1. A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy Exotic physics with Neutrino Telescopes 2013, April 5, 2013

2. ANTARES Ice Cube Precision IceCube Next Generation Upgrade Oscillation Research with Cosmics with the Abyss

4. Oscillation effects and Oscillograms Nonstandard interactions Hierarchy, 2-3mixing, CP Sterile neutrinos

5. P. Lipari, T. Ohlsson M. Chizhov, M. Maris, S.Petcov T. Kajita and physics of oscillations

6.   e 2 1 3 mass  m 2 31  m 2 21 Normal mass hierarchy |U e3 | 2 |U  3 | 2 |U  3 | 2 |U e1 | 2 |U e2 | 2 tan   23 = |U  3 | 2 / |U  3 | 2 sin   13 = |U e3 | 2 tan   12 = |U e2 | 2 / |U e1 | 2  m 2 31 = m 2 3 - m 2 1  m 2 21 = m 2 2 - m 2 1 Mixing parameters f = U PMNS mass U PMNS = U 23 I  U 13 I  U 12 flavor Mixing matrix: 1 2 3 e   = U PMNS

7.   e 2m 1m 3m 1-2 resonance 1-3 resonance Density (energy) increase  Normal mass hierarchy, neutrinos

8.   e 2m 1m 3m 1-2 resonance Density increase  Inverted mass hierarchy, neutrinos

9.   e 2m 1m 3m Density increase  Normal mass hierarchy, antineutrinos

10.   e 2m 1m 3m 1-3 resonance Density increase  Inverted mass hierarchy, antineutrinos

11. core mantle flavor-to-flavor transitions Oscillations in multilayer medium  - nadir angle core-crossing trajectory  -zenith angle  = 33 o  - accelerator - atmospheric - cosmic neutrinos Applications: 9

12. Oscillations in matter with nearly constant density (mantle) Parametric enhancement of oscillations Mantle – core - mantle Interference constant density + corrections Peaks due to resonance enhancement of oscillations Low energies: adiabatic approximation Parametric resonance  parametric peaks Smallness of  13 and  m 21 2 /  m 32 2 in the first approximation: overlap of two 2 –patterns due to 1-2 and 1-3 mixings interference of modes CP-interference interference (sub-leading effect) Two layer transitions vacuum-matter (atmosphere-Earth)

13. B = (sin 2  m, 0, cos2  m ) 2  l m  = (B x P) Equation of motion (= spin in magnetic field)  = 2  t/ l m Phase of oscillations P ee = e + e = P Z + 1/2 = cos 2  Z /2 Probability to find e e , B P x z d  P dt y where ``magnetic field’’ vector: P = (Re e + , Im e + , e + e - 1/2)

14. mantle 1 2 12

15. F (E) F 0 (E) E/E R thin layer thick layer k = 1 k = 10 Small mixing sin 2 2  = 0.08 sin 2 2  m

16. Enhancement associated to certain conditions for the phase of oscillations Another way of getting strong transition No large vacuum mixing and no matter enhancement of mixing or resonance conversion ``Castle wall profile’’ V     =   =  V. Ermilova V. Tsarev, V. Chechin E. Akhmedov P. Krastev, A.S., Q. Y. Liu, S.T. Petcov, M. Chizhov 1 2 3 4 5 6 7 mm mm   m   m of oscillations 18

17.   =   =  distance c 1 = c 2 = 0 General case: certain correlation between the phases and mixing angles E. Kh. Akhmedov, s  c  cos2   m  + s  c  cos2   m  = 0 s i = sin   i, c i = cos  i, (i = 1,2) half-phases transition probability

18. core mantle mantle core mantle 1 2 3 4 1 2 3 4 22

19. core mantle 1 2 3 4 3 2 4 1 23

20. MSW-resonance peaks 1-2 frequency 1 - P ee Parametric peak 1-2 frequency MSW-resonance peaks 1-3 frequency Parametric ridges 1-3 frequency  excluded

21. E. Kh. Akhmedov, S.Razzaque, A.S. Oscillations test dispersion relation for neutrinos NH, neutrinos

22. e e   f  U 23 I  I  = diag (1, 1, e i  ) e     e   ~ Propagation basis ~ ~ ~ ~ projection propagation A(    ) = cos  23  A e2 e i  + sin  23 A e3 A e3 A e2 CP-violation and 2-3 mixing are excluded from dynamics of propagation CP appears in projection only For instance: For E > 0.1 GeV A 22 A 33 A 23

