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Neutrino oscillations

Neutrino oscillations. Oleg Lychkovskiy ITEP 2008. Plan. Lecture I Introduction Two-flavor oscillations Three- flavor oscillations Matter effect Lecture II Overview of experiments and observations. Introduction: acquaintance with neutrinos. Typical energies: MeV-PeV >> m:

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Neutrino oscillations

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  1. Neutrino oscillations Oleg Lychkovskiy ITEP 2008

  2. Plan Lecture I Introduction Two-flavor oscillations Three-flavor oscillations Matter effect Lecture II Overview of experiments and observations.

  3. Introduction: acquaintance with neutrinos Typical energies: MeV-PeV >> m: always ultrarelativistic! SM interactions: Low energy (E<<100GeV) interactions: β – decay: (Z, A)  (Z+1,A) + e- + ve ve– capture: ve + p  n + e+ Deep inelastic scattering: π – decay: … and so on

  4. Two-flavor oscillations Key feature: flavor eigenstates, in which neutrinos are created and detected, do not coincide with mass eigenstates! m1 and m2 - masses of v1 and v2

  5. Two-flavor oscillations, wave packet formalism (at given t only x=Vt ±a/2 are relevant)

  6. Two-flavor oscillations, wave packet formalism

  7. Two-flavor oscillations, plane wave formalism Final oscillation probability does not depend on the specific form of the wave packet F(x)! Thus we may put F(x)=1, x=L and drop the integration over x! We get the same final result with less calculations:

  8. Three-flavor mixing νe , νμ , ντ- flavor eigenstates ν1 , ν2 , ν3 - mass eigenstates with masses m1, m2, m3 • 3 angles: θ12 ,θ13 , θ23 • 1 CP-violating Dirac phase: δ • 2 CP-violating Majorana phases: α1 , α2 • (physical only if ν’s are Majorana fermions)

  9. Three-flavor mixing Unknown: absolute values of masses, θ13, δ, α1 , α1 , sign of Δm232, octet of θ23

  10. Three-flavor mixing sin213 3 2 } m221 1 | m232 | or (Mass)2 | m232 | 2 } m221 3 1 sin213   e inverted hierarchy normal hierarchy

  11. Three-flavor oscillations In particular, one can see that Majorana phases do not enter the oscillation probability

  12. Three-flavor oscillations: νμ νl’L Δm221 /4E<< π, sin213neglected Assume Then, neglecting and one obtains Relevant for the majority of accelerator experiments and for atmospheric neutrinos Example: K2K (E=1GeV, L=250km)

  13. Three-flavor oscillations: νe νe,sin213neglected Assume the detector registers only electron neutrinos Neglecting |Ue3|2 = |s13|2 < 0.05, one obtains The same result one can get in a more illuminating way

  14. Three-flavor oscillations: νe νe,sin213neglected Two-flavor mixing effectively! =12 , m2=m221 Relevant for KamLAND

  15. Three-flavor oscillations: νe νe ,small baselines, 13 in play If one does not neglect s132 , oscillations with small amplitude ~ s132 and small period Losc = 4E/Δm231are superimposed on the Δm21–related oscillations. If in addition one comes to http://dayawane.ihep.ac.cn/docs/experiment.html Relevant for Double Chooz, Daya Bay Example: Double Chooz (E=4 MeV, L=1 km)

  16. Matter (MSW) effect in neutrino oscillations νe-einteraction (through W-boson exchange): averaging of this Lagrangian over the matter electrons gives an effective matter potential: νl-einteraction through Z-boson exchange does not depend on flavor and thus does not influence oscillations

  17. Matter (MSW) effect for the details see lecture notes by Y.Nir, arXiv:0708.1872

  18. Neutrinos in matter, two-flavor case, ne=const Resonance: Overwhelming matter effect: Oscillations with the maximal amplitude! No oscillations!

