1. Neutrino oscillations Oleg Lychkovskiy ITEP2008

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

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

4. Two-flavor oscillations Key feature: flavor eigenstates, in which neutrinos are created and detected, do not coincide with mass eigenstates! m 1 and m 2 - masses of v 1 and v 2

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 3 angles: θ 12, θ 13, θ 23 3 angles: θ 12, θ 13, θ 23 ν e, ν μ, ν τ - flavor eigenstates ν 1, ν 2, ν 3 - mass eigenstates with masses m 1, m 2, m 3 2 CP-violating Majorana phases: α 1, α 2 2 CP-violating Majorana phases: α 1, α 2 (physical only if are Majorana fermions) (physical only if ν’s are Majorana fermions) 1 CP-violating Dirac phase: δ 1 CP-violating Dirac phase: δ

9. Three-flavor mixing Unknown: absolute values of masses, θ 13, δ, α 1, α 1, sign of Δm 2 32, octet of θ 23

10. Three-flavor mixing e   normal hierarchy inverted hierarchy  m 2 32     (Mass) 2  m 2 21 }   m 2 32     m 2 21 } or sin 2  13

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

12. Three-flavor oscillations: ν μ  ν l’ L Δm 2 21 /4E<< π, sin 2  13 neglected 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: ν e  ν e, sin 2  13 neglected Assume the detector registers only electron neutrinos Neglecting |U e3 | 2 = |s 13 | 2 < 0.05, one obtains The same result one can get in a more illuminating way

14. Three-flavor oscillations: ν e  ν e, sin 2  13 neglected Two-flavor mixing effectively!  =  12  m 2  m 2 21 Relevant for KamLAND

15. Three-flavor oscillations: ν e  ν e, small baselines,  13 in play http://dayawane.ihep.ac.cn/docs/experiment.html If one does not neglect s 13 2, oscillations with small amplitude ~ s 13 2 and small period L osc = 4E/Δm 2 31 are superimposed on the Δm 21 – related oscillations. If in addition one comes to Relevant for Double Chooz, Daya Bay Example: Double Chooz (E=4 MeV, L=1 km)

16. Matter (MSW) effect in neutrino oscillations ν e -e interaction (through W-boson exchange): averaging of this Lagrangian over the matter electrons gives an effective matter potential: ν l -e interaction through Z-boson exchange does not depend on flavor and thus does not influence oscillations ν l -e interaction 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, n e =const Resonance: Overwhelming matter effect: Oscillations with the maximal amplitude! No oscillations!

19. Relevance of matter effect Supernova core: ρ ~ 10 12 g/cm 3 E ~10 MeV V ~ 0.1 eV Δm 21 2 /2E ·10 -11 eV Δm 21 2 /2E ~0.5 · 10 -11 eV Δm 31 2 /2E 10 -10 eV Δm 31 2 /2E ~ 10 -10 eVOverwhelming matter effect! Key parameter: Sun core:  ~ 100 g/cm 3 · V ~0.5 · 10 -11 eV E ~ (0.5-20) MeV Δm 21 2 /2E 10 -11 eV Δm 21 2 /2E ~(0.2-8)10 -11 eVrelevant Δm 31 2 /2E 10 -10 eV Δm 31 2 /2E ~ (0.6-24) 10 -10 eVirrelevant Earth: Earth: ρ =(1-10) g/cm 3 V = (0.4-4) 10 -13 eV Reactors: E ~ few MeV Δm 21 2 /2E 10 -11 eV Δm 21 2 /2E ~ (1-10)10 -11 eV Δm 31 2 /2E (3-30)10 -10 eV Δm 31 2 /2E ~ (3-30)10 -10 eV Matter effect is irrelevant Accelerators, atmospheric neutrinos: Accelerators, atmospheric neutrinos: E ~ few GeV Δm 21 2 /2E 10 -13 eV Δm 21 2 /2E ~ (0.1-1)10 -13 eV Δm 31 2 /2E (0.3-3)10 -12 eV Δm 31 2 /2E ~ (0.3-3)10 -12 eV Matter effect may be relevant

