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Inclusive fluxes

Inclusive fluxes. Solution of cascade equations with power-law boundary conditions Protons Muons and neutrinos. Boundary conditions & scaling. Air shower, primary of mass A, energy E 0 : N(X=0) = A d (E- E 0 /A) for nucleons N(X=0) = 0 for all other particles

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Inclusive fluxes

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  1. Inclusive fluxes Solution of cascade equations with power-law boundary conditions Protons Muons and neutrinos Tom Gaisser CORSIKA school

  2. Boundary conditions & scaling • Air shower, primary of mass A, energy E0 : • N(X=0) = A d (E- E0 /A) for nucleons • N(X=0) = 0 for all other particles • Uncorrelated flux from power-law spectrum: • N(X=0) = fp(E) = K E-(g+1) • ~ 1.7 E-2.7 ( cm-2 s-1 sr-1 GeV-1 ), top of atmosphere • Fji( Ei,Ej) has no explicit dimension, F  F(x) • x = Ei/Ej &∫…F(Ei,Ej) dEj / Ei  ∫…F(x) dx / x2 • Small scaling violations from mi, LQCD ~ GeV Tom Gaisser CORSIKA school

  3. Inclusive flux EAS Tom Gaisser CORSIKA school

  4. Example: flux of nucleons Approximate: l ~ constant, leading nucleon only Separate X- and E-dependence; try factorized solution, N(E,X) = f(E) g(X): Separation constant LN describes attenuation of nucleons in atmosphere Uncorrelated fluxes in atmosphere Tom Gaisser CORSIKA school

  5. Evaluate LN: Flux of nucleons: K fixed by primary spectrum at X = 0 Nucleon fluxes in atmosphere Tom Gaisser CORSIKA school

  6. Account for p  n CAPRICE98 (E. Mocchiutti, thesis) Comparison to proton fluxes Tom Gaisser CORSIKA school

  7. Protons Helium Primary spectrum • Largest source of overall uncertainty • 1995: experiments differ by 50% (see lines) • Present: AMS, BESS within 5% for protons • discrepancy for He larger, but He only 20% of nucleon flux • CAPRICE lower by 15-20% Tom Gaisser CORSIKA school

  8. Primary spectrum: new standard? • Fit BESS and AMS • Include small contributions from heavy elements • Extrapolate to high E • Use m and n measurements as constraints Tom Gaisser CORSIKA school

  9. p p m e ne nm Atmospheric neutrino beam • Up-down symmetric except for geomagnetic effects • One detector for both • long baseline • short baseline • 1 < L/E < 105 km/GeV • nm/ne ~ 2 for En < GeV D. Ayres, A.K. Mann et al., 1982 Tom Gaisser CORSIKA school Also V Stenger, DUMAND, 1980

  10. Pathlength distribution Tom Gaisser CORSIKA school

  11. 0.3 GeV 1 GeV Pathlength (3D) Tom Gaisser CORSIKA school

  12. e (or m) ne (or nm) nm Classes of atmospheric n events m Contained (any direction) n-induced m (from below) Tom Gaisser CORSIKA school

  13. Super-K atmospheric neutrino data (hep-ex/0501064) CC ne CC nm 1489day FC+PC data + 1646day upward going muon data Tom Gaisser CORSIKA school

  14. Fit 2 flavor mixing: sin2q23 = 1.0 dm2 = 2.1x10-3 eV2 38 parameters represent uncertainties in flux of atmospheric neutrinos Super-K fits Tom Gaisser CORSIKA school

  15. nm-induced upward m Super-KAMIOKANDE MACRO Tom Gaisser CORSIKA school

  16. High-energy n in Super-K • In Super-K fit, primary spectrum shifts: • Overall normalization up 11% • Slope < 100 GeV changes: -2.74  -2.71 • Slope > 100 GeV changes: -2.71  -2.66 • K/p decreases by 6% • Can we use Super-K measurements (together with muon measurements) to constrain extrapolation of neutrino spectrum to high energy? • Work in progress with P. Lipari, T. Stanev & G. Barr Tom Gaisser CORSIKA school

