1. Tom Gaisser October 29, 2002 Oxford Atmospheric neutrinos from decay of , K and  produced by interactions of cosmic rays in the atmosphere Up-down symmetric except for geomagnetic effects Useful beam for neutrino oscillations? From D. Ayres, A.K. Mann et al., PR D84 (1984) 902 & Snowmass, 1982 References: TKG & M. Honda, Ann. Revs. Nucl. Part. Sci. 52 (2002) TKG, Proc. Neutrino 2002

2. Tom Gaisser October 29, 2002 Oxford Historical context Particle physics with cosmic rays: pre-1960 Discovery of positron, muon, pion and kaon Hadronic scaling (Heitler & Janossy, 1949) --  secondary (E) = Z ps  p (E) Study of elementary particles by the photographic method Powell, Fowler & Perkins, 1959 Stability of matter: search for proton decay, 1980’s IMB & Kamioka -- water Cherenkov detectors KGF, NUSEX, Frejus, Soudan -- iron tracking calorimeters Principal background is interactions of atmospheric neutrinos Need to calculate flux of atmospheric neutrinos Two methods: From muons to parent pions infer neutrinos (Zatsepin & Kuz’min; Perkins) From primaries to , K and  to neutrinos (Cowsik, TKG & Stanev…) Giles Barr 1986/87 e  e  p  

3. Tom Gaisser October 29, 2002 Oxford Historical context (cont’d) Atmospheric neutrino anomaly - 1986, 1988 … IMB too few  decays (from interactions of  ) 1986 Kamioka  -like / e-like ratio too small. Neutrino oscillations first explicitly suggested in 1988 Kamioka paper Discovery of neutrino oscillations Super-K: “Evidence for neutrino oscillations” at Neutriino 98 Subsequent increasingly detailed analyses from Super-K 1998… Confirming evidence from MACRO and Soudan SNO results on oscillations of solar neutrinos Analyses based on ratios comparing to 1D calculations Need for precise, complete, accurate, 3D calculations  ~ P T / E is large for sub-GeV neutrinos Bending of muons in geomagnetic field important for from  decay Complicated angular/energy dependence of primaries (AMS measurement) Use improved primary spectrum and hadroproduction information  e  e  p 

4. Tom Gaisser October 29, 2002 Oxford Outline of talk Overview of calculations E < 10 GeV (contained) –Sources of uncertainty Primary spectrum Hadronic interactions –Comparison of calculations –Geomagnetic effects –3 D calculations High energy (    & e ) –Importance of kaons –Calibration of - telescopes –Prompt background Summary Distribution of E for 4 classes of events determines how oscillation effects appear P(    ) = 1 - sin 2 2  sin 2 [1.27  m 2 (eV 2 ) L km / E GeV ] for two-flavor mixing in vacuum

5. Tom Gaisser October 29, 2002 Oxford Overview of the calculation

6. Tom Gaisser October 29, 2002 Oxford 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 –overall range (neglect highest and lowest): +/-15%, E < 100 GeV +/- 30%, E ~ TeV

7. Tom Gaisser October 29, 2002 Oxford Comparison (using same event generator) sub-GeV flux increases slightly using new flux from AMS & BESS AMS/BESS Kamioka Soudan/SNO  e  e

8. Tom Gaisser October 29, 2002 Oxford Hadronic interactions - yields depend most on treatment of  production Compare 3 calculations: –Bartol (Target) –Honda et al. (1995: Fritiof; present: Dpmjet3) –Battistoni et al. (Fluka) Uncertainties from interactions ~ +/-15%

9. Tom Gaisser October 29, 2002 Oxford Comparison (using same flux) New calculations lower than old, e.g.: –Target-2.1/ -1 –Dpmjet3 / HKKM –3 new calculations agree at Kamioka but not for Soudan/SNO Larger uncertainty at high geomagnetic –Interactions < 10 GeV are important Kamioka Soudan/SNO  e  e

10. Tom Gaisser October 29, 2002 Oxford New hadro-production data Diagram: –Lego plot shows phase space weighting for sub- GeV events –Bars show existing data New sources of data –HARP –NA49 (P322) –E907 HARP P322

11. Tom Gaisser October 29, 2002 Oxford Geomagnetic cutoffs & E-W effect as a consistency check Picture shows: – 20 GeV protons in geomagnetic equatorial plane –arrive from West and from near the vertical –but not from East Comparison to data: –provides consistency test of data & analysis N From cover of “Cosmic Rays” by A.M. Hillas (1972)

12. Tom Gaisser October 29, 2002 Oxford Response functions, sub-GeV E primary ~ 10-20 x E Up/down ratio opposite at Kamioka vs Soudan/SNO

13. Tom Gaisser October 29, 2002 Oxford Cutoffs at Super-K Lipari 3D Honda Bartol flux, 0.4 < E < 3 GeV -0.5 < cos(  ) < 0.5 measured by Super-K and compared to 3 calculations N ESW Measurement of East-West effect with atmospheric neutrinos--an important confirmation of analysis & interpretation of Super-K data as neutrino oscillations

14. Tom Gaisser October 29, 2002 Oxford 3-dimensional effects Characteristic 3D feature: –excess of near horizon –shown in top, left panel –lower panels show directions of  and e –cannot see 3D effect directly; however: Horizontal excess is associated with a change in path-length distribution From Battistoni et al., Astropart. Phys. 12 (2000) 315  

15. Tom Gaisser October 29, 2002 Oxford 3-D effects at Super-K 3D--1D comparison (pink--blue/green) at Kamioka Dip near horizon: –due to high local horizontal cutoffs Size of effect: –p T (  )/E  sets scale –~ 0.1 GeV / E –therefore negligible for E > 1 GeV from M. Honda et al., Phys. Rev. D64 (2001) 053001

16. Tom Gaisser October 29, 2002 Oxford E = 0.3 GeV E = 1 GeV Soudan/SNOKamioka Path-length dependence Path length shorter near horizon on average in 3D case –cos(  ) > 0 only, –phase space favors nearby interaction scattering to large angle –5-10% (E ~0.3-1 GeV) Effect not yet included in Super-K analysis from M. Honda et al., Phys. Rev. D64 (2001) 053001  m 2 L/E …increase  m 2 1%?