23. P( e   ) = |cos  23  A e2 e i  + sin  23 A e3 | 2 ``atmospheric’’ amplitude``solar’’ amplitude Due to specific form of matter potential matrix (only V ee = 0) dependence on  and  23  is explicit P( e   )  = |A e2 A e3 | cos (  -  ) P(    )  = - |A e2 A e3 | cos  cos  P(    )  = - |A e2 A e3 | sin  sin  For maximal 2-3 mixing  = arg (A e2 * A e3 )  = 0

24.  A S = 0 P int = 0 - solar magic lines (  +  ) =  /2 + 2  k  (E, L) = -  +  /2 +  k  A A = 0 - interference phase condition depends on  P int = 2s 23 c 23 |A e2 ||A e3 |cos(  +  ) P( e   ) = c 23 2 |A e2 | 2 + s 23 2 |A e3 | 2 + 2s 23 c 23 |A e2 ||A e3 |cos(  +  ) Explicitly  = arg (A S A A *) Dependence on  disappears, interference term is zero if V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. - atmospheric magic lines 31

25.  A S = 0 P int = 0  =  /2 +  k  A A = 0 interference phase does not depends on  For    channel - The survival probabilities is CP-even functions of  - no CP-violation - dependences on phases factorize P int ~ 2s 23 c 23 |A S ||A A |cos  cos  Dependence on  disappears Form the phase line grid

26. Grid (domains) does not change with  Int. phase line moves with  -change PP

27. PP

28. PP

29. 10 1 100 0.1 E, GeV MINOS T2K CNGS NuFac 2800 0.005 0.03 0.10 T2KK IceCube LENF IC Deep Core NOvA PINGU-1 e      contours of constant oscillation probability in energy- nadir (or zenith) angle plane HyperK OK for CP ICAL, INO LAr

31.   e 2 1 MASS 1 2 3 3  m 2 23  m 2 32  m 2 21 Inverted mass hierarchy (ordering 3-1-2) Normal mass hierarchy (ordering 1-2-3) - For non-zero  CP the antineutrino spectrum is different (distribution of the   and   - flavors in 1  and 2 ) - Mass states are marked by amount of the electron flavor with cyclic permutation FLAVOR

32. Inversion of mass hierarchy is related to neutrino – antineutrino transition In matter V  -V neutrino  antineutrino inversion of mass hierarchy 2EV  m 2  m 2  -  m 2 Under simultaneous transition NH  IH nu  antinu In 2 approximation is invariant Mixing does not change Moduli of the oscillation phase does not change P NH = P IH P IH = P NH Hierarchy asymmetries for neutrinos and antineutrinos have opposite signs

33. normal  inverted neutrino  antineutrino For 2 system e - e e -   25

34. Estimator of sensitivity S – asymmetry |S| - significance Quick estimation of total significance S tot ~ s n 1/2 S =

35. E - E  E + m N E h - m N E  + E h y = = sin 2  = fraction of total energy transferred into hadrons 1. Separation of neutrino and antineutrino signals N ~ 1, N ~ (1 - y) 2 for each bin y – distribution allows to extract fractions of nu and nubar 2. Better reconstruction of the neutrino direction reduction of the kinematic smearing x y m N (E  + m N ) 2 E E  selecting events with small y reduces possible angles between and  3. Better control over systematics 4. Reduction of degenerasy Mathieu Ribordy, A. Y.S., i1303.0758 [hep-ph] and sensitivity

36. with experimental smearing  E  = (0.7 E ) 1/2  0 = 20 o y-integrated bad nu – nubar separation bad angular resolution

37. sin 2  32, fit = 0.50 sin 2  32, true = 0.42 Future measurements – improve accuracy of determination of the angle Effect has the same sign Regions of strong effects of the angle and hierarchy do not overlap significantly Large effect is in he region of small number of events

38. Integrating over the zenith angle Energy dependence of the cascade events S. Razzque and A.Y.S., in preparation

39. Shape does not change the amplitude changes Large significance at low energies

41.   e 2 1 4 mass  m 2 31  m 2 21 3  m 2 41 s P ~ 4|U e4 | 2 |U  4 | 2 restricted by short baseline exp. BUGEY, CHOOZ, CDHS, NOMAD LSND/MiniBooNE: vacuum oscillations  m 41 2 ~ 1 eV 2 U  4 = 0.2 P ~ 4|U e4 | 2 (1 - |U e4 | 2 ) For reactor and source experiments - additional radiation in the universe - bound from LSS?

