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Neutrino Physics II

Neutrino Physics II. Hitoshi Murayama Taiwan Spring School March 28, 2002. 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. Outline. Solar Neutrino Oscillations Vacuum Oscillation Matter Effect in the Sun Matter Effect in the Earth Seasonal Effect Future of Solar Neutrinos Reactor neutrino

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Neutrino Physics II

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  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. 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. We don’t get enough We need survival probabilities of 8B: ~1/3 7Be: <1/3 pp: ~2/3 Can we get three numbers correctly with two parameters?

  6. Dark Side of Neutrino Oscillation • Traditional parameterization of neutrino oscillation in terms of (Dm2, sin22q) covers only a half of the parameter space (de Gouvêa, Friedland, HM) • Convention: n2 heavier than n1 • Vary q from 0˚ to 90˚ • sin22q covers 0˚ to 45˚ • Light side (0 to 45˚) and Dark Side (45˚ to 90˚ )

  7. Dark Side of Neutrino Oscillation • To cover the whole parameter space, can’t use (Dm2, sin22q) but (Dm2, tan2q) instead. (Fogli, Lisi, Montanino;de Gouvêa, Friedland, HM) • In vacuum, oscillation probability depends only on sin22q, i.e., invariant under q 90-q • Seen as a reflection symmetry on the log scale tan2q  cot2q • Or use sin2qon the linear scale sin2q  cos2q

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

  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 8B, 7Be are depleted more than average 7Be:

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

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

  12. Use “instantaneous” eigenstates n+ and n– Propagation of ne L

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

  14. Survival Probability cont. • Thermal effects  DE~kT~1keV • The last term averages out if • Now we need Pc

  15. Level Crossing • For small angles and q<45, ne is higher at the core while lower outside, and hence two levels cross g>>1 Pc0 adiabatic limit g<<1 Pccos2q non-adiabatic limit

  16. “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 Dm2/p dependence Survival Probability No level crossing Non-adiabatic

  17. LMA SMA LOW

  18. Survival Probability

  19. Matter Effect in the Earth

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

  21. Day/Night Spectra at SuperK

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

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

  24. No spectrum distortion yet at SuperK

  25. No spectrum distortion yet at SNO

  26. Absence of spectrum distortion removes SMA

  27. Seasonal Effect • Earth’s orbit is slightly eccentric • The Earth-Sun distance changes 3.5% from max to min • 1/r2 law says 7% change in neutrino flux from max (summer) to min (winter)

  28. So far no seasonal effect in 8B

  29. Vacuum Oscillation again

  30. Quasi-Vacuum oscillation • Vacuum region actually reached slowly as Dm2 decreased • Transition region between “MSW” and “vacuum” region: quasi-vacuum • Both matter effect and oscillatory term need to be kept

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

  32. Future of Solar Neutrinos

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

  34. What Next on Solar Neutrinos? • We’d like to convincingly verify oscillation with man-made neutrinos • Hard for low Dm2 • Need low En, high Fn • Use neutrinos from nuclear reactors • To probe LMA, need L~100km, 1kt

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

  36. Location, Location, Location

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

  38. KamLAND first neutrino event

  39. Can see the dip when Dm2>210–5eV2 (Pierce, HM) Can measure mass & mixing parameters Measurements at KamLAND Data/theory

  40. If LMA confirmed... • Dream case for neutrino oscillation physics! • Dm2solar 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 energysolar neutrinos crucial

  41. CP Violation • Possible only if: • Dm122, s12 large enough (LMA) • q13 large enough

  42. 7Be neutrino monochromatic seasonal effect probes VAC region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too! VAC by seasonal variation

  43. VAC by seasonal variation • Fit to seasonal variation to measure parameters Can pep n resolve degeneracy?

  44. 7Be neutrino monochromatic Day/night effect probes LOW region (de Gouvêa, Friedland, HM) Borexino crucial Hopefully KamLAND, too! LOW by day/night effect

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

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

  47. SMA: Sharp falloff in probability in the pp neutrino region the survival Because of the condition for the level crossing Measure the falloff  Dm2 measurement SMA by pp neutrinos

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

  49. 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

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