1. Neutrino tomography: Learning about the Earth’s interior using the propagation of neutrinos Neutrino sciences 2005: Neutrino geophysics University of Hawaii at Manoa December 16, 2005 Walter Winter Institute for Advanced Study, Princeton

2. December 16, 2005Neutrino geophysics - Walter Winter2 Contents Introduction Introduction Requirements from geophysics and high energy physics Requirements from geophysics and high energy physics Principles, Applications, Challenges of Principles, Applications, Challenges of –Neutrino absorption tomography –Neutrino oscillation tomography Summary Summary

3. December 16, 2005Neutrino geophysics - Walter Winter3 Neutrino “propagation” tomography Neutrino source Neutrino propagation Neutrino detection Well known flux, flavor composition, etc. Well known propagation model Well known propagation model Propagation depends on matter structure Propagation depends on matter structure Matter structure (partly) unknown Matter structure (partly) unknown Well known detector systematics, X- sections, etc. ? Learn about matter structure Different from geoneutrino approach!

4. December 16, 2005Neutrino geophysics - Walter Winter4 Neutrino propagation models “Standard” “Standard” –Neutrino interactions (CC/NC) leading to attenuation effects –Neutrino interactions (CC/NC) leading to attenuation effects –Three-flavor neutrino oscillations; “ideal energies” (later): Others which are affected by the presence of matter? Others which are affected by the presence of matter? –Mass-varying neutrinos –Non-standard interactions –Matter-induced neutrino decay, …

5. Neutrino tomography: Sources 10 -4 10 -3 10 4 10 3 10 5 10 6 10 710 10 9 10 11 10 8 10 12 keV MeVGeVTeV E [eV] Natural Man-made (flux and flavor composition well known) ? Neutrino oscillations Neutrino absorption

6. Requirements from geophysics? Mantle Core Inner Core Inner core: Solid? Thermal state? Anisotropies? Dynamics?  Least known part (see e.g. Steinle- Neumann et al, physics/0204055) Outer core: Liquid  No seismic s-wave propagation  Less knowledge than mantle??? Local inhomogeneities (for oil etc.): Established methods  Competitor has to be cheap and effective Mantle: Tested very well by seismic waves However: - Uncertainties in 3D models ~ 5% (http://cfauvcs5.harvard. edu/lana/rem/mapview.htm) - Matter density derived by EOS; normal modes? Density of whole Earth: Mass+rot. inertia known  Least information on innermost parts

7. December 16, 2005Neutrino geophysics - Walter Winter7 Requirements from high-energy physics? Assume that there is a possible geophysics application: Assume that there is a possible geophysics application: Usefulness for geophysics Effort for particle physics = additional cost and R&D BALANCE Additional cost NoneLowHigh Use for geophysics LowX-- MediumX?- HighXX? What is the primary purpose of the experiment? Can the geophysics application be added at low additional cost? Use existing data? Do the application in either case!

8. December 16, 2005Neutrino geophysics - Walter Winter8 Neutrino absorption tomography (NAT) Neutrino source Neutrino propagation Neutrino detection - Atmospheric (high E tail) - Cosmic: AGNs, Black holes, Quasars, Pulsars? - TeV neutrino beam? Weak interactions damp initial flux by absorption/deflection/regeneration Weak interactions damp initial flux by absorption/deflection/regeneration  Integrated effect leads to attenuation (different for muon and tau neutrinos) Depends on nucleon density Depends on nucleon density  7% absorbed at 1 TeV (L=2 R E )  Earth opaque (  ) at about 15 TeV - Neutrino telescopes (IceCube, Antares, Nestor etc.) - Moving detectors? Scattered?