42. H Nunokawa O L G Peres R Zukanovich-Funchal Phys. Lett B562 (2003) 279 S Choubey JHEP 0712 (2007) 014  - s oscillations with  m 2 ~ 1 eV 2 are enhanced in matter of the Earth in energy range 0.5 – few TeV IceCube This distorts the energy spectrum and zenith angle distribution of the atmospheric muon neutrinos S Razzaque and AYS, 1104.1390, [hep-ph]

43. antineutrinos MSW resonance dip neutrinos Effect of phase shift for the     oscillations due to matter effects

44. For different mixing schemes Varying |U  0 | 2 In general Zenith angle distribution depends on admixture of  in 4 th mass state < 3% stat. error

45. Shift of phase quantifies effect of sterile neutrino S Razzaque, A Y S arXiv:1203.5406

47.   e 2 1 0 mass  m 2 31  m 2 21 3  m 2 dip s - additional radiation in the Universe if mixed in 3 Very light sterile neutrino - solar neutrino data Motivated by no problem with LSS (bound on neutrino mass) m 0 ~ 0.003 eV can be tested in atmospheric neutrinos with DC IceCube sin 2 2  ~ 10 -3 sin 2 2  ~ 10 -1 DE scale? M 2 M Planck M ~ 2 - 3 TeV

48.  ’ –  s resonanceE R ~ 12 GeV    s resonance peak at 6-8 GeV IceCube Deep Core Interplay of    s and    oscillations Phase shift and decrease of amplitude of oscillations: P. De Holanda, A. S. difference with sterile ~ 20 % suppression of rate of events in the muon energy bins 5 – 15 GeV

49. Smearing 1 Smearing 2 No smearing

51. H = U(  23 ) U*(  23 ) + R 0 0 0 1 0      ’ 2EV d  m 31 2 R 0 =  m 31 2 2E V d  -potential due to scattering on d-quarks V NSI = V d [4   2 +  ’ 2 ] 0.5  m 31 2 2E V NSI ~ resonance, strong NSI effect  ,  ’ ~ 0.01E R ~ 60 – 100 GeV

52. P(    ) Arman Esmaili, AYS resonance

53. P(    )

56. T. Ohlsson, He Zhang, Shun Zhou, 1303.6130 [hep-ph] (    )

58. - mass hierarchy - deviation of 2-3 mixing from maximal one - CP violation Probe of nature of neutrino mass (soft-hard); Neutrino images of the Earth Atmospheric vs. LBL - sterile neutrinos - tests of fundamental symmetries - non-standard interactions

59. Neutrino fluxes averaged over all directions M. Honda et al astro-ph/0611418 Flavor ratios Charge asymmetries 1.33 1.00 39

62. Vertically upgoing atmospheric neutrinos taking into account effects of violation of Lorentz invariance  c/c = 10 -27 maximal mixing M. C. Gonzalez-Garcia F. Halzen M. Maltoni, Hep-ph/0502223 Violation of Lorentz invariance: different asymptotic (E  infty) values of velocity of two neutrino components 70

63. Radiography of the Earth core and mantle M. C. Gonzalez-Garcia F. Halzen, M. Maltoni, H. Tanaka arXiv:0711.0745 [hep-ph] Zhenith angle distribution of events in IceCube for different energy thresholds for PREM model Ratio of zenith angle distribution of expected events for PREM model and for homogeneous Earth matter distribution (stat. error) 71

64. Flavor ratio decrease with energy and deviates from 2 2.1  1.6 Two components: - directly produced by e  and  e - from invisible muon decay Seasonal variations, variations with solar activity Background for diffuse SN fluxes FLUKA Enlarging the energy range weaker screening effect O. Peres, A.S, [arXiv:0903.5323] 61

65. e e   f  U 23 I  U 13 I  = diag (1, 1, e i  ) e     e   Propagation basis projection propagation For sub-subGeV events 3  2

66. Effect of 2-3 mixing Effect of 1-3 mixing and CP-phase O. Peres, A.S 62

67. Effects on neutrinos from invisible muon decays        e Muons with E < 150 MeV: no Cherenkov lights. They stop in a detector and decays: Atmospheric neutrinos with E ~ 150 – 300 MeV produce (in the detector and around it) Ratio of total number of events as functions of 2-3 mixing for different values of    and  O. Peres, A.S 63

68. Energy spectrum of e-like events in Hyper-Kamiokande (540 kt, 4 years) for two Values of CP-phase O. Peres, A.S ~ 10 – 15 % effects Sensitivity to 2-3 mixing 64

69. Energy spectrum of e-like events in Hyper-Kamiokande (540 kt, 4 years) for two Values of CP-phase O. Peres, A.S ~ 5 - 10 % effects Sensitivity to 13-mixing and  -phase 65

70. Measuring oscillograms with atmospheric neutrinos E > 2 - 3 GeV with sensitivity to the resonance region Huge Atmospheric Neutrino Detector Better angular and energy resolution Spacing of PMT ? V = 5 - 10 MGt Should we reconsider a possibility to use atmospheric neutrinos? develop new techniques to detect atmospheric neutrinos with low threshold in huge volumes? 0.5 GeV

71. a). Resonance in the mantle b). Resonance in the core c). Parametric ridge A d). Parametric ridge B e). Parametric ridge C f). Saddle point a). b). c). e). d). f).