20. Remarks upon the previous lecture Misprint: tree-flavor three-flavor Misprint: tree-flavor three-flavor MSW effect = Mikheyev-Smirnov-Wolfenstein effect MSW effect = Mikheyev-Smirnov-Wolfenstein effect “octant”=… = 1/4 of the coordinate plane “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 3 angles: θ 12, θ 13, θ 23 3 angles: θ 12, θ 13, θ 23 ν e, ν μ, ν τ - flavor eigenstates ν 1, ν 2, ν 3 - mass eigenstates with masses m 1, m 2, m 3 2 CP-violating Majorana phases: α 1, α 2 2 CP-violating Majorana phases: α 1, α 2 (physical only if are Majorana fermions) (physical only if ν’s are Majorana fermions) 1 CP-violating Dirac phase: δ 1 CP-violating Dirac phase: δ

23. SOURSE ν/ν, flavor relevant energy MSW what was (can be) extracted Sunνeνe 0.5-19 MeV of major importance θ 12 θ 12  m 2 21 Reactorsνeνe 1-6 MeV irrelevant, θ 12  m 2 21, θ 12 θ 13 Cosmic rays (atmospheric ) ν’s) ν μ, ν μ, minor fraction of other flavor s 0.1 GeV - 10 TeV relevant θ 23 θ 23  m 2 32 octant of θ 23 Accelerators ν μ, ν μ, minor fraction of other flavors 0.5-50 GeV relevant, θ 23  m 2 32, θ 23 θ 13, θ 13, δ hierarchy, octant Supernova all species 1-40 MeV of major importance hierarchy, θ 13

24. Solar neutrinos

25. Neutrino oscillations in the matter of the Sun  θ 13 We are interested in ν e  ν e oscillations and we neglect θ 13 n e =n e (r), r is the distance from the center of the Sun Effectively two-flavor case with 1-2 mixing: θθ 12 θ =θ 12,  m 2 =  m 2 21 θ= θ(r), m=m(r), θ= θ(r) adiabaticity condition holds:

26. Neutrino oscillations in the matter of the Sun At the Earth (r=R) where averaging over the production point r 0 is performed

27. Neutrino oscillations in the matter of the Sun Probability weakly depends on  m 2 21, but, nevertheless, is sensitive to its sign!

28. Radiochemical experiments Homestake: ν e + 37 Cl  37 Ar + e - 37 Ar  37 Cl + e + + ν e E th =0.86 MeV t 1/2 =35 days Result: ~ 4 times less neutrinos, than predicted by the SSM SAGE, GALLEX/GNO: ν e + 71 Ga  71 Ge + e - 71 Ge  71 Ga+ e + + ν e 71 Ge  71 Ga + e + + ν e E th =0.23 MeV t 1/2 =11.4 days Result: ~ 2 times less neutrinos, than predicted by the SSM

29. Cherenkov detector experiments Kamiokande ((1-3) kt of H 2 O) and Super-Kamiokande (50 kt of H 2 O): ν l + e  ν l + e SNO: (1 kt of D 2 O): ν e + d  p + p + e ν l + d  p + n + ν l ν l + e  ν l + e E th >5 MeV The total flux was measured, and it coincided with the SSM prediction! SSM verified the ν e deficite is due to oscillations! SSM verified the ν e deficite is due to oscillations!