9. Overview: Whole-Earth tomography Isotropic flux (cosmic diffuse, atmospheric) TeV-Beam Cosmic point src + Data might be available at no additional cost - Many directions - High precisions? Isotropy of flux no problem (only time dep.) - - Atm. : low stat. (high E) - No cosmic flux obs. yet - Isotropy of flux? - Directional resolution - Build and safely operate a TeV neutrino beam - Moving decay tunnel - Moving detectors - Moving detector or Earth rotation (=IceCube not useful) - No sources obs. yet Refs. Jain, Ralston, Frichter, 1999; Related: Reynoso, Sampayo, 2004; Gonazales-Garcia, Halzen, Maltoni, 2005 De Rujula, Glashow, Wilson, Charpak, 1983; Askar`yan, 1984; Borisov, Dolgoshein, Kalinovskii, 1986 Wilson, 1984; Kuo, Crawford, Jeanloz, Romanowicz, Shapiro, Stevenson, 1994

10. December 16, 2005Neutrino geophysics - Walter Winter10 A TeV neutrino beam Rule of thumb: E ~ 1/10 E p (peak energy) Current measure: LHC E p ~ 7 TeV, E ~ 700 GeV ? ~ 5% absorption at 2 R E, 700 GeV Statistics only: ~ 400 events to see this effect ~ 5,000,000 events to measure density at percent level That may not be unrealistic numbers! Main challenge: Expensive. Is there other physics one needs a TeV neutrino beam for? Example: Sterile neutrino oscillation physics at long baselines for  M 2 ~ 1 eV 2 ? Use neutrino factory? But: Huge muon accelerator, huge storage ring Proton accelerator pEpEp Target , K   e E Max. 4 MW believed today  Limits pot/time x E p Conventional technique to create a beam

11. December 16, 2005Neutrino geophysics - Walter Winter11 TeV neutrino beam: Ideas Several TeV neutrino beam Sound generation by particle shower? Muon production under surface (<200m); detect heavy materials? Muon production in sea water under moving muon detector Use off-axis decetor to measure norm.: E lower, therefore absorption lower Sound detection by microphone array? De Rujula, Glashow, Wilson, Charpak, 1983 (De Rujula, Glashow, Wilson, Charpak, 1983)

12. December 16, 2005Neutrino geophysics - Walter Winter12 NAT: Cosmic diffuse flux ~ 10 to 10000 TeV neutrinos from unresolved cosmic objects detected by km 3 neutrino telescope Example for “low cost” application? Major challenge: Solid angle of the Earth’s core is very small ~ 1% of the neutrino sky seen through the inner core  Flux is small where precision needed Also challenges: angular resolution, Isotropy of flux, … Jain, Ralston, Frichter, 1999 (Jain, Ralston, Frichter, 1999) Useful to resolve degs among seismic models in mantle?

13. December 16, 2005Neutrino geophysics - Walter Winter13 NAT: Summary of challenges Atmospheric (high-E part) (Gonazales-Garcia, Halzen, Maltoni, 2005) The only detected source so far! Example IceCube: Several hundred events at > 10 TeV But: Only O(10) events seen through inner core Required: ~ 17000 for per cent level measurement Atmospheric (high-E part) (Gonazales-Garcia, Halzen, Maltoni, 2005) The only detected source so far! Example IceCube: Several hundred events at > 10 TeV But: Only O(10) events seen through inner core Required: ~ 17000 for per cent level measurement TeV neutrino beam: Feasible? Direction changeable? Cost? Moving detectors? Other applications? TeV neutrino beam: Feasible? Direction changeable? Cost? Moving detectors? Other applications? Cosmic point sources/diffuse flux No detection yet Flux known, or relative measurement? Stable (point source)? Isotropic (diffuse flux)? Backgrounds? Cross sections at >> TeV can only be extrapolated Cosmic point sources/diffuse flux No detection yet Flux known, or relative measurement? Stable (point source)? Isotropic (diffuse flux)? Backgrounds? Cross sections at >> TeV can only be extrapolated

14. December 16, 2005Neutrino geophysics - Walter Winter14 Neutrino oscillation tomography (NOT) Neutrino source Neutrino propagation Neutrino detection “Natural”: - Sun - Supernova - Atmosphere “Man-made”: - Superbeam - factory -  -Beam Three-flavor neutrino oscillations affected by coherent forward scattering in matter (MSW) Three-flavor neutrino oscillations affected by coherent forward scattering in matter (MSW) Depends on electron density; conversion in  depends on Y e : electrons/nucleon ~ 0.5 Depends on electron density; conversion in  depends on Y e : electrons/nucleon ~ 0.5 “Optimal” E determined by Osc. effect large: and Matter effect large: “Optimal” E determined by Osc. effect large: and Matter effect large: Depends on neutrino energy+source: - Water Cherenkov det. - Magnetized iron det. - Many other possibilities

