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A. Yu. Smirnov

Neutrinos:. race for the mass hierarchy. A. Yu. Smirnov. International Centre for Theoretical Physics, Trieste, Italy. ICTP, December 11, 2012. Content:. Race for the neutrino mass hierarchy. Neutrino oscillograms of the Earth. PINGU, ORCA and mass hierarchy. Searches for CP violation.

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A. Yu. Smirnov

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  1. Neutrinos: race for the mass hierarchy A. Yu. Smirnov International Centre for Theoretical Physics, Trieste, Italy ICTP, December 11, 2012

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

  3. Mass and Mixing spectrum ne nm nt 0.023 Mixing parameters |Um3|2 |Ut3|2 n3 tan2q12 =|Ue2|2 / |Ue1|2 |Ue3|2 sin2q13 = |Ue3|2 tan2q23 = |Um3|2 / |Ut3|2 mass Dm231 |Ue2|2 n2 Dm221 n1 Mixing matrix: |Ue1|2 nf = UPMNSnmass flavor n1 n2 n3 ne nm nt Normal mass hierarchy = UPMNS Dm231 = m23 - m21 Dm221 = m22 - m21 UPMNS = U23Id U13I-d U12

  4. ne Mass hierarchy (ordering) nm nt Normal hierarchy Inverted hierarchy Cosmology w32 n3 n2 bb-decay n1 w32 MASS w31 wij= Dm2ij /2E n2 n1 n3 w31 w31 > w32 w31 < w32 D31 ~ 2D32 S. Petcov M. Piai Oscillations Fourier analysis w Matter effect makes the e-flavor heavier changes two spectra differently

  5. Why it is important? Theory Implications Similar to quark spectrum Quasi-degenerate - symmetry Phenomenology Supernova neutrinos Quark-lepton symmetry Atmospheric neutrinos Unification Flavor symmetries

  6. Race for hierarchy Matter effect Precise measurements on 1-3 mixing of Dm2 Cosmology at reactors Sm Double beta Supernova mee Atmospheric decay neutrinos neutrinos LBL Earth matter effects, energy spectra PINGU experiments NOvA ORCA INO LBNO Sterile neutrinos may help? Neutrino beam Fermilab-PINGU

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

  8. Supernova neutrinos and mass hierarchy Level crossing scheme Inverted hierarchy Normal hierarchy Dm2 (effective) the Earth matter effect – in the neutrino channel only the Earth matter effect in the antineutrino channel only Cossible collective effects may affect this picture

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

  10. ``Set-up'' qn • zenith • angle Q = p - qn Q - nadir angle Oscillations in multilayer medium core-crossing trajectory Q = 33o Applications: flavor-to-flavor transitions - accelerator - atmospheric - cosmic neutrinos core mantle

  11. The earth density profile A.M. Dziewonski D.L Anderson 1981 PREM model Fe inner core Si outer core (phase transitions in silicate minerals) transition zone lower mantle crust upper mantle Re = 6371 km liquid solid

  12. excluded Oscillograms Lines of equal probability excluded M. Maltoni

  13. 1 - Pee MSW-resonance peaks 1-3 frequency excluded Parametric ridges 1-3 frequency Parametric peak 1-2 frequency MSW-resonance peaks 1-2 frequency 5p/2 3p/2 p/2

  14. Graphical representation Equation of motion (= spin in magnetic field) z dP dt = (B x P) ne B P where ``magnetic field’’ vector: 2p lm B = (sin 2qm, 0, cos2qm) nt, P = (Re ne+ nt, Im ne+ nt, ne+ ne - 1/2) x Phase of oscillations y f= 2pt/ lm Pee = ne+ne = PZ+ 1/2 = cos2qZ/2 Probability to find ne

  15. Resonance enhancement in mantle 1 mantle 1 2 mantle 2

  16. Parametric enhancement 1 mantle 2 3 1 4 core 2 mantle core mantle 3 mantle 4

  17. Parametric enhancement of 1-2 mode 1 mantle core 3 4 2 2 mantle 4 3 1

  18. Oscillograms of the Earth • E. Kh. Akhmedov, • Razzaque, • A.S. Oscillations test dispersion relation for neutrinos

  19. Oscillograms contours of constant oscillation probability in energy- nadir (or zenith) angle plane 100 IceCube ne nm , nt NuFac 2800 0.005 CNGS 0.03 IC Deep Core Pyhasalmi 0.10 10 LENF E, GeV MINOS NOvA PINGU-1 HyperK T2K 1 T2KK 0.1

  20. Hierarchy with Huge atmospheric neutrino detectors

  21. Atmospheric neutrinos Enormous physics potential which is not completely explored and largely unused Energy range: 0.01 – 105 GeV Baselines: 0 – 13000 km Matter effects: 3 – 15 g/cm3 Flavor content nue, numu which change with energy and zenith angle Lepton number nu - antinu Achievements: Discovery of neutrino oscillations Measurements of 2-3 mixing and mass splitting Bounds on new physics - sterile neutrinos - non-standards interaction - violation of fundamental symmetries, CPT

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

  23. Suppression of effects different flavors: ne and nm Screening factors (1 - r s232 ) Original fluxes neutrinos and antineutrinos (1 - ke) Reduces CP-asymmetry (1 – km) averaging and smoothing effects reconstruction of neutrino energy and direction Integration averaging Detection identification of flavor

  24. Numbers of events Triple suppression NeIH - NeNH ~ (PA - PA) (1 – km) [r s232 - (1 – k e)/(1 - km)] CP asymmetry Neutrino - antineutrino factor Flavor suppression (screening factors) unavoidable can be avoided PA = |Ae3|2 ka = (s Fa)/(s Fa) NmIH - NmNH ~ (Pmm - Pmm) (1 – km) - r-1(1 – ke) (Pem - Pem)]

