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A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy ICTP, December 11, 2012

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Race for the neutrino mass hierarchy Neutrino oscillograms of the Earth Searches for CP violation PINGU, ORCA and mass hierarchy E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 v.5

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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 0.023

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e 2 1 1 2 3 3 MASS 32 ij = m 2 ij /2E D 31 ~ 2D 32 Inverted hierarchyNormal hierarchy Oscillations 31 Cosmology 31 32 31 > 32 31 < 32 makes the e-flavor heavier changes two spectra differently Fourier analysis S. Petcov M. Piai Matter effect -decay

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Quark-lepton symmetry Unification Flavor symmetries Quasi-degenerate - symmetry Similar to quark spectrum Supernova neutrinos Atmospheric neutrinos

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Earth matter effects, energy spectra NOvA Neutrino beam Fermilab-PINGU Sterile neutrinos may help? LBNO

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MSW flavor conversion inside the star inside the star Propagation in vacuum Oscillations inside the Earth Collective flavor trasformation Collective flavor trasformation Shock wave effect on conversion Shock wave effect on conversion

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Normal hierarchy Inverted hierarchy Level crossing scheme m 2 (effective) the Earth matter effect in the antineutrino channel only the Earth matter effect – in the neutrino channel only Cossible collective effects may affect this picture and mass hierarchy

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

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core mantle flavor-to-flavor transitions Oscillations in multilayer medium - nadir angle core-crossing trajectory -zenith angle = 33 o - accelerator - atmospheric - cosmic neutrinos Applications:

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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

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excluded M. Maltoni excluded Lines of equal probability

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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

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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)

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mantle 1 2 12

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core mantle mantle core mantle 1 2 3 4 1 2 3 4

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core mantle 1 2 3 4 3 2 4 1

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

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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 Pyhasalmi

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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 Enormous physics potential 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

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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 M Maltoni talks, unpublished E. Kh Akhmedov, S Razzaque, A.S. arXiv: 1205.7071 A.Y.S., hep-ph/0610198. E Kh Akhmedov, A Dighe, P. Lipari, A Y. S., Nucl. Phys. B542 (1999) 3-30 hep-ph/9808270 Uncertainties of original fluxes Flavor identification Reconstruction of direction Energy resolution Low statistics Developments of new detection methods? TITAND? Y. Suzuki High statistics will solve the problems

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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 – )

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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 = ( )/( )

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Oscillation physics with Huge atmospheric neutrino detectors ANTARES DeepCore Oscillations at high energies 10 – 100 GeV in agreement with low energy data no oscillation effect at E > 100 GeV Ice Cube Oscillations 2.7

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Precision IceCube Next Generation Upgrade Oscillation Research with Cosmics with the Abyss

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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

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20 new strings (~60 DOMs each) in 30 MTon DeepCore volume Few GeV threshold in inner 10 Mton volume Existing IceCube strings Existing DeepCore strings New PINGU-I strings PINGU v2 125 m Denser array Energy resolution ~ 3 GeV

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normal inverted neutrino antineutrino For 2 system e - e e - 25

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

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+ n + h muon track cascade measurements EEhEEh reconstruction E = E + E h E h E 10 5 events/year E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071

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Oscillations test dispersion relation for neutrinos Quick estimation of significance S tot ~ s n 1/2

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Background 5 – 7 %

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S = [ ij S ij 2 ] Smearing with Gaussian reconstruction functions characterized by (half) widths = A E E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 ) = B (m p / E ) 1/2 Reconstruction of neutrino energy and angle Significance S tot = [ ij S ij 2 ] 1/2 S ij 2 = [ N ij IH - N ij NH ] 2 / ij 2 ij 2 = N ij NH + (f N ij NH ) 2 Uncorrelated systematic error

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S = [ ij S ij 2 ] Smearing with Gaussian reconstruction functions characterized by (half) widths = A E E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 ) = B (m p / E ) 1/2 Reconstruction of neutrino energy and angle Significance S tot = [ ij S ij 2 ] 1/2 S ij 2 = [ N ij IH - N ij NH ] 2 / ij 2 ij 2 = N ij NH + (f N ij NH ) 2 Uncorrelated systematic error Systematics reduces significance by factor 2