15. December 16, 2005Neutrino geophysics - Walter Winter15 Neutrino oscillations: Two flavors, vacuum Mixing and mass squared difference:  “disappearance”:  “appearance”: Amplitude Frequency Baseline: Source - Detector Energy

16. December 16, 2005Neutrino geophysics - Walter Winter16 Picture of three-flavor oscillations Coupling strength:  13 Atmospheric oscillation: Amplitude:  23 Frequency:  m 31 2 Solar oscillation: Amplitude:  12 Frequency:  m 21 2 Sub- leading effect:  CP Effective two-flavor oscillations: Oscillation name FlavorsParameters Solar (Limit for  13 =0) Atmospheric (Limit for  13 =0) LBL, Reactor ( ) Only upper bound so far

17. December 16, 2005Neutrino geophysics - Walter Winter17 Matter effects in -oscillations (MSW) Ordinary matter contains electrons, but no ,  Ordinary matter contains electrons, but no ,  Coherent forward scattering in matter has net effect on electron flavor because of CC (rel. phase shift) Coherent forward scattering in matter has net effect on electron flavor because of CC (rel. phase shift) Matter effects proportional to electron density and baseline Matter effects proportional to electron density and baseline Hamiltonian in matter: Hamiltonian in matter: Y: electron fraction ~ 0.5 (electrons per nucleon) (Wolfenstein, 1978; Mikheyev, Smirnov, 1985)

18. December 16, 2005Neutrino geophysics - Walter Winter18 Matter effects (two flavors,  const.) Parameter mapping (same form): Vacuum: Matter: Parameter mapping (same form): Vacuum: Matter: “Matter resonance”: In this case: - Effective mixing maximal - Effective osc. frequency min.  = 4.5 g/cm 3 (Earth matter) Solar osc.: E ~ 100 MeV !!! LBL osc.: E ~ 6.5 GeV Resonance energy:

19. December 16, 2005Neutrino geophysics - Walter Winter19 Numerical evaluation for three flavors Evolution operator method: H(  j ) is the Hamiltonian in constant density Note that in general Evolution operator method: H(  j ) is the Hamiltonian in constant density Note that in general  Additional information by interference effects compared to neutrino absorption tomography

20. December 16, 2005Neutrino geophysics - Walter Winter20 Matter profile inversion problem Matter density profileMeasurement (observables) Easy to calculate Generally unsolved Some attempts for direct inversion: Simple models: For instance, only cavity (e.g., Nicolaidis, 1988; Ohlsson, Winter, 2002) Linearization for low densities (e.g., Akhmedov, Tortola, Valle, 2005) Discretization of profile with many parameters: Use non-deterministic algorithms to fit N parameters (genetic algorithms, etc.) (Ohlsson, Winter, 2001) (Ermilova, Tsarev, Chechin, 1988)

21. NOT with solar neutrinos Oscillation phases in matter: Oscillation phases in matter: Theoretical results (sun+supernova) Theoretical results (sun+supernova) - For arriving mass eigenstates,  P (cavity-no cavity) depends on  2, but not  1 - Damping of contributions from remote distances x 2 - Solar neutrinos less sensitive to deep interior of Earth! (~factor 10 suppressed) Statistics issues (sun) Statistics issues (sun) - Change in oscillation probability  P/P < 0.1%; tiny effect - Use rotation of Earth to measure effect of cavity Exposure time (cavity in line of sight sun-detector) 0 < t exp < 24h (at poles) - Detector mass M ~ 130 Mt/t exp [hr] >> 5 Mt (poles) - Challenges: Statistics, area of detectors > cavity, backgrounds - Challenges: Statistics, area of detectors > cavity, backgrounds (Ioannisian, Smirnov, 2003; Ioannisian, Smirnov, 2004; Ioannisian, Kazarian, Smirnov, Wyler, 2004) Solar neutrinos: Â << 1 “Low density medium”