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

  26. Precision IceCube Next Generation Upgrade PINGU ORCA Oscillation Research with Cosmics with the Abyss

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

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

  29. mass hierarchy e - e e - e e - m e - m For 2n system normal  inverted neutrino  antineutrino m - m m - m 25

  30. Probabilities antineutrinos neutrinos NH – solid IH – dashed x = m - blue x = e - red

  31. Nu-mu - events E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 nm + n  m + h cascade muon track measurements Em qm Eh reconstruction En = Em + Eh Eh Emqm  qn 105 events/year

  32. Hierarchy asymmetry Oscillations test dispersion relation for neutrinos Quick estimation of significance Stot ~ s n1/2

  33. Cascade events

  34. Nu-tau contribution nt  t  m Background 5 – 7 %

  35. Smearing the distributions E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 Reconstruction of neutrino energy and angle Smearing with Gaussian reconstruction functions characterized by (half) widths ( sE , sq ) sE = A E n sq = B (mp / E n)1/2 Significance S tot = [Sij Sij2 ]1/2 Sij2 = [ NijIH - NijNH]2 / sij2 S = [ Sij Sij2 ] sij2 = NijNH + (f NijNH) 2 Uncorrelated systematic error

  36. Smearing the distributions E. Akhmedov, S. Razzaque, A. Y. S. arXiv: 1205.7071 Reconstruction of neutrino energy and angle Smearing with Gaussian reconstruction functions characterized by (half) widths ( sE , sq ) sE = A E n sq = B (mp / E n)1/2 Significance S tot = [Sij Sij2 ]1/2 Sij2 = [ NijIH - NijNH]2 / sij2 S = [ Sij Sij2 ] sij2 = NijNH + (f NijNH) 2 Systematics reduces significance by factor 2 Uncorrelated systematic error

  37. Smeared asymmetries sE= 0.2E sq ~ 1/E0.5 sq ~ 0.5/E0.5

  38. Smeared asymmetries sE= 2 GeV sq ~ 1/E0.5 sq ~ 0.5/E0.5

  39. Total significance S tot = [Sij Sij2 ]1/2 Improvements of reconstruction of the neutrino angle leads to substantial increase of significance

  40. CP-violation nc = i g0 g2 n + n  nc CP- transformations: applying to the chiral components Under CP-transformations: UPMNS UPMNS * d  - d usual medium is C-asymmetric which leads to CP asymmetry of interactions V  - V Degeneracy of effects: Matter can imitate CP-violation

  41. CP asymmetry Shape does not change the amplitude changes Large significance at low energies

  42. Conclusions 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

  43. Parameter degeneracy Dm231 versus hierarchy q23

  44. CP violation Grid of magic lines and CP domains

  45. CP-violation Due to specific form of matter potential matrix (only Vee = 0) P(nenm) = |cos q23Ae2e id + sin q23Ae3|2 ``solar’’ amplitude ``atmospheric’’ amplitude dependence on d and q23is explicit For maximal 2-3 mixing f = arg (Ae2* Ae3) P(ne nm)d = |Ae2 Ae3| cos (f - d ) P(nm nm)d = - |Ae2 Ae3| cosf cos d P(nm nt)d = - |Ae2 Ae3| sinf sind S = 0

  46. Sensitivity to CP phase d - true (experimental) value of phase df - fit value Interference term: D P = P(d) - P(df) = Pint(d) - Pint(df) For ne nm channel: DP = 2 s23 c23 |AS| |AA| [ cos(f + d) - cos (f + df)] (along the magic lines) AS = 0 AA = 0 D P = 0 (f+d ) = - (f + df) + 2p k int. phase condition f(E, L) = - ( d + df)/2 + p k depends on d

  47. ``Magic lines'' V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. For nmnm channel Pint ~ 2s23c23|AS||AA|cosf cosd • - The survival probabilities is CP-even functions of d • no CP-violation • dependences on phases factorize Dependence on d disappears form magic grid AS = 0 AA = 0 Pint = 0 f= p/2 + p k interference phase does not depends on d Form the phase line grid

  48. Evolution For E > 0.1 GeV CP-violation and 2-3 mixing are excluded from dynamics of propagation Propagation basis ~ nf = U23Idn Id = diag (1, 1, eid ) ne ne ne ne Ae2 nm ~ ~ nm n2 n2 Ae3 ~ ~ nt n3 nt n3 projection propagation projection CP appears in projection only A22 A33 A23 A(nenm) = cosq23Ae2eid + sinq23Ae3 For instance:

  49. ``Magic lines'' V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. For nmnm channel Pint ~ 2s23c23|AS||AA|cosf cosd • - The survival probabilities is CP-even functions of d • no CP-violation • dependences on phases factorize Dependence on d disappears form magic grid AS = 0 AA = 0 Pint = 0 f= p/2 + p k interference phase does not depends on d Form the phase line grid

  50. ``Magic lines" V. Barger, D. Marfatia, K Whisnant P. Huber, W. Winter, A.S. Explicitly P(ne nm) = c232|Ae2|2 + s232|Ae3|2 + 2s23c23|Ae2||Ae3|cos(f + d) f = arg (Ae2 Ae3*) Pint = 2s23c23|Ae2||Ae3|cos(f + d) Dependence on d disappears, interference term is zero if Ae2 = 0 - solar magic lines Pint = 0 - atmospheric magic lines Ae3 = 0 - interference phase condition (f+d ) = p/2 + 2p k f(E, L) = - d + p/2 + p k depends on d

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