17. Tom Gaisser October 29, 2002 Oxford –Cosmic-ray albedo beautifully measured by AMS at 380 km –Biggest effect near geomagnetic equator (vertical cutoff ~ 10 GV) –Albedo: sub-cutoff protons from grazing interactions of cosmic rays > cutoff (S.B. Treiman, 1953) – trapped for several cycles –Re-entry rate is low (dashed line) Is the second spectrum important for atmospheric ? 10 GV P. Zuccon et al.

18. Tom Gaisser October 29, 2002 Oxford Technical aspects of 3D calculation Brute force –Generate showers randomly all over globe –  ~ A detector /A earth ~ 10 -10 –Use large A eff Lipari, Waltham Neglect bending in geomagnetic field Battistoni et al. DST approach: two passes –Giles Barr et al. –Equivalent to brute force but with higher efficiency,  ~ ?

19. Tom Gaisser October 29, 2002 Oxford Higher energy atmospheric Mean E ~ 100 GeV for -induced upward 

20. Tom Gaisser October 29, 2002 Oxford High energy ( e.g.     ) Importance of kaons –main source of > 100 GeV –p  K + +  important –Charmed analog important for prompt leptons vertical 60 degrees

21. Tom Gaisser October 29, 2002 Oxford 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

22. Tom Gaisser October 29, 2002 Oxford MINOS:  + /  - discrimination 1 < E  < 70 GeV a) No Oscillationsb) Oscillations: full mixing,  m 2 = 0.0025eV 2  1 GeV contained 10 GeV, contained External (x 10 -4 ) Angular distribution of   Events in 5 yr w / wo osc. Contained + 400 / 260 Contained - 620 / 440 External + 160 / 120 External - 400 / 280 TKG & Todor Stanev astr0-ph/0210512

23. Tom Gaisser October 29, 2002 Oxford Vertically upward interactions inside detector E EE EE Nine angular bins in direction            so      - d   /dy ~ const, but d  /dy ~ (1-y) 2, so      oscillates vs E  - Problems:    smears effect; statistics too low in MINOS

24. Tom Gaisser October 29, 2002 Oxford Global view of atmospheric spectrum Prompt  ee Solar  Plot shows sum of neutrinos + antineutrinos Slope = 3.7 Slope = 2.7 Uncertainty in level of charm a potential problem for finding diffuse neutrinos Possible E -2 diffuse astrophysical spectrum (WB bound)

25. Tom Gaisser October 29, 2002 Oxford Uncertainties & absolute normalization Primary spectrum –+/- 10% up to 100 GeV (using AMS, BESS only) –+/- 20% below 100 GeV, +/- 30% ~TeV (all data) –Note lack of measurements in TeV range Hadronic interactions –+/- 15% below 100 GeV –1D o.k. for comparing calculations and for tracking effects of uncertainties in input –Other sources at per cent level (local terrain, seasonal variations, anisotropy outside heliosphere) –New measurements: HARP, E907, P322 Uncertainty in 

26. Tom Gaisser October 29, 2002 Oxford Summary (low energy) Evidence for oscillation uses ratios: –Contained events (    ) data / ( e /  ) calculated upward / downward –Neutrino-induced upward muons stopping / through-going vertical / horizontal –Broad response functions minimize dependence on slope of primary spectrum Uncertainties tend to cancel in comparison of ratios Observation of geomagnetic effects confirms experiment & interpretation

27. Tom Gaisser October 29, 2002 Oxford Summary (high energy) Kaon decays  dominate atmospheric , e above 100 GeV Well-understood atmospheric , e useful for calibration Uncertainty in level of prompt neutrinos (from charm decay) will limit search for diffuse astrophysical neutrinos

28. Tom Gaisser October 29, 2002 Oxford What next? Use neutrino fluxes for calibration, etc. –MINOS, SNO, Neutrino telescopes… –Learn about charmed analog of K  production Finish and use Giles’ 3D scheme Incorporate new hadro-production results –HARP below 15 GeV –NA 49, E907 ~ 100 GeV

29. Tom Gaisser October 29, 2002 Oxford Comparison to muons –  +,  - vs atmospheric depth –newer measurements lower by 10-15% than earlier –comparison not completely internally consistent: ascent vs float balloons rise rapidly fraction detected is small compared to  decayed to Data from CAPRICE, 3D calculation of Engel et al. (2001)

30. Tom Gaisser October 29, 2002 Oxford Solar modulation Neutron monitors –well correlated with cosmic-ray flux –provide continuous monitor –response like sub-GeV neutrinos with no cutoff –SNO, Soudan: <20% variation –Kamioka: <5% (10 %) for downward (upward) P. Lipari

31. Tom Gaisser October 29, 2002 Oxford a) No Oscillations b) Oscillations: full mixing  m 2 = 0.0025 eV 2  1 GeV contained 10 GeV, contained External (x 10 -4 ) Angular distribution of  

32. Tom Gaisser October 29, 2002 Oxford

33. Tom Gaisser October 29, 2002 Oxford Soudan 5.9 kT yr M. Goodman, Neutrino 2002 Electrons Muons Black lines: calculated, no oscillation Blue lines: fitted with oscillations