22. 22 NOT Theory: Inversion problem (in “low density medium” = sun+supernovae) Reconstruct matter density profile from day-night regeneration effect: Now use V << 2  (“low density medium”), V L << 1 (L<1700km) and linearize f(  ): (Akhmedov, Tortola, Valle, 2005) Measured as function of E

23. December 16, 2005Neutrino geophysics - Walter Winter23 Low density inversion problem: Challenges Need to know f(  ) for Use, for instance, iteration procedure to reconstruct unknown regions in integral: Need to know f(  ) for Use, for instance, iteration procedure to reconstruct unknown regions in integral: Finite energy resolution “washes out” edges Finite energy resolution “washes out” edges Statistics: ~ 10 Mt detector? Statistics: ~ 10 Mt detector? However: Strongly sensitive to asymmetric profiles! However: Strongly sensitive to asymmetric profiles! (Akhmedov, Tortola, Valle, 2005) (Courtesy E. Akhmedov)

24. 24 Supernova neutrinos and statistics Idea: Compare spectra at D 1 (surface) and D 2 (core shadow) for “snapshot” of the Earth’s interior Idea: Compare spectra at D 1 (surface) and D 2 (core shadow) for “snapshot” of the Earth’s interior Advantage: Advantage: Results: Per cent level measurement of core density requires two Hyper-K-sized detectors (D=10 kpc, E=3 10 53 ergs) Results: Per cent level measurement of core density requires two Hyper-K-sized detectors (D=10 kpc, E=3 10 53 ergs) Challenges: Challenges: –Relies on different temperatures of fluxes: if fluxes equal, no oscillation effect –Deviations from energy equipartition (more electron antineutrinos) unfavorable –~0.2% precision for solar oscillation parameters prerequisite –Some knowledge on flux parameters required since all mass eigenstates arrive; unlikely to be obtained from detection of one flavor only –Matter density uncertainties in mantle might spoil core density extraction (damping of remote structures!) (Lindner, Ohlsson, Tomas, Winter, 2002) High energy tail: strong matter effects compared to solar nus!  2 = 35

25. December 16, 2005Neutrino geophysics - Walter Winter25 Neutrino beams for oscillations Artificial source: Accelerator Often: Near detector to measure X-sections, control systematics, … Far detector Baseline: L ~ E/  m 2 (osc. length)   ?

26. December 16, 2005Neutrino geophysics - Walter Winter26 Example: Neutrino factory Main purpose: Measure  13,  CP, mass hierarchy, etc. Main purpose: Measure  13,  CP, mass hierarchy, etc. Muon decays in straight sections of storage ring Muon decays in straight sections of storage ring Decay ring naturally spans two baselines, typically ~ 700 – 3000 km Decay ring naturally spans two baselines, typically ~ 700 – 3000 km Technical challenges: Target power, muon cooling, maybe steep decay tunnels Technical challenges: Target power, muon cooling, maybe steep decay tunnels Timescale: 2025? Timescale: 2025? (from: CERN Yellow Report ) (Huber, Lindner, Rolinec, Winter, 2002-2004)

27. December 16, 2005Neutrino geophysics - Walter Winter27 Positional information for single baseline Example: 500 MeV superbeam (20 bins, 10000 events/bin, ~ 10Mt detector?) Assume:  = 1g/cm 3 Cavity at d 0 = 300 km sin 2 2  13 = 0.03 (Ohlsson, Winter, 2002) Size of cavity can be measured ~ +- 50 km Position can be measured +- 100 km NEW!!! Degeneracy can only be resolved by suppressed three-flavor effect For l 0 < ~100 km: Cavity cannot be established

28. December 16, 2005Neutrino geophysics - Walter Winter28 Resolution of structures for single baseline Example: 20 GeV neutrino factory, L=11750 km I=100,000 events in total, ~ factor 10-100 beyond current “typical” numbers, ~ Mt detector? Use genetic algorithm to fit N=14 layers (symmetric profile) Edges at higher CL not resolvable Fluctuations of few hundered km cannot be resolved Show some characteristic examples close to 1s, 2s, 3s contours (14 d.o.f.) (Ohlsson, Winter, 2001) Analytically: One cannot resolve structures smaller than (L osc ) matter Neutrino oscillations are sensitive to average densities on these length scales!

