NeutrinoNeutrino tomography:tomography: LearningLearning aboutabout thethe Earth’sEarth’s interiorinterior usingusing thethe propagationpropagation ofof neutrinosneutrinos

NeutrinoNeutrino sciencessciences 2005:2005: NeutrinoNeutrino geophysicsgeophysics UniversityUniversity ofof HawaiiHawaii atat ManoaManoa December 16, 2005

WalterWalter WinterWinter InstituteInstitute forfor AdvancedAdvanced Study,Study, PrincetonPrinceton ContentsContents

„ IntroductionIntroduction „ RequirementsRequirements fromfrom geophysicsgeophysics andand highhigh energyenergy physicsphysics „ Principles,Principles, Applications,Applications, ChallengesChallenges ofof –– NeutrinoNeutrino absorptionabsorption tomographytomography –– NeutrinoNeutrino oscillationoscillation tomographytomography „ SummarySummary

December 16, 2005 Neutrino geophysics - Walter Winter 2 NeutrinoNeutrino “propagation”“propagation” tomographytomography

NeutrinoNeutrino NeutrinoNeutrino propagationpropagation NeutrinoNeutrino sourcesource detectiondetection

?

Well known „ Well known propagation model Well known flux, flavor „ Propagation depends on matter structure detector composition, systematics, X- „ Matter structure (partly) unknown etc. sections, etc.

Different from Learn about matter structure geoneutrino approach! December 16, 2005 Neutrino geophysics - Walter Winter 3 NeutrinoNeutrino propagationpropagation modelsmodels

„ “Standard”“Standard” – Neutrino interactions (CC/NC) leading to attenuation effects

– Three-flavor neutrino oscillations; “ideal energies” (later):

„ OthersOthers whichwhich areare affectedaffected byby thethe presencepresence ofof matter?matter? – Mass-varying neutrinos – Non-standard interactions – Matter-induced neutrino decay, …

December 16, 2005 Neutrino geophysics - Walter Winter 4 NeutrinoNeutrino tomography:tomography: SourcesSources Natural

-4 -3 3 4 5 6 7 8 9 10 11 12 10 10 10 10 10 10 10 10 10 10 10 10 E [eV]

keV MeV GeV TeV

Man-made ? (flux and flavor composition well known) Neutrino oscillations Neutrino absorption RequirementsRequirements fromfrom geophysics?geophysics?

Outer core: Liquid Local inhomogeneities (for oil etc.): Established methods ¾ No seismic s-wave ¾Competitor has to be cheap and effective propagation Mantle: Tested very well ¾ Less knowledge by seismic waves than mantle??? However: Inner core: Solid? - Uncertainties in 3D Thermal state? Inner models ~ 5% Anisotropies? Core Dynamics? Core ¾Least known part (see e.g. Steinle- Mantle Neumann et al, physics/0204055) Density of whole Earth: Mass+rot. inertia known (http://cfauvcs5.harvard. edu/lana/rem/mapview.htm) - Matter density derived ¾Least information on innermost parts by EOS; normal modes? RequirementsRequirements fromfrom highhigh--energyenergy physics?physics?

„ Assume that there is a possible geophysics application:

Effort for particle Usefulness for physics = additional geophysics BALANCE cost and R&D

Use existing data? What is the Do the application in either case! Additional cost primary purpose of the experiment? None Low High Low X - - Can the geophysics Use for Use for Medium X ? - application be geophysics added at low High X X ? additional cost?

December 16, 2005 Neutrino geophysics - Walter Winter 7 NeutrinoNeutrino absorptionabsorption tomographytomography (NAT)(NAT) NeutrinoNeutrino NeutrinoNeutrino propagationpropagation NeutrinoNeutrino sourcesource detectiondetection Scattered?