  17. Overview of the calculation Tom Gaisser CORSIKA school

  18. Neutrino response to primary spectrum Primary energy / nucleon Neutrino energy Tom Gaisser CORSIKA school

  19. /nucleon) All-nucleon spectrum Tom Gaisser CORSIKA school

  20. n = nm + nm Analytic approximations for E>10 GeV Similar forms for muons but … Zpm = 0.67 Tom Gaisser CORSIKA school

  21. Atmospheric n-induced m QGSjet 0.167 0.081 0.032 0.028 0.0047 0.0032 No oscillations With oscillations Paolo Lipari calculation with standard Z-factors Tom Gaisser CORSIKA school

  22. ----TG calculation, Primary spectrum: N(E) = 1.7 E-2.70 Agrawal et al., PRD53 (1996) 1314 Lipari, standard Z-factors, Primary spectrum: N(E) = 1.75 E-2.71 Vertical muon flux Tom Gaisser CORSIKA school

  23. vertical 60 degrees Importance of kaons at high E • Importance of kaons • main source of n > 100 GeV • p  K+ + L important • Charmed analog important for prompt leptons at higher energy Tom Gaisser CORSIKA school

  24. Differences in kaon production Tom Gaisser CORSIKA school

  25. A C B C/A B/A Comparison of 3 calculations used by Super-K Y. Ashi et al. (Super-K Collaboration) hep-ex/0501064 Tom Gaisser CORSIKA school

  26. Comparison of n flux calculations: Importance of K at high energhy A B C Tom Gaisser CORSIKA school

  27. n / anti-n ratios Tom Gaisser CORSIKA school

  28. histogram : NUSIM histogram : CORSIKA line : Lipari dots: AMANDA-II data line : Bartol Unfolded neutrino energy spectrum (2000) line : Honda ~x2 atmospheric neutrinos Paolo Desiati can we use AMANDA-II atmospheric neutrino data to probe these uncertainties ? E3·dN/dE (cm-2 s-1 sr-1GeV2) Log10(Eν) CORSIKA ~ - 30:50% than NUSIM/Lipari Tom Gaisser CORSIKA school

  29. Calibration with atmospheric n • MINOS, etc. • Neutrino telescopes • Example*** of nm / ne • flavor ratio • angular dependence ***Note: this is maximal effect: horizontal = 85 - 90 deg in plots Tom Gaisser CORSIKA school

  30. Calibration using ~universal m energy spectra at depth See D Chirkin et al. for application to calibrating Nhit in AMANDA Tom Gaisser CORSIKA school

  31. Plot shows sum of neutrinos + antineutrinos Possible E-2 diffuse astrophysical spectrum (WB bound / 2 for osc) nm ne Current AMANDA upper limit 2.6 x 10-7 GeV/cm2 sr s Solar n RPQM for prompt n Bugaev et al., PRD58 (1998) 054001 Slope = 2.7 Prompt m Slope = 3.7 Global view of atmospheric n spectrum Tom Gaisser CORSIKA school

  32. W-B flux accounting for oscillations Diffuse signal vs charmed background in IceCube E-2 “signal” spectrum: E2dN/dE=10-7 GeV/cm2sr s IceCube Collaboration J. Ahrens et al., Astropart.Phys. 20 (2004) 507-532 Tom Gaisser CORSIKA school

  33. Concluding comments • Discovery of neutrino oscillations depends on measured ratios; therefore robust • Super-K fits suggests relatively hard spectrum • Z-factors “explain” differences of calculations • Uncertainty in level of charm production limits sensitivity to diffuse astrophysical neutrinos • Tau-neutrinos (and cascades) important tags • nm : ne : nt ~ 1 : low : lower (high energy atmos.) • ~ 1 : 1 : 1 for astrophysical Tom Gaisser CORSIKA school

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