What is not known about ‘s …

1. What is not known about ‘s … • Whatisthemasssequenceof eigenstates (hierarchy)? • Complexphase in mixingmatrix (CP violation)? • Can leptonic CP violationexplainbaryon-antibaryonasymmetry? • Istheneutrino a Dirac orMajorana (3 phases!) particle ? • Isthere a „sterile“ heavy right-handedneutrino? • Howcanmixingmatrixandmassesbeexplained, whyarethey • different thanthoseofquarks?

2. … open questions in neutrino physics inverted hierarchy normal hierarchy Unclear where mass gap will be … Difficult to measure … … supernovae !  content  content e content Flavor eigenstate

3. Expected SN rate distribution (IceCube) Lawrence Livermore model, 10 kpc distance (~ distance to center) normal neutrino hierarchy inverted neutrino hierarchy Totani et al. Astrop. Phys. 496, 216 (1998) preliminary clear differences in model shapes for normal and inverted hierarchy!

4. MSW-Effekt Mikheyev, Smirnow, Wolfenstein Known from solid state physics: Particles can gain „effective mass“ in presence of interactions … Scattering on electrons: W – exchange only possible for e, forward scattering dominates Electrons see additional potential Gives larger effective mass!

5. …MSW-Effekt … the idea Energy of echanges in presence of potential V: And so does mass: e 3M  2M Mass m Mass m  1M resonance conditions Electron density Ne … adiabatic transition between neutrino flavors one resonance in sun, two resonances in supernovae bound to occur ! Earth has ~ constant density Electron density Ne

6. … MSW/collective effects Things can be much more complicated …. • not necessarily adiabatic • Collective neutrino oscillation as one quantum state due to  interactions … • Dependence on assume neutrino mass hierarchy … Important for supernovae, as neutrino density extremely high !!

7. Distortions of energy spectra Examples for collective oscillations in supernovae Note that neutrinos leave star in mass eigenstates, no vacuum oscillations !!!!

8. Neutrino Interaction and Detection • Neutrino cross sections from lowest to highest energies • Neutrino interactions and detection methods • Lepton propagation • Electrons • Muons • Tauons • Muon track reconstruction • Effective area and rate determination • Dealing with small number of events • Background processes

9. low energy neutrino cross sections important for solar and supernova neutrinos ! Charged current cross section in water / ice: • inverse beta decay is dominant σ~ E2 , 1% uncertainty • difficult to detect eneutrinos in ice, dominated by electron scattering σ~E ! • 16-O cross sections highly uncertain (factor 2?), strong rise with energy

10. e elastic scattering Three diagrams contribute in lowest order: cross sections differ (sin2W, contributing diagrams): important for n oscillations in matter!

11. Intermediate neutrino cross sections GENIE Universal, Object-Oriented Neutrino Generator Nucl. Instr. Meth. 614,1, 2010 ~ E Exclusive cross sections not very well known .. ..relevant e.g. oscillation studies, Wimps, etc …

12. Neutrino cross sections • Obviousquestions: • Whyisthere a kink? • Whyare neutral currentcross • sectionslower? • Whyare anti-crosssections • lower? • Whyisthere a resonance? neutral current charged current e + e- W-  laboratory energies

13. Neutrino deep-inelastic scattering • Dominant processes for neutrino energies above ~100 GeV: • Fragments of nucleon form new hadrons  “hadronisation” • Reactions investigated in detail in particle physics experiments … • neutrino reactions up to fixed target energy of 1 TeV • structure functions (e.g. HERA) up to centre-of-mass energies of ~300 GeV equivalent fixed target energy of 50 TeV

14. 3 valence quarks Many virtual quark anti-quark pairs (sea quarks) Many gluons (carriers of the strong force) Content of the nucleon … only quarks and anti-quarks interact with neutrinos