-Atmospheric ν „ Weak interactions damp initial flux by - Neutrino (high E tail) absorption/deflection/regeneration telescopes - Cosmic: ¾Integrated effect leads to attenuation (IceCube, AGNs, Black (different for muon and tau neutrinos) Antares, Nestor etc.) holes, Quasars, „ Depends on nucleon density Pulsars? - Moving „ - TeV neutrino detectors? beam? ¾7% absorbed at 1 TeV (L=2 RE)

¾Earth opaque (νμ) at about 15 TeV December 16, 2005 Neutrino geophysics - Walter Winter 8 Overview:Overview: WholeWhole--EarthEarth tomographytomography Isotropic flux TeV-Beam Cosmic point src (cosmic diffuse, atmospheric)

Data might be available at - Many directions Isotropy of flux no ++ no additional cost - High precisions? problem (only time dep.) - Atm. ν: low stat. (high E) - Build and safely operate a - Moving detector or -- - No cosmic flux obs. yet TeV neutrino beam Earth rotation (=IceCube - Isotropy of flux? - Moving decay tunnel not useful) - Moving detectors - No sources obs. yet - Directional resolution - Moving detectors - No sources obs. yet Refs. Jain, Ralston, Frichter, 1999; De Rujula, Glashow, Wilson, Wilson, 1984; Related: Reynoso, Sampayo, Charpak, 1983; Askar`yan, Kuo, Crawford, Jeanloz, 2004; Gonazales-Garcia, 1984; Borisov, Dolgoshein, Romanowicz, Shapiro, Halzen, Maltoni, 2005 Kalinovskii, 1986 Stevenson, 1994 AA TeVTeV neutrinoneutrino beambeam Conventional „ Rule of thumb: E ~ 1/10 E (peak energy) technique ν p to create a „ Current measure: LHC Proton ν beam Ep ~ 7 TeV, Eν ~ 700 GeV ? „ ~ 5% absorption at 2 R , 700 GeV accelerator νμ E Statistics only: Target <0.1% νe ~ 400 events to see this effect ~ 5,000,000 events to measure pE π, K E p ν density at percent level That may not be unrealistic numbers! Max. 4 MW believed today „ Main challenge: Expensive. Is there other physics one needs a TeV ¾Limits pot/time x Ep neutrino beam for? Example: Sterile neutrino oscillation physics at long baselines for ΔM2 ~ 1 eV2? „ Use neutrino factory? But: Huge muon accelerator, huge storage ring

December 16, 2005 Neutrino geophysics - Walter Winter 10 TeVTeV neutrinoneutrino beam:beam: IdeasIdeas

Sound detection by microphone array? Use off-axis decetor to measure norm.: E Several TeV lower, therefore neutrino absorption lower beam

Sound Muon production generation by under surface Muon production particle shower? (<200m); detect in sea water under heavy materials? moving muon detector (De Rujula, Glashow, Wilson, Charpak, 1983) December 16, 2005 Neutrino geophysics - Walter Winter 11 NAT:NAT: CosmicCosmic diffusediffuse fluxflux

~ 10 to 10000 TeV neutrinos from unresolved cosmic objects detected by km3 neutrino telescope Useful to resolve • Example for “low cost” application? degs among seismic models in mantle? • Major challenge: Solid angle of the Earth’s core is very small ~ 1% of the neutrino sky seen through the inner core ¾Flux is small where precision needed • Also challenges: angular resolution, Isotropy of flux, … (Jain, Ralston, Frichter, 1999)1999

December 16, 2005 Neutrino geophysics - Walter Winter 12 NAT:NAT: SummarySummary ofof challengeschallenges

„ Atmospheric ν (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? „ 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

December 16, 2005 Neutrino geophysics - Walter Winter 13 NeutrinoNeutrino oscillationoscillation tomographytomography (NOT)(NOT) NeutrinoNeutrino NeutrinoNeutrino propagationpropagation NeutrinoNeutrino sourcesource detectiondetection

“Natural”: „ Three-flavor neutrino oscillations affected by Depends on - Sun coherent forward scattering in matter (MSW) neutrino - Supernova „ Depends on electron density; conversion in ρ energy+source:

- Atmosphere depends on Ye: electrons/nucleon ~ 0.5 - Water Cherenkov det. „ “Optimal” Eν determined by “Man-made”: Osc. effect large: and Matter effect large: - Magnetized - Superbeam iron det. - ν factory - Many other - β-Beam possibilities

