Neutrino tomography Learning about the Earths interior using

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 December 16, 2005 Neutrino geophysics - Walter Winter

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

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

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

Neutrino tomography: Sources Natural 10 -4 10 -3 104 ke. V 105 106 Me. V 107 108 109 1010 Ge. V 1012 E [e. V] Te. V ? Man-made (flux and flavor composition well known) 1011 Neutrino oscillations Neutrino absorption

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

Requirements from high-energy physics? n Assume that there is a possible geophysics application: Usefulness for geophysics BALANCE Use existing data? Do the application in either case! Low Use for Medium geophysics High December 16, 2005 Effort for particle physics = additional cost and R&D Additional cost None Low High X - - X ? - X X ? Neutrino geophysics - Walter Winter What is the primary purpose of the experiment? Can the geophysics application be added at low additional cost? 7

Neutrino absorption tomography (NAT) Neutrino source Neutrino propagation Neutrino detection Scattered? -Atmospheric n n Weak interactions damp initial flux by (high E tail) - Cosmic: AGNs, Black holes, Quasars, Pulsars? - Te. V neutrino beam? absorption/deflection/regeneration ØIntegrated effect leads to attenuation (different for muon and tau neutrinos) n Depends on nucleon density n - Neutrino telescopes (Ice. Cube, Antares, Nestor etc. ) - Moving detectors? Ø 7% absorbed at 1 Te. V (L=2 RE) ØEarth opaque (nm) at about 15 Te. V December 16, 2005 Neutrino geophysics - Walter Winter 8

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

A Te. V neutrino beam Proton accelerator p Conventional technique to create a n beam nm Target <0. 1% ne Ep p, K Max. 4 MW believed today n n n En n ØLimits pot/time x Ep n December 16, 2005 Rule of thumb: En ~ 1/10 Ep (peak energy) Current measure: LHC Ep ~ 7 Te. V, En ~ 700 Ge. V ? ~ 5% absorption at 2 RE, 700 Ge. V Statistics only: ~ 400 events to see this effect ~ 5, 000 events to measure density at percent level That may not be unrealistic numbers! Main challenge: Expensive. Is there other physics one needs a Te. V neutrino beam for? Example: Sterile neutrino oscillation physics at long baselines for DM 2 ~ 1 e. V 2? Use neutrino factory? But: Huge muon accelerator, huge storage ring Neutrino geophysics - Walter Winter 10

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

NAT: Cosmic diffuse flux ~ 10 to 10000 Te. V neutrinos from unresolved cosmic objects detected by km 3 neutrino telescope Useful to resolve degs among seismic models in mantle? • 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 ØFlux is small where precision needed • Also challenges: angular resolution, Isotropy of flux, … December 16, 2005 (Jain, Ralston, Frichter, 1999) 1999 Neutrino geophysics - Walter Winter 12

NAT: Summary of challenges n n n Atmospheric n (high-E part) (Gonazales-Garcia, Halzen, Maltoni, 2005) The only detected source so far! Example Ice. Cube: Several hundred events at > 10 Te. V But: Only O(10) events seen through inner core Required: ~ 17000 for per cent level measurement Te. V 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 >> Te. V can only be extrapolated December 16, 2005 Neutrino geophysics - Walter Winter 13

Neutrino oscillation tomography (NOT) Neutrino source “Natural”: - Sun - Supernova - Atmosphere “Man-made”: - Superbeam - n factory - b-Beam December 16, 2005 Neutrino propagation Neutrino detection n Three-flavor neutrino oscillations affected by Depends on coherent forward scattering in matter (MSW) neutrino n Depends on electron density; conversion in r energy+source: depends on Ye: electrons/nucleon ~ 0. 5 - Water Cherenkov det. n “Optimal” En determined by - Magnetized Osc. effect large: and Matter effect large: iron det. - Many other possibilities Neutrino geophysics - Walter Winter 14

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

Picture of three-flavor oscillations Atmospheric oscillation: Amplitude: q 23 Frequency: Dm 312 Subleading effect: d. CP Coupling strength: q 13 Effective two-flavor oscillations: Oscillation name Solar (Limit for q 13=0) Atmospheric (Limit for q 13=0) LBL, Reactor ( December 16, 2005 Flavors Solar oscillation: Amplitude: q 12 Frequency: Dm 212 Only upper bound so far Parameters ) Neutrino geophysics - Walter Winter 16

Matter effects in n-oscillations (MSW) n n Ordinary matter contains electrons, but no m, t Coherent forward (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) scattering in matter has net effect on electron flavor because of CC (rel. phase shift) Matter effects proportional to electron density and baseline Hamiltonian in matter: Y: electron fraction ~ 0. 5 (electrons per nucleon) December 16, 2005 Neutrino geophysics - Walter Winter 17

Matter effects (two flavors, r const. ) n Parameter mapping (same form): Vacuum: Matter: “Matter resonance”: In this case: - Effective mixing maximal - Effective osc. frequency min. Resonance energy: December 16, 2005 r = 4. 5 g/cm 3 (Earth matter) Solar osc. : E ~ 100 Me. V !!! LBL osc. : E ~ 6. 5 Ge. V Neutrino geophysics - Walter Winter 18

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

Matter profile inversion problem Matter density profile Measurement (observables) Easy to calculate Generally unsolved Some attempts for direct inversion: (Ermilova, Tsarev, Chechin, 1988) • 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) December 16, 2005 Neutrino geophysics - Walter Winter 20