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

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

32. KamLAND Sources of : 55 Japanese reactors Sources of : 55 Japanese reactors Baselines: L=(140 - 210) km Baselines: L=(140 - 210) km energies: 1.7 MeV < E < 9.3 MeV energies: 1.7 MeV < E < 9.3 MeV Probability of survival: Probability of survival: Sensitive to Δm 2 21 and θ 12 Status: running

33. KamLAND !!!The latest result: Also 70 ± 27 geo-neutrinos registered! arXiv: 0801.4589v2 arXiv: 0801.4589v2

34. Chooz Source: Chooz nuclear station Source: Chooz nuclear station Baseline: L=1.05 km Baseline: L=1.05 km energies: 3 MeV < E < 9 MeV energies: 3 MeV < E < 9 MeV Probability of survival: Probability of survival: The final result: sin 2 2θ 13 < 0.2 90%CL Status: finished

35. Future experiments: Double Chooz and Daya Bay Goal: measuring θ 13 Daya Bay sin 2 2θ 13 < 0.01 by 2013 Double Chooz sin 2 2θ 13 < 0.03 by 2012 Double Chooz sensitivity evolution arXiv:hep-ex/0701020v3 near detectors will be built near detectors will be built the initial spectrum will be measured, not calculated the initial spectrum will be measured, not calculated

36. Double Chooz and Daya Bay sensitivities

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

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

39. Atmospheric neutrino fluxes

40. SK atmospheric neutrino results Phys.Rev. D71 (2005) 112005, arXiv:hep-ex/0501064v2 arXiv:hep-ex/0501064v2 sin 2 2θ 23 > 0.92 1.5 10 -3 < < 3.4 10 -3 eV 2 1.5 · 10 -3 <  m 2 32 < 3.4 · 10 -3 eV 2 90% CL 90% CL Evidence for appearance! Phys.Rev.Lett.97:171801,2006, hep-ex/0607059 Prospects for resolving hierarchy ambiguity arXiv:0707.1218

41. Accelerator neutrino experiments ν μ and ν μ are produced in meson decays energies: few GeV energies: few GeV baselines: hundreds of kilometers baselines: hundreds of kilometers μ   oscillations Main goals: appearance observations: search for   e or   τ measuring  13 precise measurement of  m 2 23,  23 mass hierarchy  CP

42. Accelerator neutrino experiments К2К MINOS OPERA MiniBooNE Т2К NOVA       LSND   e  m 23 2, sin 2 2  23 sterile  13  CP (?) For К2К, MINOS (?) and OPERA (?) L Δm 2 21 /4E<< π,  13 =0 approximation is valid T2К, NOvA and, probably, OPERA and MINOS, will go beyond this approximation!

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

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

45. Expected: 158.1 + 9.2 – 8.6 Observed: 112 - # Events Expected shape (no oscillation) Best fit Best fit values sin 2 2  = 1.00  m 2 [eV 2 ] = (2.80  0.36)  10 -3 Kolmogorov-Smirnov test Best fit probability = 37% Null oscillation probability (shape + # events) = 0.0015% (4.3  ) K2K final result - Shape distortion PRD74:072003,2006 +

46. Near Det: 980 tons Far Det: 5400 tons 735 km 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) Precise study of “atmospheric” neutrino oscillations, using the NUMI beam and two detectors MINOS

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

48.  m 2 23 and  23 : SK/K2K/MINOS |  m 2 23 |  |  m 2 13 |= (2.4  0.2)x10 -3 eV 2  23 ~ 45 o

49. After 5 years running: expected accuracy of  m 23 2 and sin 2 2  23  10% chance for first indication of non-zero  13 MINOS: projected sensitivity M.Ishitsuka, talk at NNN07

50. OPERA High energy, long baseline beam ( E  17 GeV L ~ 730 km )    direct search pure beam: 2% anti  <1% e P(    ) = cos 4  13 sin 2  23 sin 2 [1.27  m 2 23 L(km)/E(GeV) ] E/L ~ 2.3  10 -2  10  m 2 23 (atm) Pb Emulsion layers   1 mm   kink  after 5 years data taking: ~22000 interactions ~120  interactions ~12  reconstructed <1 background event Target mass ~1300t

51. OPERA:    sensitivity full mixing, 5 years run 4.5 x10 19 pot/y M.Spinetti, talk at NNN07 New MINOS

52. Second generation LBL experiments T2K NOVA Off Axis Neutrino Beams Increases flux on oscillation maximum Reduces high-energy tail and NC backgrounds Reduces e contamination from K and  decay