29. December 16, 2005Neutrino geophysics - Walter Winter29 Pure baseline effect! A 1: Matter resonance Density measurements with three flavors (Term 1) 2 (Term 2) 2 (Term 1)(Term 2) Prop. To L 2 ; compensated by flux prop. to 1/L 2 (Cervera et al, 2000; Freund, 2001; Akhmedov et al, 2004)

30. December 16, 2005Neutrino geophysics - Walter Winter30 Term 1: Depends on energy; can be matter enhanced for long L; sharp drop off the resonance Term 1: Depends on energy; can be matter enhanced for long L; sharp drop off the resonance  Very sensitive to density! Term 2: Always suppressed for long L; zero at “magic baseline” (Huber, Winter, 2003) Term 2: Always suppressed for long L; zero at “magic baseline” (Huber, Winter, 2003)  Term 2 always suppresses CP and solar terms for very long baselines  Matter density measurement relatively correlation-free for large  13 Correlations with osc. Parameters? (  m 31 2 = 0.0025,  =4.3 g/cm 3, normal hierarchy) (Fig. from hep-ph/0510025)

31. December 16, 2005Neutrino geophysics - Walter Winter31 Core density measurement: Principles  Idea: Measure Baseline- averaged density:  Equal contribution of innermost parts. Measure least known innermost density!  Use “standard neutrino factory” E  = 50 GeVE  = 50 GeV Running time: 4 years in each polarityRunning time: 4 years in each polarity Detector: 50 kt magnetized iron calorimeterDetector: 50 kt magnetized iron calorimeter 10 21 useful muon decays/ year (~4 MW)10 21 useful muon decays/ year (~4 MW) 10% prec. on solar params10% prec. on solar params Atmospheric parameters best measured by disapp. channelAtmospheric parameters best measured by disapp. channel (for details: Huber, Lindner, Winter, hep-ph/0204352) (Winter, 2005)

32. December 16, 2005Neutrino geophysics - Walter Winter32 Core density measurement: Results First: consider “ideal” geographical setup: Measure  IC (inner core) with L=2 R E First: consider “ideal” geographical setup: Measure  IC (inner core) with L=2 R E Combine with L=3000 km to measure oscillation parameters Combine with L=3000 km to measure oscillation parameters Key question: Does this measurement survive the correlations with the unknown oscillation parameters? Key question: Does this measurement survive the correlations with the unknown oscillation parameters?  For sin 2 2  13 > 0.01 a precision at the per cent level is realistic  For 0.001 < sin 2 2  13 < 0.01: Correlations much worse without 3000 km baseline (Winter, 2005) (1 , 2 , 3 ,  CP =0, Dashed: systematics only)

33. December 16, 2005Neutrino geophysics - Walter Winter33 Density measurement: Geography Something else than water in “core shadow”? Inner core shadow Outer core shadow (Winter, 2005)

34. December 16, 2005Neutrino geophysics - Walter Winter34 “Realistic geography” … and sin 2 2  13 =0.01. Examples for  IC : There are potential detector locations! There are potential detector locations! Per cent level precision not unrealistic Per cent level precision not unrealistic BNL CERN JHF Inner core shadow (Winter, 2005)

35. December 16, 2005Neutrino geophysics - Walter Winter35 Core density measurement: Summary Survives realistic statistics and unknown oscillation parameters! Survives realistic statistics and unknown oscillation parameters! Potential detector locations for major laboratories Potential detector locations for major laboratories Could be implemented as a side product after a successful NF neutrino oscillation program Could be implemented as a side product after a successful NF neutrino oscillation programChallenges: How expensive? Enough use for geophysics? How expensive? Enough use for geophysics? So far only 1 d.o.f. measurement tested; maybe also time dependence So far only 1 d.o.f. measurement tested; maybe also time dependence sin 2 2  13 larger than about 0.01 necessary sin 2 2  13 larger than about 0.01 necessary Storage ring configuration with steep slopes? Storage ring configuration with steep slopes?But: This might not be the only application for a very long NF baseline: This might not be the only application for a very long NF baseline: –“Magic baseline” to resolve degeneracies: L ~ 7 500 km (Huber, Winter, 2003) –Test of “parametric resonance”: L > 10 665 km (Akhmedov, 1998; Petcov, 1998) –Direct test of MSW effect independent of  13 : L > 5 500 km (Winter, 2004) –Mass hierarchy for  13 =0: L ~ 6 000 km (de Gouvea, Jenkins, Kayser, 2005; de Gouvea, Winter, 2005)

