1. Neutrino Physics II Hitoshi Murayama Taiwan Spring School March 28, 2002

2. 中性微子物理（二） 村山 斉 台湾春期学校 二千二年三月二十八日

3. 3 Outline 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

4. Solar Neutrino Oscillation

5. 5 We don’t get enough 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?

6. 6 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˚ )

7. 7 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 

8. 8 Fit to the rates of solar neutrino events from all experiments (Fogli et al) How do we understand this plot?

9. 9 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:

10. 10

11. 11 Matter Effect CC interaction in the presence of non- relativistic electron Neutrino Hamiltonian Electron neutrino higher energy in the Sun

12. 12 Electron Number Density Nearly exponential for most of the Sun’s interior  oscillation probability can be solved analytically with Whittaker function

13. 13 Propagation of e Use “instantaneous” eigenstates + and – L

14. 14 Survival Probability Decoheres upon Averaging over Production region Hopping probability

15. 15 Survival Probability cont. Thermal effects   E~kT~1keV The last term averages out if Now we need P c

16. 16 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

17. 17 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

18. 18 SMA LMA LOW

19. 19 Survival Probability

20. 20 Matter Effect in the Earth

21. 21 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

22. 22 Day/Night Spectra at SuperK

23. 23 Absence of day/night effect cuts into LMA 7 Be

24. 24 Spectrum Distortion Survival probability may be energy- dependent Knowing 8 B spectrum measured in the laboratory, one can look for spectrum distortion in data

25. 25 No spectrum distortion yet at SuperK

26. 26 No spectrum distortion yet at SNO

27. 27 Absence of spectrum distortion removes SMA

28. 28 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)

29. 29 So far no seasonal effect in 8 B

30. 30 Vacuum Oscillation again

31. 31 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

32. 32 LOW extends down to VAC, especially in the dark side!

33. Future of Solar Neutrinos

34. 34 More from SNO NC/CC  confirmation of neutrino conversion  sterile neutrino? Day/night effect  LMA CC spectrum  SMA, VAC Seasonal effect  VAC

35. 35 What Next on Solar Neutrinos? We’d like to convincingly verify oscillation with man-made neutrinos Hard for low  m 2 Need low E, high  Use neutrinos from nuclear reactors To probe LMA, need L~100km, 1kt

36. 36 KAMioka Liquid scintillator ANti-Neutrino Detector 1kt KamLAND Detectors electron anti-neutrinos from nuclear power plants by inverse beta decay

37. 37 Location, Location, Location

38. 38 KamLAND sensitivity on LMA First terrestrial expt relevant to solar neutrino problem KamLAND will exclude or verify LMA definitively Data taking since Nov 2001

39. 39 KamLAND first neutrino event

40. 40 Measurements at KamLAND Can see the dip when  m 2 >2  10 –5 eV 2 (Pierce, HM) Can measure mass & mixing parameters Data/theory

41. 41 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

42. 42 CP Violation Possible only if: –  m 12 2, s 12 large enough (LMA) –  13 large enough

43. 43 VAC by seasonal variation 7 Be neutrino monochromatic seasonal effect probes VAC region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too!

44. 44 VAC by seasonal variation Fit to seasonal variation to measure parameters Can pep resolve degeneracy?

45. 45 LOW by day/night effect 7 Be neutrino monochromatic Day/night effect probes LOW region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too!

46. 46 LOW by zenith angle dependence More information in zenith angle depend. (de Gouvêa, Friedland, HM)

47. 47 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

48. 48 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

49. 49 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

50. 50 Conclusions Solar neutrino data can be fit well with neutrino oscillation hypothesis Definitive signals come from near-future experiments –LMA:KamLAND, day/night at SNO –LOW: day/night at Borexino/KamLAND –VAC: seasonal effect at Borexino/KamLAND –SMA: pp neutrino