53. T2K (Tokai to Kamioka) ~1GeV  beam (  100 of K2K) JPARC facility on-axisoff-axis beam JPARC MINOS Opera K2K E(GeV) 50 120 400 12 Int(10 12 ppp) 330 40 24 6 Rate (Hz) 0.29 0.53 0.17 0.45 Power (MW) 0.77 0.41 0.5 0.0052 Statistics at SK OAB 2.5 deg, 1 yr = 10 21 POT, 22.5 kt ~ 2200  tot ~ 1600  charged current e < 0.5% at  peak

54. OA3°  Target Horns Decay Pipe SuperK OA2° OA2.5° T2K off-axis beam 0 deg 0o0o

55. Principle Goals of T2K Background uncertainty 10%  CP = 0  CP =  /2  CP = -  /2  CP =  - - Search for e appearance  13 sensitivity  1 o (90% c.l.) -Measurement  m 2 23 with accuracy of 1%  (sin 2 2  23 )  0.01  (  m 2 23 ) < 1  10 -4 eV 2  m 2 =2.5x10 -3

56. CHOOZ limit T2K sensitivity to  13 ambiguities:  CP -  13 sign  m 2 23  23

57. NO A Mass hierarchy can be resolved if  13 near to present limit using both anti- beams and sin 2 2  13 from T2K + reactor experiments matter effects increase (decrease) oscillations for normal (inverted) hierarchy for P(   e ) depends on sin 2 2  13 sign  m 2 23  CP

58.  13 sensitivities vs time A.Blondel et al., hep-ph/0606111 Short baseline reactor experiments Double-Chooz and Daya Bay  13 ( insensitive to  CP ) Daya Bay goal

59. Summary for accelerator experiments K2K confirmation of atmospheric neutrino oscillations discovered by SK MINOS confirmed the SK и K2K results high precision measurements of oscillation parameters MiniBooNe rules out (98% cl) the LSND result as   e oscilations with  m 2 ~ 1 eV 2 new anomaly appears run with anti- beam OPERA data taking begun in 2007 T2K-I neutrino beam in 2009 Main goal for next 5 years:  13

60. Neutrino production in SN

61. Matter effect in Supernova Adiabaticity almost everywhere, resonant layers are possible exeptions Adiabaticity almost everywhere, resonant layers are possible exeptions Three flavors in play, two different resonanses Three flavors in play, two different resonanses H-резонанс: H-резонанс: L-резонанс: L-резонанс:

62. Adiabaticity conditions Adiabaticity of H-resonance depends on θ 13 ! L- resonance is always adiabatical! In resonance layer the adiabaticity parameter reads

63. Level crossing scheme for SN

64. Mass hierarchy and θ 13 NH=Normal Hierarchy, IH=Inverted Hierarchy L=Large θ 13 : θ 13 >0.03 S=Small θ 13 : θ 13 < 0.003 NH, L IH, L NH and IH, S 011 101

65. Takahashi, Sato, hep-ph/0205070 R=10 kpc Future SN neutrino signal in SK

66. θ 13 measurment with SN If and the hierarchy is inverted, than θ 13 is measurable! Takahashi, Sato, hep-ph/0205070

67. Conclusions Present knowledge: central value 2  interval  m 2 12 (10 -5 eV 2 ) 7.6 7.1 - 8.3  m 2 31 (10 -3 eV 2 ) 2.4 2.0 - 2.8 sin 2  12 0.32 0.26 - 0.40 sin 2  23 0.50 0.34 - 0.67 sin 2  13 0.0 <0.05 5-year goals: to increase the sensitivity for  m 2 12,  m 2 31, sin 2  12, sin 2  23 up to (1-10)% sin 2  13 sensitivity at the level 0.003 mass hierarchy,  (?)