36. December 16, 2005Neutrino geophysics - Walter Winter36 NOT with atmospheric neutrinos? Use magn. iron clorimeter Use magn. iron clorimeter Measure  disappearance Measure  disappearance Compare neutrinos and antineutrinos Compare neutrinos and antineutrinos For instance: Obtain information on composition (Y e ) For instance: Obtain information on composition (Y e ) Challenge: Extreme statistics Challenge: Extreme statistics (Geiser, Kahle, 2002; from poster presented at Neutrino 2002) sin 2 2  13 = 0.08

37. December 16, 2005Neutrino geophysics - Walter Winter37 NOT: Challenges Statistics, statistics, statistics Earth matter effects have to be significant in terms of statistics; major challenge for most applications (e.g., solar day-night effect) Statistics, statistics, statistics Earth matter effects have to be significant in terms of statistics; major challenge for most applications (e.g., solar day-night effect) Knowledge on source Source flux and flavor composition has to be well known or measured “on the surface”; especially challenging for “natural sources”, such as supernova neutrinos Knowledge on source Source flux and flavor composition has to be well known or measured “on the surface”; especially challenging for “natural sources”, such as supernova neutrinos Oscillation parameters Oscillation parameters –Propagation model depends on six oscillation parameters, which are not yet precisely known –Size of  13 determines amplitude of e -  flavor transitions Feasibility/complementarity/competitiveness Relevant geophysics application with reasonable extra-effort? Technically feasible? Feasibility/complementarity/competitiveness Relevant geophysics application with reasonable extra-effort? Technically feasible?

38. December 16, 2005Neutrino geophysics - Walter Winter38 Excursion: Geophysics requirements for “standard” precision measurements For instance: Measure  CP with high precision for large  13 at short L ~ 3 000 km For instance: Measure  CP with high precision for large  13 at short L ~ 3 000 km Acts as “background uncertainty” 5% matter density uncertainty in mantle not acceptable for these measurements! Has to be of the order of 1% (Fig. from Ohlsson, Winter, 2003; see also: Koike, Sato, 1999; Jacobsson et al 2001; Burguet- Castell et al, 2001; Geller, Hara, 2001; Shan, Young, Zhang, 2001; Fogli, Lettera, Lisi, 2001; Shan, Zhang, 2002; Huber, Lindner, Winter, 2002; Ota, Sato, 2002; Shan et al, 2003; Kozlovskaya, Peltoniemi, Sarkamo, 2003; others)

39. December 16, 2005Neutrino geophysics - Walter Winter39 Neutrino tomography: Summary (1) Neutrino absorption tomography Principle: Attenuation effects through neutrino interactions Energies: > TeV Baselines (reconstruction problem): Many Sources: Cosmic, atmosphere, beam? Challenges: Sources, technical Neutrino oscillation tomography Principle: Neutrino oscillations affected by MSW effect Energies: MeV to GeV Baselines (reconstruction problem): at least one Sources: Sun, supernovae, beams, atmosphere? Challenges: Mainly statistics

40. December 16, 2005Neutrino geophysics - Walter Winter40 Neutrino tomography: Summary (2) Some applications at low/no cost Problem: Probably no gain for geophysics Some applications at low/no cost Problem: Probably no gain for geophysics Others quite expensive: How much effort beyond “standard” program? Others quite expensive: How much effort beyond “standard” program? Conceptually different approaches: Reconstruction of profile, local inhomogeneities, core density measurement Conceptually different approaches: Reconstruction of profile, local inhomogeneities, core density measurement What do geophysicists really need? What complementary information is useful? What do geophysicists really need? What complementary information is useful?