72. Y. Suzuki - Proton decay searches - Supernova neutrinos - Solar neutrinos Totally Immersible Tank Assaying Nucleon Decay TITAND-II: 2 modules: 4.4 Mt (200 SK) Under sea deeper than 100 m Cost of 1 module 420 M $ Modular structure

73. Y. Suzuki Totally Immersible Tank Assaying Nucleon Decay Module: - 4 units, one unit: tank 85m X 85 m X 105 m - mass of module 3 Mt, fiducial volume 2.2 Mt - photosensors 20% coverage ( 179200 50 cm PMT) TITAND-II: 2 modules: 4.4 Mt (200 SK)

74. Contours of constant oscillation probability in energy- nadir (or zenith) angle plane P. Lipari, T. Ohlsson M. Chizhov, M. Maris, S.Petcov T. Kajita e      Michele Maltoni 1 - P ee excluded

75. LSND MiniBooNE Gallex,GNO Double-Chooz SAGE G.Mention et al, arXiv: 1101.2755  m 41 2 = 1 - 2 eV 2

76. sin 2 2  ~ 10 -3 m 0 ~ 0.003 eV M 2 M Planck m 0 = M ~ 2 - 3 TeV mixing h v EW M  ~ sin 2 2  ~ 10 -1 v EW M  ~ h = 0.1

77. inner core outer core upper mantle transition zone crust lower mantle (phase transitions in silicate minerals) liquid solid Fe Si PREM model A.M. Dziewonski D.L Anderson 1981 R e = 6371 km

78. of oscillograms 1. One MSW peak in the mantle domain 2. Three parametric peaks (ridges) in the core domain 3. MSW peak in the core domain 1-3 mixing: 1-2 mixing: 1. Three MSW peaks in the mantle domain 2. One (or 2) parametric peak (ridges) in the core domain 1D  2D - structuresregular behavior

79. solar magic lines atmospheric magic lines relative phase lines Regions of different sign of  P Interconnection of lines due to level crossing factorization is not valid

80. P. de Holanda, A.S. Phys. Rev. D69 (2004) 113002 hep-ph 0307266 Q Ar exp <Q Ar LMA 2.55 +/- 0.25 SNU> 3.1 SNU No turn up of the spectrum in SK Light sterile neutrinoR  =  m 01 2 /  m 21 2 << 1  - mixing angle of sterile- active neutrinos  dip in survival probability Motivation for the low energy solar neutrino experiments BOREXINO, KamLAND …

81. sin 2 2  = 10 -3 (red), 5 10 -3 (blue) SK-I SK-III SNO-LETA R  = 0.2  m 2 = 1.5 10 -5 eV 2 SNO-LETA Borexino P. De Holanda, A.S.

82. Earth matter effects Flavor evolution of neutrino states is highly adiabatic Strong suppression of the neutronization peak: e  3 NH Adiabaticity is broken in shock front if the relative width of the front:  R/R < 10 -4  10 km Shock wave effect if larger – no shock wave effect: probe of the width of front Normal mass hierarchy: in the antineutrino channel only Inverted mass hierarchy: in the neutrino channel only If the earth matter effect is observed for antineutrinos NH is established! Permutation of the electron and non-electron neutrino spectra

83. Energy range: 0.01 – 10 5 GeV Baselines: 0 – 13000 km Matter effects: 3 – 15 g/cm 3 Flavor content nue, numu Lepton number nu - antinu Discovery of neutrino oscillations Measurements of 2-3 mixing and mass splitting which is not completely explored and largely unused Bounds on new physics - sterile neutrinos - non-standards interaction -violation of fundamental symmetries, CPT which change with energy and zenith angle

84. PINGU: 18, 20, 25 ? new strings (~1000 DOMs) in DeepCore volume IceCube : 86 strings (x 60 DOM) 100 GeV threshold Gton volume Existing IceCube strings Existing DeepCore strings New PINGU strings D. Cowen Deep Core IC : - 8 more strings (480 DOMs) - 10 GeV threshold - 30 Mton volume Digital Optical Module

