1. Mumbai, August 1, 2005 Tom Gaisser Atmospheric neutrinos Primary spectrum Hadronic interactions Fluxes of muons and neutrinos Emphasis on high energy

2. Mumbai, August 1, 2005 Tom Gaisser Atmospheric neutrino beam Up-down symmetric except for geomagnetic effects One detector for both – long baseline – short baseline 1 < L/E < 10 5 km/GeV  / e ~ 2 for E < GeV at production e  e  p  D. Ayres, A.K. Mann et al., 1982 Also V Stenger, DUMAND, 1980

3. Mumbai, August 1, 2005 Tom Gaisser Overview of the calculation

4. Mumbai, August 1, 2005 Tom Gaisser Summary of Atmospheric Neutrino Calculations Zatsepin, Kuz’minSP JETP 14:1294(1961)Mu Many calculations~ 1965 --- ~19901D D.H. PerkinsAsp.Phys. 2: 249 (1994)Mu Honda, Kajita, Kasahara, MidorikawaPRD 52: 4985 (1995)1DFRITIOF Agrawal, Gaisser, Lipari, StanevPRD 53: 1314 (1996)1DTarget Battistoni et alAsp.Phys 12:315 (2000) Asp.Phys 19:269 (2003) 3DBFLUKA P. LipariAsp.Phys 14:171 (2000)3D V. Plyaskin PL B516:213 (2001) hep-ph/0303146 3D GHEISHA Tserkovnyak et alAsp.Phys 18:449 (2003)3D CALOR-FRITIOF GFLUKA/GHEISHA Wentz et alPRD 67 073020 (2003)3D Corsika: DPMJET VENUS, UrQMD Liu, Derome, BuénerdPRD 67 073022 (2003)3D Favier, Kossalsowski, ViallePRD 68 093006 (2003)3DGFLUKA Barr, Gaisser, Lipari, Robbins, StanevPRD 70 023006 (2004)3DCTarget Honda, Kajita, Kasahara, MidorikawaPRD 64 053011 (2001) PRD 70 043008 (2004) 3DDPMJET A

5. Mumbai, August 1, 2005 Tom Gaisser Comparison of 3 calculations used by Super-K Differences come from –Assumptions about primary spectrum –Treatment of hadronic interactions ACBACB C/A B/A Y. Ashi et al. (Super-K Collaboration) hep-ex/0501064    

6. Mumbai, August 1, 2005 Tom Gaisser Flavor ratio at production r =  / e at production sets background for search for effects of solar and s 13 mixing  e = P 2 (r cos 2  23 -1) Peres & Smirnov, 2004  0 for r = 2,  23 =45 o r sub-GeV ~2.04 – 2.1

7. Mumbai, August 1, 2005 Tom Gaisser Range of flux calculations

8. Mumbai, August 1, 2005 Tom Gaisser 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%

9. Mumbai, August 1, 2005 Tom Gaisser Primary spectrum: new standard? Fit BESS and AMS Include small contributions from heavy elements Extrapolate to high E Use  and measurements as constraints

10. Mumbai, August 1, 2005 Tom Gaisser Classes of atmospheric events Contained (any direction) -induced  (from below) e (or  )  

11. Mumbai, August 1, 2005 Tom Gaisser Super-K atmospheric neutrino data (hep-ex/0501064) 1489day FC+PC data + 1646day upward going muon data CC e CC 

12. Mumbai, August 1, 2005 Tom Gaisser Super-K fits 38 parameters represent uncertainties in flux of atmospheric neutrinos Fit 2 flavor mixing: sin 2  23 = 1.0  m 2 = 2.1x10 -3 eV 2

13. Mumbai, August 1, 2005 Tom Gaisser  -induced upward  MACRO Super-KAMIOKANDE

14. Mumbai, August 1, 2005 Tom Gaisser High-energy 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

15. Mumbai, August 1, 2005 Tom Gaisser Neutrino response to primary spectrum Neutrino energy Primary energy / nucleon

16. Mumbai, August 1, 2005 Tom Gaisser All-nucleon spectrum /nucleon)

17. Mumbai, August 1, 2005 Tom Gaisser Analytic approximations for E>10 GeV      Similar forms for muons but … Z  = 0.67

18. Mumbai, August 1, 2005 Tom Gaisser Atmospheric -induced  No oscillations Paolo Lipari calculation with standard Z-factors With oscillations QGSjet 0.167 0.081 0.032 0.028 0.0047 0.0032

19. Mumbai, August 1, 2005 Tom Gaisser Vertical muon flux Agrawal et al., PRD53 (1996) 1314 Lipari, standard Z-factors, Primary spectrum: N(E) = 1.75 E -2.71 ----TG calculation, Primary spectrum: N(E) = 1.7 E -2.70

20. Mumbai, August 1, 2005 Tom Gaisser Importance of kaons at high E Importance of kaons –main source of > 100 GeV –p  K + +  important –Charmed analog important for prompt leptons at higher energy vertical 60 degrees

21. Mumbai, August 1, 2005 Tom Gaisser Differences in kaon production

22. Mumbai, August 1, 2005 Tom Gaisser Comparison of flux calculations: Importance of K at high energhy A B C

23. Mumbai, August 1, 2005 Tom Gaisser  / anti- ratios

24. Mumbai, August 1, 2005 Tom Gaisser atmospheric neutrinos can we use AMANDA-II atmospheric neutrino data to probe these uncertainties ? Unfolded neutrino energy spectrum (2000) Log 10 (E ν ) E 3 ·dN/dE (cm -2 s -1 sr -1 GeV 2 ) histogram : NUSIM line : Lipari line : Bartol line : Honda histogram : CORSIKA dots: AMANDA-II data ~x2 CORSIKA ~ - 30:50% than NUSIM/Lipari Paolo Desiati

25. Mumbai, August 1, 2005 Tom Gaisser Calibration with atmospheric MINOS, etc. Neutrino telescopes Example *** of  / e –flavor ratio –angular dependence *** Note: this is maximal effect: horizontal = 85 - 90 deg in plots

26. Mumbai, August 1, 2005 Tom Gaisser Global view of atmospheric spectrum Prompt  ee Solar  Plot shows sum of neutrinos + antineutrinos Slope = 3.7 RPQM for prompt Bugaev et al., PRD58 (1998) 054001 Slope = 2.7 Possible E -2 diffuse astrophysical spectrum (WB bound / 2 for osc) Current AMANDA upper limit 2.6 x 10 -7 GeV/cm 2 sr s

27. Mumbai, August 1, 2005 Tom Gaisser Diffuse signal vs charmed background in IceCube IceCube Collaboration J. Ahrens et al., Astropart.Phys. 20 (2004) 507-532 E -2 “signal” spectrum: E 2 dN/dE=10 -7 GeV/cm 2 sr s W-B flux accounting for oscillations

28. Mumbai, August 1, 2005 Tom Gaisser 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