December 16, 2005 Neutrino geophysics - Walter Winter 14 NeutrinoNeutrino oscillations:oscillations: TwoTwo flavors,flavors, vacuumvacuum MixingMixing andand massmass squaredsquared difference:difference:

Frequency ννα “disappearance”:“disappearance”: Amplitude Baseline: Source - Detector νν “appearance”:“appearance”: β Energy

December 16, 2005 Neutrino geophysics - Walter Winter 15 PicturePicture ofof threethree--flavorflavor oscillationsoscillations

Atmospheric Solar oscillation: Sub-leading oscillation: Amplitude: θ23 Amplitude: θ effect: δ 12 Frequency: Δm 2 CP 2 31 Frequency: Δm21

Coupling strength: θ13 Only upper Effective two-flavor oscillations: bound so far Oscillation name Flavors Parameters

Solar (Limit for θ13=0)

Atmospheric (Limit for θ13=0) LBL, Reactor ( )

December 16, 2005 Neutrino geophysics - Walter Winter 16 MatterMatter effectseffects inin νν--oscillationsoscillations (MSW)(MSW)

„ Ordinary matter contains electrons, but no μ, τ „ Coherent forward scattering in matter (Wolfenstein, 1978; Mikheyev, Smirnov, 1985) 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 MatterMatter effectseffects (two(two flavors,flavors, ρρ const.)const.)

„ ParameterParameter mappingmapping (same(same form):form): Vacuum:Vacuum: Matter:Matter:

“Matter resonance”: In this case: - Effective mixing maximal - Effective osc. frequency min.

Resonance energy: ρ = 4.5 g/cm3 (Earth matter) Solar osc.: E ~ 100 MeV !!! LBL osc.: E ~ 6.5 GeV December 16, 2005 Neutrino geophysics - Walter Winter 18 NumericalNumerical evaluationevaluation forfor threethree flavorsflavors

„ EvolutionEvolution operatoroperator method:method:

H(H(ρρj)) isis thethe HamiltonianHamiltonian inin constantconstant densitydensity

NoteNote thatthat inin generalgeneral

¾ AdditionalAdditional informationinformation byby interferenceinterference effectseffects comparedcompared toto neutrinoneutrino absorptionabsorption tomographytomography

December 16, 2005 Neutrino geophysics - Walter Winter 19 MatterMatter profileprofile inversioninversion problemproblem 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 NOTNOT withwith solarsolar neutrinosneutrinos

„ Oscillation phases in matter: „ Theoretical results (sun+supernova)

- For arriving mass eigenstates, ΔP (cavity-no cavity) depends on Φ2, but not Φ1 - Damping of contributions from remote distances x2 - Solar neutrinos less sensitive to deep interior of Earth! (~factor 10 suppressed) „ Statistics issues (sun) - Change in oscillation probability ΔP/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 < 24h (at poles) - Detector mass M ~ 130 Mt/texp [hr] >> 5 Mt (poles) - Challenges: Statistics, area of detectors > cavity, backgrounds (Ioannisian, Smirnov, 2003; Ioannisian, Smirnov, 2004; Solar neutrinos:  << 1 Ioannisian, Kazarian, Smirnov, Wyler, 2004) “Low density medium” NOTNOT Theory:Theory: InversionInversion problemproblem (in(in “low“low densitydensity medium”medium” == sun+supernovae)sun+supernovae) Reconstruct matter density profile from day-night regeneration effect:

Now use V << 2δ (“low density medium”), V L << 1 (L<1700km) and linearize f(δ):

Measured as function of E

22 (Akhmedov, Tortola, Valle, 2005) LowLow densitydensity inversioninversion problem:problem: ChallengesChallenges „ NeedNeed toto knowknow f(f(δδ)) forfor Use,Use, forfor instance,instance, iterationiteration procedureprocedure toto reconstructreconstruct unknownunknown regionsregions inin integral:integral:

(Courtesy E. Akhmedov) „ FiniteFinite energyenergy resolutionresolution “washes“washes out”out” edgesedges „ Statistics:Statistics: ~~ 1010 MtMt detector?detector? „ However:However: StronglyStrongly sensitivesensitive toto asymmetricasymmetric profiles!profiles! (Akhmedov, Tortola, Valle, 2005) December 16, 2005 Neutrino geophysics - Walter Winter 23 SupernovaSupernova neutrinosneutrinos andand statisticsstatistics