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

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

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

Supernova neutrinos and statistics n n Idea: Compare spectra at D 1 (surface) and D 2 (core shadow) for “snapshot” of the Earth’s interior High energy tail: strong Advantage: matter effects compared to solar nus! Dc 2 = 35 n n Results: Per cent level measurement of core density requires two Hyper-K-sized detectors (D=10 kpc, E=3 1053 ergs) 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!) 24 (Lindner, Ohlsson, Tomas, Winter, 2002)

Neutrino beams for oscillations Artificial source: Accelerator n b? na Far detector Often: Near detector to measure Xsections, control systematics, … December 16, 2005 Baseline: L ~ E/Dm 2 (osc. length) Neutrino geophysics - Walter Winter 25

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

Positional information for single baseline Example: 500 Me. V superbeam (20 bins, 10000 events/bin, ~ 10 Mt detector? ) Assume: r = 1 g/cm 3 Cavity at d 0 = 300 km sin 22 q 13 = 0. 03 Position can be measured +- 100 km NEW!!! Size of cavity can be measured ~ +- 50 km (Ohlsson, Winter, 2002) December 16, 2005 Degeneracy can only be resolved by suppressed three-flavor effect Neutrino geophysics - Walter Winter For l 0 < ~100 km: Cavity cannot be established 27

Resolution of structures for single baseline Example: 20 Ge. V 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) Show some characteristic examples close to 1 s, 2 s, 3 s contours (14 d. o. f. ) Fluctuations of few hundered km cannot be resolved Edges at higher CL not resolvable (Ohlsson, Winter, 2001) Analytically: One cannot resolve structures smaller than (Losc)matter Neutrino oscillations are sensitive to average densities on these length scales! December 16, 2005 Neutrino geophysics - Walter Winter 28

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

Correlations with osc. Parameters? n Term 1: Depends on energy; can be matter enhanced for long L; sharp drop off the resonance Ø Very sensitive to density! n Term 2: Always suppressed for long L; zero at “magic baseline” (Huber, Winter, 2003) Ø Ø Term 2 always suppresses CP and solar terms for very long baselines Matter density measurement relatively correlation-free for large q 13 (Dm 312 = 0. 0025, r=4. 3 g/cm 3, normal hierarchy) (Fig. from hep-ph/0510025) December 16, 2005 Neutrino geophysics - Walter Winter 30

Core density measurement: Principles q Idea: Measure Baselineaveraged density: Ø Equal contribution of innermost parts. Measure least known innermost density! q Use “standard neutrino factory” • • • Em = 50 Ge. V Running time: 4 years in each polarity Detector: 50 kt magnetized iron calorimeter 1021 useful muon decays/ year (~4 MW) 10% prec. on solar params Atmospheric parameters best measured by disapp. channel (Winter, 2005) (for details: Huber, Lindner, Winter, hep-ph/0204352) December 16, 2005 Neutrino geophysics - Walter Winter 31

Core density measurement: Results n n n Ø Ø First: consider “ideal” geographical setup: Measure r. IC (inner core) with L=2 RE Combine with L=3000 km to measure oscillation parameters Key question: Does this measurement survive the correlations with the unknown oscillation parameters? For sin 22 q 13 > 0. 01 a precision at the per cent level is realistic For 0. 001 < sin 22 q 13 < 0. 01: Correlations much worse without 3000 km baseline December 16, 2005 (Winter, 2005) (1 s, 2 s, 3 s, d. CP=0, Dashed: systematics only) Neutrino geophysics - Walter Winter 32

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

“Realistic geography” … and sin 22 q 13=0. 01. Examples for r. IC: BNL JHF CERN (Winter, 2005) There are potential detector locations! n Per cent level precision not unrealistic n December 16, 2005 Neutrino geophysics - Walter Winter Inner core shadow 34

Core density measurement: Summary Survives realistic statistics and unknown oscillation parameters! n Potential detector locations for major laboratories n Could be implemented as a side product after a successful NF neutrino oscillation program Challenges: n How expensive? Enough use for geophysics? n So far only 1 d. o. f. measurement tested; maybe also time dependence n sin 22 q 13 larger than about 0. 01 necessary n Storage ring configuration with steep slopes? But: n This might not be the only application for a very long NF baseline: n – – “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 q 13: L > 5 500 km (Winter, 2004) Mass hierarchy for q 13=0: L ~ 6 000 km (de Gouvea, Jenkins, Kayser, 2005; December 16, 2005 de Gouvea, Winter, 2005) Neutrino geophysics - Walter Winter 35

NOT with atmospheric neutrinos? n n n sin 22 q 13 = 0. 08 n n Use magn. iron clorimeter Measure nm disappearance Compare neutrinos and antineutrinos For instance: Obtain information on composition (Ye) Challenge: Extreme statistics (Geiser, Kahle, 2002; from poster presented at Neutrino 2002) December 16, 2005 Neutrino geophysics - Walter Winter 36

NOT: Challenges n n n 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 Oscillation parameters – Propagation model depends on six oscillation parameters, which are not yet precisely known – Size of q 13 determines amplitude of ne-nm flavor transitions n Feasibility/complementarity/competitiveness Relevant geophysics application with reasonable extra-effort? Technically feasible? December 16, 2005 Neutrino geophysics - Walter Winter 37

Excursion: Geophysics requirements for “standard” precision measurements n For instance: Measure d. CP with high precision for large q 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) December 16, 2005 Neutrino geophysics - Walter Winter 38

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

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