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~ 1/E 0.5 = 0.2E ~ 0.5/E 0.5

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~ 1/E 0.5 = 2 GeV ~ 0.5/E 0.5

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S tot = [ ij S ij 2 ] 1/2 Improvements of reconstruction of the neutrino angle leads to substantial increase of significance

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Under CP-transformations: c CP- transformations: c = i 0 2 + applying to the chiral components U PMNS U PMNS * - V - V usual medium is C-asymmetric which leads to CP asymmetry of interactions Degeneracy of effects: Matter can imitate CP-violation

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

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Determination of the 1-3 mixing has given start of the race for the neutrino mass hierarchy Mass hierarchy: important implications for phenomenology and theory Dedicated new experiments to determine the hierarchy: LBL accelerator, reactor, INO magnetized ICAL, also Supernova neutrinos, double beta decay, cosmology Good chance that multi-megaton scale under ice (water) atmospheric neutrino detectors with low energy threshold (PINGU, ORCA) will be the first. Intensive study of capacity of these detectors is under way

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m 2 31 hierarchy versus 23

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Grid of magic lines and CP domains

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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

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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:

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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 V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. form magic grid

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e e f U 23 I I = diag (1, 1, e i ) e e ~ Propagation basis ~ ~ ~ ~ projection propagation A( e ) = 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

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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 V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. form magic grid

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A e2 = 0 P int = 0 - solar magic lines ( + ) = /2 + 2 k (E, L) = - + /2 + k A e3 = 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 e2 A e3 *) Dependence on disappears, interference term is zero if V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. - atmospheric magic lines

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Grids do not change with Int. phase line (blue) moves with -change PP P = P( ) - P( f ) = const White: atmospheric Black: solar e

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PP

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PP

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- 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

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

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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

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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

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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).

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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

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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)

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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

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Fig 4

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Fig. 4

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Fig 6

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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)

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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

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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

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Normal hierarchy Inverted hierarchy Level crossing scheme m 23 2 (Atm) = m 23 2 (effective) m 2 (effective) 74

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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

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Fig 7

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Searching for sterile neutrinos

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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 neglecting 1-2 mass splitting

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e 2 nd and 3 rd parametric peaks MSW resonance in core MSW resonance in mantle

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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

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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 32

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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:

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(- 0.7 – 0.8) (- 0.9 - 0.8) (- 1. - 0.9) 50 Mt yr Blue – normal Red – inverted 1 error For different zenith angle bins O. Mena, I Mocioiu, S. Razzaque, arXiv:0803.3044 IceCube Deep core - Effective area – too big - Relation between neutrino and muon energies

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e 2 1 MASS 1 2 3 3 m 2 23 m 2 32 m 2 21 Inverted mass hierarchy Normal mass hierarchy ? ~ Tri-bimaximal mixing 1-3 mixing bi-maximal? tri-maximal FLAVOR m 2 32 = 2.4 x 10 -3 eV 2 m 2 21 = 7 x 10 -5 eV 2 - symmetry?

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Neutrinos (resonance channels): P ee = |U e3 | 2 No earth matter effect Antineutrinos (no resonances): P ee = P E 1e = |U 1e | 2 without Earth matter effect: the Earth matter effect in the antineutrino channel only Disappearance of neutronization peak ~ complete permutation of spectraPartial permutation of spectra: mixed soft spectrum p = 1 - |U e1 | 2 p = 1 - |U e3 | 2 ~1/3

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Neutrinos (L resonance ): = |U 2e | 2 without Earth matter effect P ee = |U e3 | 2 No Earth matter effect Antineutrinos (H - resonance): P ee = P E 2e the Earth matter effect – in the neutrino channel only ~ Complete permutation of spectra p = 1 - |U e2 | 2 Partial suppression of neutronization peak ~ 2/3 Partial permutation: mixed hard spectra p = 1 - |U e3 | 2

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Experiment Parameters Effect Construction Result Cost

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No collective effects

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