85. Three grids of lines: Solar magic lines Atmospheric magic lines Interference phase lines

87. E. Kh Akhmedov M. Maltoni A.Y.S. JHEP 05, (2007) 077 [hep-ph/0612285] JHEP 06 (2008) 072 [arXiv:0804.1466] PRL 95 (2005) 211801 arXiv:0506064 unpublished, see M Maltoni talks E. Kh Akhmedov, S Razzaque, A.S. in preparation A.Y.S., hep-ph/0610198. E Kh Akhmedov, A Dighe, P. Lipari, A Y. Smirnov, Nucl. Phys. B542 (1999) 3-30 hep-ph/9808270 Uncertainties of original fluxes Flavor identification Reconstruction of direction Energy resolution Statistics Developments of new detection methods? TITAND? Y. Suzuki High statistics solve the problems

88. Integration averaging averaging and smoothing effects reconstruction of neutrino energy and direction Original fluxes identification of flavor different flavors: e  and  Detection neutrinos and antineutrinos Screening factors (1 - r s 23 2 ) Reduces CP- asymmetry (1 -  e ) (1 –   )

89. Reduces the depth of oscillations interference P( e   ) = s 23 2 |A e3 | 2 Modifies phase  = arg (A 22 A 33 *) E Kh Akhmedov, S Razzaque, A. Y.S. Reduces the average probability P(    ) = 1 – ½ sin 2 2  23 - s 23 4 |A e3 | 2 + ½ sin 2 2  23 (1 - |A e3 | 2 ) cos  P(    ) = ½ sin 2 2  23 - s 23 2 c 23 2 |A e3 | 2 - ½ sin 2 2  23 (1 - |A e3 | 2 ) cos  for hierarchy determination ½ ½

90. P A = |A e3 | 2 N e IH - N e NH ~ (P A - P A ) (1 –   ) [r s 23 2 - (1 –  e )/(1 -   )] Flavor suppression (screening factors) Neutrino - antineutrino factor unavoidable CP asymm etry can be avoided N  IH - N  NH ~ (P  - P  ) (1 –   ) - r -1 (1 –  e ) (P e  - P e  )] Triple suppression   = (   )/(   )

91. E. Kh Akhmedov M. Maltoni A.Y.S. JHEP 05, (2007) 077 [hep-ph/0612285] JHEP 06 (2008) 072 [arXiv:0804.1466] PRL 95 (2005) 211801 [arXiv:0506064] unpublished, see M Maltoni talks. E. Kh Akhmedov, S Razzaque, A. Y. Smirnov JHEP 1302 (2013) 0.82, [1205.7071 [hep-ph]] A.Y.S., hep-ph/0610198. E Kh Akhmedov, A Dighe, P. Lipari, A Y. Smirnov, Nucl. Phys. B542 (1999) 3-30 hep-ph/9808270 Flavor identification Reconstruction of direction Energy resolution + mild technological developments ? TITAND? Y. Suzuki M. Ribordy and A.Y. Smirnov, 1303.0758 [hep-ph] PINGU, ORCA Uncertainties of original fluxes Statistics

92. e   2 nd and 3 rd parametric peaks MSW resonance in core MSW resonance in mantle

93. neutrinos antineutrinos NH – solid IH – dashed x =  - blue x = e - red

94. excluded

95. With and without NSI T. Ohlsson, He Zhang, Shun Zhou, 1303.6130 [hep-ph] ( e   )

97.  A S = 0  - true (experimental) value of phase  f - fit value  P = P(  ) - P(  f )  P = 0 (along the magic lines) (  +  ) = - (  +  f ) + 2  k  (E, L) = - (  +  f )/2 +  k = P int (  ) - P int (  f )  A A = 0 int. phase condition depends on  Interference term:  P = 2 s 23 c 23 |A S | |A A | [ cos(  +  ) - cos (  +  f )] For e   channel:

101. | Effects of 1-3 mixing and sterile neutrino as compared with 2 - mixing case

103. E th = 0.1 TeV S = N(osc.)/N(no osc.)

104. Normal mass hierarchy in the flavor block; m 0 ~ 1 eV |U e4 | 2 |U  | 2 are large enough, so that level crossings are adiabatic Three new level crossings V e - V s = 2 G F (n e – n n /2) Resonance in the antineutrino cannel

105. - dip - wiggles

107.  + n   + h muon track cascade Measurements EEhEEh Reconstruction E = E  + E h E h E      ~ 10 5 events/year E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071  V eff = 14.6 [log(E /GeV )] 1.8 Mt Effective volume