Overview of Atmospheric Neutrino Calculations and High-Energy Interactions

1. Atmospheric neutrinos Primary spectrum Hadronic interactions Fluxes of muons and neutrinos Emphasis on high energy Tom Gaisser

2. 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 at production D. Ayres, A.K. Mann et al., 1982 Tom Gaisser Also V Stenger, DUMAND, 1980

3. Overview of the calculation Tom Gaisser

4. Summary of Atmospheric Neutrino Calculations A Tom Gaisser

5. A C B C/A B/A Comparison of 3 calculations used by Super-K nm + nm • Differences come from • Assumptions about primary spectrum • Treatment of hadronic interactions Y. Ashi et al. (Super-K Collaboration) hep-ex/0501064 Tom Gaisser

6. Flavor ratio at production • r =nm/ne at production sets background for search for effects of solar and s13 mixing • De = P2(r cos2q23 -1) Peres & Smirnov, 2004 •  0 for r = 2, q23=45o • rsub-GeV ~2.04 – 2.1 Tom Gaisser

7. Range of n flux calculations Tom Gaisser

8. 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

9. 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

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

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

12. 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

13. nm-induced upward m Super-KAMIOKANDE MACRO Tom Gaisser

14. 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

15. Neutrino response to primary spectrum Primary energy / nucleon Neutrino energy Tom Gaisser

16. /nucleon) All-nucleon spectrum Tom Gaisser

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

18. 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

19. ----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

20. 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

21. Differences in kaon production Tom Gaisser

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

23. n / anti-n ratios Tom Gaisser

24. 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

25. 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

26. 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

27. 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

28. Concluding comments • Discovery of neutrino oscillations depends on measured ratios; therefore robust • Super-K fits suggests relatively hard spectrum • Air-shower data also suggests hard spectrum • Z-factors “explain” differences of calculations • Uncertainty in level of charm production limits sensitivity to diffuse astrophysical neutrinos Tom Gaisser