15. GF = Fermi constant = 1.17 x 10-5 GeV-2 xd(x) = momentum distribution of d-type quarks xu(x) = momentum distribution of u-type anti-quarks Incoherent sum of elastic nq and nq cross sections! Neutrino deep-inelastic cross section x : fraction of nucleon momentum carried by quark (0<x<1)y : fraction of neutrino momentum transferred to X (0<y<1)Q2 = xys = -(4-momentum of W/Z)2 Charged current cross section for nl+pl-+X (lowest order, s < 104 GeV2):

16. Why are σ(q) and σ(q) different? weak interaction couples to left-handed fermions .. neutrinohashelicity -½ quarkprefershelicity -½ spin 0 systemhasno directionalpreference spinneedstobeconserved! gives y-dependenceand reduces anti- crosssection ..

17. … in more detail … before scattering after scattering after scattering forbidden

18. valence and sea-quark distributions example: valence u-quarks and sea-quarks at small and large Q2 valencequarks „dwarfed“ byseaquarksat large Q2  differencesvanish (plot) experimentallymeasured down to x ~ 10-4 extrapolationto x=0 difficult but importantat high energies  uncertainties! (plot)

19. effect is energy dependent … • at low energies valence- • quarks important: • no symmetry in quarks & anti-quarks charged current neutral current • at high energies sea-quarks • dominate reactions: • symmetric in quarks and anti-quarks

20. Uncertainty due to sea quarks N.Armesto et al., Phys.Rev.D77(2008)013001 = 10-40 m2 pointand diffuse searches GZK neutrinos for E<40TeV, s~E ; for larger E, roughly s~E0.4  why?

21. Effect of the W propagator at laboratory energies > 40 TeV, Fermi theory does not hold any more …  effect of exchange of real massive W needs to be accounted for important x and Q2ranges: not theregimeof HERA.. reasonablecrosssectionapproximation:

22. Glashow resonance resonant production of real W- from hitting ambient electrons: neutrino laboratory energy: 6.7 PeV = 6.7 x 1015 eV resonance width: 130 TeV peak cross section: 5 x 10-35 m2

23. tau interaction muon track hadronic shower hadronic shower electromagn. shower hadronic shower hadronic shower Neutrino Interaction Signatures  

24. e, μ, τ What will happen in the Detector? electron, muon or tauon narrow Cherenkov cone for muons … some widening due to bremsstrahlung Long shower for very high energy electrons (LPM - effect) hadronic part usually neglected in reconstruction … for neutral current interactions: only hadronic cascade available! Let‘s look at the propagation of electrons, muons and tauons …

25. Electron interactions and propagation Processesleadingtoenergylossofelectrons: LPM suppression

26. 100 MeV 25 GeV formation zone (2μm) LPM-Effect Landau Pomeranchuk Migdal Prediction: Bremsstrahlung suppression at very high energies and target densities Reason: Uncertainty Principle: Bremsstrahlung not a local effect! If something happens in „formation zone“ (e.g. multiple scattering):  photon radiation supressed ! Ice Suppression Rock + di-electric effects …

27. Muon energy loss dE/dx  a + b E

28. … muon energy loss pair creation dominant! bremsstrahlung 1/E dE/dx photonuclear

29. muon range average range Rin ice: R

30. Moliere-Scattering deviation from straight track for one hundert 10 TeV muons: verysmalleffectformuons, canbeneglected! (Not so forelectrons …)

31. Angle between muon and neutrino average for high energies: angle= 0.7o / E[TeV]0.6 angle (μ,) degrees 0.7 TeV 1o 20 TeV 0.1o 0.01o 320 TeV pmuon MeV … depends somewhat on kinematic cuts …

32. Muon and electron topologies High energies O(100-10000 GeV) Low energies O(10-100 MeV)

33. tau neutrino interactions high energy: virtual background-freesourceofextraterrestrialneutrinos (1:1:1) smallatmosphericcontribution due tocharmdecays  many (20 GeV) fromoscillationsover Earth diameter Tau neutrinos will regenerate in Earth  lessabsorption !

