .

51. Neutrino Mixing in Vacuum
𝑃 𝜈 𝑒 → 𝜈 𝜇 = 𝜈 𝜇 𝜈 𝑒 𝑡 2 = 𝑒 −𝑖𝑧 −sin𝜃 cos 𝜃 + sin 𝜃 cos 𝜃 𝑒 𝑖𝛥 𝑚 2 𝑥/𝑝 2 = sin 2 2𝜃 sin 2 Δ 𝑚 2 𝐿 4 𝐸 𝜈 = sin 2 2𝜃 sin Δ 𝑚 2 𝐿 km 𝐸 𝜈 GeV  is called the mixing angle, if neutrinos are massless, then m2=0 and there will be no oscillation.

53. Solar Neutrinos Put in E and L = 1AU? Not that simple!
Enhanced oscillation due to the matter effect (MSW effect)
Three-flavor neutrino mixing

54. Oscillation in Matter
Mikheyev–Smirnov–Wolfenstein (MSW) effect: enhanced oscillation in matter
𝑒 − in matter change  energy levels, enhanced oscillation and mixing angle becomes tan 2 𝜃 𝑚 = 𝑡𝑎𝑛 2𝜃 1− 2𝑝 2 𝐺 𝐹 𝑛 𝑒 /Δ 𝑚 2 cos 2𝜃
>5MeV 𝜈 𝑒 ⟶ 𝜈 𝜇 inside the Sun
No effect on p-p , but affects 8B 

55. Solar Neutrinos Put in E and L = 1AU? Not that simple!
Enhanced oscillation due to the matter effect (MSW effect)
Taking these into account, the survival probability of e arrive on Earth is 57%, consistent with the experiments
Best-measured  =34

56. Three-Flavour  Oscillation
Since there are 3 flavours of , the actual scenario is more complicated.
where 𝑠 𝑖𝑗 ≡ sin 𝜃 𝑖𝑗 and 𝑐 𝑖𝑗 ≡ cos 𝜃 𝑖𝑗 .
 are usually neglected in solar neutrino oscillation, i.e. 13 is assumed to be 0, since Δ 𝑚 ≈ Δ 𝑚 ≈30× Δ 𝑚 12
However, in March 2012, Daya Bay Experiment found 𝜃 13 =0.092±0.017, i.e. non-zero at 5.2 level.
May need to consider ?
𝜈 𝑒 𝜈 𝜇 𝜈 𝜏 = 𝑐 23 𝑠 − 𝑠 23 𝑐 𝑐 𝑠 13 𝑒 −𝑖𝛿 − 𝑠 13 𝑒 −𝑖𝛿 0 𝑐 𝑐 12 𝑠 − 𝑠 12 𝑐 𝑒 𝑖 𝛼 1 / 𝑒 𝑖 𝛼 2 / 𝜈 1 𝜈 2 𝜈 3 ,

57. PRL (2012) 107,

58. Unsolved Problems
Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay
Mass hierarchy?

59. Unsolved Problems
Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay
Mass hierarchy?

60. Unsolved Problems
Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay
Mass hierarchy?
Dirac or Majorana statistics? i.e. 𝜈= 𝜈 ? Neutrinoless double beta decay

61. Unsolved Problems
Absolute neutrino mass scales? Nuclear beta decay, neutrinoless double beta decay
Mass hierarchy?
Dirac or Majorana statistics? i.e. 𝜈= 𝜈 ? Neutrinoless double beta decay
4th flavor?

62. Neutrino Astronomy

63. Neutrino Astronomy Sources: Neutrino Observatories:
Sun, supernova, AGN, GRB, neutron star merger, etc
Neutrino Observatories:
IceCube, Super-Kamiokande

66. Science, 342, (2013)
28 events >30TeV from beyond solar system

68. KM3NeT