  19. Relevance of matter effect Key parameter: Earth:ρ=(1-10) g/cm3 V = (0.4-4) 10-13 eV Reactors:E ~ few MeV Δm212 /2E ~(1-10)10-11 eV Δm312 /2E ~ (3-30)10-10eV Matter effect is irrelevant Accelerators, atmospheric neutrinos:E ~ few GeV Δm212 /2E ~(0.1-1)10-13eV Δm312 /2E ~ (0.3-3)10-12eV Matter effect may be relevant Supernova core: ρ~1012 g/cm3 E ~10 MeV V ~ 0.1 eV Δm212 /2E ~0.5 ·10-11 eV Δm312 /2E ~ 10-10 eV Overwhelming matter effect! • Sun core: • ~100 g/cm3 V ~0.5 ·10-11eV • E ~ (0.5-20) MeV • Δm212 /2E ~(0.2-8)10-11eV • relevant • Δm312 /2E ~ (0.6-24) 10-10eV • irrelevant

  20. Remarks upon the previous lecture Misprint: tree-flavorthree-flavor MSW effect = Mikheyev-Smirnov-Wolfenstein effect “octant”=… = 1/4 of the coordinate plane

  21. Lecture II.Neutrino oscillations.Overview of experiments and observations.Based on the review by O.Lychkovskiy, A.Mamonov, L.Okun, M.Rotaev,to be published in UFN (УФН).

  22. Three-flavor mixing νe , νμ , ντ- flavor eigenstates ν1 , ν2 , ν3 - mass eigenstates with masses m1, m2, m3 • 3 angles: θ12 ,θ13 , θ23 • 1 CP-violating Dirac phase: δ • 2 CP-violating Majorana phases: α1 , α2 • (physical only if ν’s are Majorana fermions)

  23. Solar neutrinos

  24. Neutrino oscillations in the matter of the Sun We are interested in νe νe oscillations and we neglect θ13 Effectively two-flavor case with 1-2 mixing: θ =θ12, m2=m221 adiabaticity condition holds: ne=ne(r), r is the distance from the center of the Sun ,m=m(r), θ= θ(r)

  25. Neutrino oscillations in the matter of the Sun At the Earth (r=R) where averaging over the production point r0 is performed

  26. Neutrino oscillations in the matter of the Sun Probability weakly depends on m221, but, nevertheless, is sensitive to its sign!

  27. Radiochemical experiments Homestake: νe + 37Cl 37Ar + e- 37Ar 37Cl + e+ + νe Eth=0.86 MeV t1/2=35 days Result: ~4 times less neutrinos, than predicted by the SSM SAGE, GALLEX/GNO: νe + 71Ga 71Ge + e- 71Ge 71Ga+ e+ + νe Eth=0.23 MeV t1/2=11.4 days Result: ~2 times less neutrinos, than predicted by the SSM

  28. Cherenkov detector experiments Kamiokande ((1-3) kt of H2O) and Super-Kamiokande (50 kt of H2O): νl + e νl + e SNO: (1 kt of D2O): νe + d p + p + e νl + d p + n + νl νl + e νl + e Eth>5 MeV The total flux was measured, and it coincided with the SSM prediction! SSM verified the νe deficite is due to oscillations!

  29. Borexino Main goal: mono-energetic (E= 862 кэВ) 7Be neutrinos Scintillation detector: low threshold (Eth= 0.5 MeV), but no direction measured !!!First real-time low-energy solar neutrinos: 47 ± 7stat±12syst 7Beν / (day· 100 t) (arXiv:0708.2251)

  30. Reactor experiments  oscillations • νe: • produced in β-decays in nuclear reactors: • (A,Z) (A,Z+1) + e- + νe • detected through νe + p  n + e+ • scintillation detectors used • antineutrino energy: few MeV Short-baseline, L=O(1) km: Chooz, Double Chooz, Daya Bay Long-baseline, L=O(100) km: KamLAND

  31. KamLAND • Sources of : 55 Japanese reactors • Baselines: L=(140 - 210) km • energies: 1.7 MeV < E < 9.3 MeV • Probability of survival: Sensitive toΔm221 and θ12 Status: running

  32. KamLAND !!!The latest result: arXiv: 0801.4589v2 Also 70±27 geo-neutrinosregistered!

  33. Chooz • Source: Chooz nuclear station • Baseline: L=1.05 km • energies: 3 MeV < E < 9 MeV • Probability of survival: The final result: sin22θ13 < 0.2 90%CL Status: finished

  34. Future experiments:Double Chooz and Daya Bay Goal: measuring θ13 Double Chooz sin22θ13 <0.03 by 2012 Daya Bay sin22θ13 <0.01 by 2013 near detectors will be built the initial spectrum will be measured, not calculated Double Chooz sensitivity evolution arXiv:hep-ex/0701020v3