34. a „double bang“ event … will be very rare … low ionization by   no bremsstrahlung !

35. Muon Infinite track reconstruction perpendiculardistance DOM-track:  900  time atdistanceofclostestapproch: expectedflight time ofphoton: cherenkov angle =C=acos(1/(np ())) photon velocity cice=c/(ng() arbitrarystartingpoint smalldifferencebetweenphaseandgroupvelocity O(1 - 5 %) [μm]

36. …more precise Number of Cherenkov photons: Cherenkov angle:  track nuclear process  muon energy bremsstrahlung  muon energy pair creation  muonenergy ionization adds 8% to Cherenkov radiationfrommuons While muon Cherenkov radiation is at fixed angle, widening by showers/ionization

37. … angular distribution Cherenkov light ~ constant for E > 1 GeV nominal Cherenkov angle

38. Photon radiation from muon in IceCube

39. Background processes • Atmospheric neutrinos • Atmospheric muons

40.  production: p and K decays The lightest charged mesons can only decay through weak interaction: p+ = |ud>  µ+ + nµ and p- = |du>  µ- + nµ(~100%) K+ = |us>  µ+ + nµ and K- = |su>  µ- + nµ( 63%) Kinematics: En(from p) < 0.25 x EpEn(from K) < 0.78 x EK Above ∼ 100GeV, interaction length of  and K in atmosphere shorter than their decay length   energy spectrum dN/dE ∼ E−3.7 Muons co-produced with neutrinos may decay and produce further neutrinos: µ+  e+ + nµ + ne and µ- e-+ nµ + ne at ∼ 1TeV the ne / nµ flux < 0.1 because ne flux dominated by K0L decays

41. with oscillation w/o oscillation extraterrestric neutrinos =K E-2.2 Theoretical  fluxes horizontal atmospheric muons energy dependent oscillations only important below O(50 GeV)

42. much fewer electron and tau neutrinos Tau neutrinos only from charm decays …

43. Rejection of atmospheric muons ~ average depth of detectors background compared to signal IceCube IceCube 1900 m Antares 2200 m Km3Net Km3Net 3500 m cos(θ) IceCube Veto „critical point“ (μ flux): IceCube: cos (θ)~ 0.15 Km3Net: cos (θ)~ 0.25 I3-Veto: cos (θ)~ 0.40 (smaller eff. V)

44. Can one further reduce atmospheric ‘s? Schönert et al., Phys. Rev. D.79(4):043009, 2009, arXiv:0812.4308 usedowngoingneutrinocandidates!!!! atmosphericneutrinosfrompionandkaon decaysmostlyaccompaniedbymuon … canvetomuonfrompionswithsurface detector (energythreshold!) or in „not toodeep“ detector IceCubecan in principlevetodowngoing muonsabove 10 TeV …

45. Nice studies with atmospheric muons …Icecube sees ~ >1010 atmospheric muons per year ... 13 σ 7 years Milagro 2.2 1011 events 1 TeV median energy 1 year IceCube 40 2 1010 events 20 TeV median energy • Reason für structures unclear • nearby cosmic accelerator? Structure of local magnetic field? • can study energy and time dependence …

46. Moon shadow

47. Atmospheric influence Detailed studies of atmospheric parameters in 15-30 km height Excellent agreement with climate models Possibly learn about kaon/charm contribution

48. Additional slides

49. Dirac versus Majorana neutrinos • In the Standard Model, all fermions are described by Dirac spinors: • fermions and anti-fermions are different • Neutral fermions (= neutrinos) could in principle be their own anti-particles: • described by Majoranaspinors • This would allow for lepton-number violating processes such as neutrino-less double-beta decay (0nbb) • Strong theoretical interest: • Neutrino masses require either a Dirac (nR) or a Majoranan • Combining both mass terms might “naturally” explain why neutrino masses are so small • No obvious relation to neutrino astronomy  …

50. … neutrino hierarchy KATRIN experiment: limit on absolute e (=)mass