„ Idea: Compare spectra at D1 (surface) and D2 (core shadow) for “snapshot” of the Earth’s interior High energy tail: strong „ Advantage: matter effects compared to solar nus! Δχ2 = 35

„ 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!) (Lindner, Ohlsson, Tomas, Winter, 2002) 24 NeutrinoNeutrino beamsbeams forfor oscillationsoscillations

νβ? Artificial να source: Accelerator Far detector

Often: Near detector Baseline: to measure X- 2 sections, control L ~ E/Δm systematics, … (osc. length)

December 16, 2005 Neutrino geophysics - Walter Winter 25 Example:Example: NeutrinoNeutrino factoryfactory (from: CERN Yellow Report ) „ Main purpose: Measure θ13, δCP, mass hierarchy, etc. „ Muon decays in straight sections of storage ring „ Decay ring naturally spans two baselines, typically ~ 700 – 3000 km

„ 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 PositionalPositional informationinformation forfor singlesingle baselinebaseline Example: 500 MeV superbeam (20 bins, 10000 events/bin, ~ 10Mt detector?)

Assume: ρ = 1g/cm3

Cavity at d0 = 300 km 2 sin 2θ13 = 0.03

Position can be measured +- 100 km NEW!!!

Size of cavity can be Degeneracy can only For l0 < ~100 km: measured ~ +- 50 km be resolved by suppressed Cavity cannot be three-flavor effect established (Ohlsson, Winter, 2002) December 16, 2005 Neutrino geophysics - Walter Winter 27 ResolutionResolution ofof structuresstructures forfor singlesingle baselinebaseline 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) Show some characteristic examples close to 1s, 2s, 3s contours (14 d.o.f.)

Fluctuations of few hundered km cannot be resolved

Edges at higher CL not resolvable

(Ohlsson, Winter, 2001)

osc Analytically: One cannot resolve structures smaller than (L )matter Neutrino oscillations are sensitive to average densities on these length scales! December 16, 2005 Neutrino geophysics - Walter Winter 28 DensityDensity measurementsmeasurements withwith threethree flavorsflavors

Pure baseline effect! A 1: Matter resonance

(Cervera et al, 2000; Freund, 2001; Akhmedov et al, 2004)

(Term 1)(Term 2) Prop. To L2; compensated by (Term 1)2 2 flux prop. to (Term 2) 1/L2 December 16, 2005 Neutrino geophysics - Walter Winter 29 CorrelationsCorrelations withwith oscosc.. Parameters?Parameters?

„ Term 1: Depends on energy; can be matter enhanced for long L; sharp drop off the resonance ¾ Very sensitive to density!

„ Term 2: Always suppressed for long L; zero at “magic baseline” (Huber, Winter, 2003) ¾ Term 2 always suppresses CP and solar terms for very long baselines ¾ Matter density measurement 2 3 relatively correlation-free for large θ13 (Δm31 = 0.0025, ρ=4.3 g/cm , normal hierarchy) (Fig. from hep-ph/0510025)

December 16, 2005 Neutrino geophysics - Walter Winter 30 CoreCore densitydensity measurement:measurement: PrinciplesPrinciples ‰ Idea:Idea: MeasureMeasure BaselineBaseline-- averagedaveraged density:density: ¾ Equal contribution of innermost parts. Measure least known innermost density! ‰ UseUse “standard“standard neutrinoneutrino factory”factory”

• Eμ = 50 GeV • Running time: 4 years in each polarity • Detector: 50 kt magnetized iron calorimeter • 1021 useful muon decays/ year (~4 MW) (Winter, 2005) • 10% prec. on solar params • Atmospheric parameters best measured by disapp. channel (for details: Huber, Lindner, Winter, hep-ph/0204352)

December 16, 2005 Neutrino geophysics - Walter Winter 31 CoreCore densitydensity measurement:measurement: ResultsResults (Winter, 2005) „ First: consider “ideal” geographical setup: Measure ρIC (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? 2 ¾ For sin 2θ13 > 0.01 a precision at the per cent level is realistic 2 ¾ For 0.001 < sin 2θ13 < 0.01:

Correlations much worse (1σ, 2σ, 3σ, δCP=0, Dashed: systematics only) without 3000 km baseline

December 16, 2005 Neutrino geophysics - Walter Winter 32 DensityDensity measurement:measurement: GeographyGeography Something else than water in “core shadow”? (Winter, 2005)

Outer core Inner core shadow shadow

December 16, 2005 Neutrino geophysics - Walter Winter 33 “Realistic“Realistic geography”geography” …… andand sinsin222θθ =0.01.=0.01. ExamplesExamples forfor ρρ :: 13 IC JHF BNL CERN

(Winter, 2005) Inner core shadow „ ThereThere areare potentialpotential detectordetector locations!locations! „ PerPer centcent levellevel precisionprecision notnot unrealisticunrealistic

December 16, 2005 Neutrino geophysics - Walter Winter 34 CoreCore densitydensity measurement:measurement: SummarySummary „ Survives realistic statistics and unknown oscillation parameters! „ Potential detector locations for major laboratories „ Could be implemented as a side product after a successful NF neutrino oscillation program Challenges: „ How expensive? Enough use for geophysics? „ So far only 1 d.o.f. measurement tested; maybe also time dependence 2 „ sin 2θ13 larger than about 0.01 necessary „ Storage ring configuration with steep slopes? But: „ 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 θ13: L > 5 500 km (Winter, 2004) – Mass hierarchy for θ13=0: L ~ 6 000 km (de Gouvea, Jenkins, Kayser, 2005; de Gouvea, Winter, 2005)

December 16, 2005 Neutrino geophysics - Walter Winter 35 NOTNOT withwith atmosphericatmospheric neutrinos?neutrinos? „ UseUse magnmagn.. ironiron clorimeterclorimeter

„ MeasureMeasure ννμ disappearancedisappearance „ CompareCompare neutrinosneutrinos andand

2 antineutrinosantineutrinos sin 2θ13 = 0.08

„ ForFor instance:instance: ObtainObtain informationinformation onon compositioncomposition (Y(Ye)) „ Challenge:Challenge: ExtremeExtreme statisticsstatistics

(Geiser, Kahle, 2002; from poster presented at Neutrino 2002)

December 16, 2005 Neutrino geophysics - Walter Winter 36 NOT:NOT: ChallengesChallenges „ 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 „ Oscillation parameters – Propagation model depends on six oscillation parameters, which are not yet precisely known

– Size of θ13 determines amplitude of νe-νμ flavor transitions „ Feasibility/complementarity/competitiveness Relevant geophysics application with reasonable extra-effort? Technically feasible?

December 16, 2005 Neutrino geophysics - Walter Winter 37 Excursion:Excursion: GeophysicsGeophysics requirementsrequirements forfor “standard”“standard” precisionprecision measurementsmeasurements „ ForFor instance:instance: MeasureMeasure

δδCP withwith highhigh precisionprecision forfor largelarge θθ13 Acts as atat shortshort LL ~~ 33 000000 kmkm “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 NeutrinoNeutrino tomography:tomography: SummarySummary (1)(1)

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

December 16, 2005 Neutrino geophysics - Walter Winter 39 NeutrinoNeutrino tomography:tomography: SummarySummary (2)(2)

„ SomeSome applicationsapplications atat low/nolow/no costcost Problem:Problem: ProbablyProbably nono gaingain forfor geophysicsgeophysics „ OthersOthers quitequite expensive:expensive: HowHow muchmuch efforteffort beyondbeyond “standard”“standard” program?program? „ ConceptuallyConceptually differentdifferent approaches:approaches: ReconstructionReconstruction ofof profile,profile, locallocal inhomogeneitiesinhomogeneities,, corecore densitydensity measurementmeasurement „ WhatWhat dodo geophysicistsgeophysicists reallyreally need?need? WhatWhat complementarycomplementary informationinformation isis useful?useful?

December 16, 2005 Neutrino geophysics - Walter Winter 40