  35. Double Chooz and Daya Bay sensitivities

  36. Atmospheric neutrinos • Source: cosmic rays, interacting with the atmosphere. • Major fraction: • Minor fraction: • Negligible fraction: • Detection reactions: deep inelastic scattering • νμ + N  μ + hadrons • Experiments: • Kamiokande, IMB, Super-Kamiokande, Amanda, Baikal, MACRO, • Soudan, IceCube, … • “Baselines”: L=(0 - 13000) km • Energies: 0.1 GeV < E < 10 TeV

  37. Atmospheric neutrinos Approximate expressions: large theoretical flux uncertainties Original flux and energy spectrum are poorly known no simple precise expressions! MSW-effect and 3-flavor oscillations in play, extended source

  38. Atmospheric neutrino fluxes

  39. SK atmospheric neutrino results sin22θ23 > 0.92 1.5 ·10-3 < m232< 3.4 · 10-3eV2 90% CL Evidence for appearance! Phys.Rev.Lett.97:171801,2006, hep-ex/0607059 Prospects for resolving hierarchy ambiguity arXiv:0707.1218 Phys.Rev. D71 (2005) 112005, arXiv:hep-ex/0501064v2

  40. Accelerator neutrino experiments  oscillations • νμ and νμ are produced in meson decays • energies: few GeV • baselines: hundreds of kilometers μ Main goals: appearance observations: search for   e or  τ measuring13 precise measurement of m223 ,23 mass hierarchy CP

  41. Accelerator neutrino experiments К2К MINOS OPERA MiniBooNE Т2К NOVA   m232, sin2223   LSND sterile   e 13 CP(?) For К2К, MINOS (?) and OPERA (?) L Δm221 /4E<< π, 13=0 approximation is valid T2К, NOvA and, probably, OPERA and MINOS, will go beyond this approximation!

  42. Accelerator neutrino experiments Next several slides are from the talk by Yury Kudenko at NPD RAS Session ITEP, 30 November 2007

  43. First LBL experiment К2К  disappearance 1999-2005  98.2% e1.3% L/E 200 L=250 km <E>  1.3 GeV Signal of  oscillation at K2K Reduction of  events Distortion of energy spectrum Predictions of  flux and interactions at Far Detector by Far/Near ratio ~1 event/2 days at SK

  44. K2K final result PRD74:072003,2006 + - # Events - Shape distortion Expected: 158.1 + 9.2 – 8.6 Observed: 112 Expected shape (no oscillation) Best fit Null oscillation probability (shape + # events) = 0.0015% (4.3) Kolmogorov-Smirnov test Best fit probability = 37% Best fit values sin22 = 1.00 m2 [eV2] = (2.80  0.36)10-3

  45. MINOS 735 km Far Det: 5400 tons Near Det: 980 tons Precise study of “atmospheric” neutrino oscillations, using the NUMI beam and two detectors Beam:NuMI beam, 120 GeV Protons- beam Detectors:ND, FD Far Det:5.4 kton magnetized Fe/Sci Tracker/Calorimeter at Soudan, MN (L=735 km) Near Det:980 ton version of FD, at FNAL (L  1 km)

  46. New MINOS result J.Thomas, talk at Lepton-Photon2007 2.50 POT analyzed ≈ 2x statistics of 2006 result Improved analysis # expected (no osc.) 73830 # observed 563 Comparison of new and old MINOS results m223 =(2.38 +0.20 -0.16) x 10-3 sin2223=1.00 -0.08

  47. m223 and 23: SK/K2K/MINOS |m223|| m213|= (2.4  0.2)x10-3 eV2 23 ~ 45o

  48. MINOS: projected sensitivity M.Ishitsuka, talk at NNN07 After 5 years running: expected accuracy of m232 and sin2223 10% chance for first indication of non-zero 13

  49. 1 mm t  Pb Emulsion layers High energy, long baseline n beam ( E  17 GeV L ~ 730 km ) OPERA   direct search P(  ) = cos413sin223sin2[1.27m223L(km)/E(GeV)] kink Target mass ~1300t E/L ~ 2.310-2  10m223 (atm)   pure beam: 2% anti  <1% e  after 5 years data taking: ~22000  interactions ~120  interactions ~12  reconstructed <1 background event  

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