1. Bartol Flux Calculation presented by Giles Barr, Oxford ICRR-Kashiwa December 2004

2. Outline Neutrino calculation +Computational considerations Results Systematic errors (excluding hadron production and primary fluxes which is tomorrow) Improvements

3. Primary cosmic ray N N K π π μ ν Track forward. When first neutrino hits detector, perform cutoff calculation – i.e. track back. Forward stepping – equal steps except: –smaller near Earth surface or when near end of range. –large steps for high energy muons Backward stepping – adaptive step sizes depending on the amount of bending and the distance from the earth. Injection height 80km

4. Primary cosmic ray N N K π π μ ν Avoid rounding errors when stepping down. Use local Δh during tracking. Do not use centre of earth as origin and compute each step θ1θ1 ΔhΔh θ2θ2

5. Shower graphic from ICRC L smaller in 3D Earth’s surface Threshold 300 MeV Threshold 1 GeV Detector 80km altitude No energy threshold 80km altitude Earth’s surface

6. SuperKamiokande Collaboration hep-ex/0404034 3D bigger >30% 10%-30% 3%-10% <3% 1D bigger 3%-10% 10%-30% 3D: Is it important?

7. Detector shape Main technique: –Use flat detector on surface of Earth. –Extend to make MC calculation more efficient, but do not want to extend in vertical direction as 3-D effect is very sensitive in that direction (P.Lipari). → Flat. Second technique: –Spherical detector – neutrino hits detector if direction is within θ cut of neutrino direction; weight event by apparent detector size. Bend at 20km Bend α=60 o

8. How big can the detector be ?

9. Kamioka

11. Correction if your detector is too big...

12. Weight problem... With flat detector, weight by 1/cosθ D –Shortcut in 1D, since θ P = θ D, generate primaries flat in cosθ P, weight by cosθ P Total weight cosθ P / cosθ D = 1. –In 3D, θ P ≠ θ D, so must face situation of very large 1/cosθ D. Various tricks. Modified individual weights Weight zero very close to divergence and weight a bit higher in neighboring region cos  1.00 → 0.10 weight 1/cos  cos  0.10 → 0.01 weight 1/(0.9×cos  cos  0.01 → 0.00 weight 0 ‘Binlet’ weights Weight of each bin 1/cos  determined at bin centre. With 20 bins, bias is large (~5%), therefore it is done with 80 binlets (bias ~1.5%). Bias If the flux is flat within a bin: No bias. Otherwise, bias =   fractional difference in flux from centre to edge of bin  fraction of bin set to weight 0 (0.1) Bias If the flux is flat within the bin: No bias. Otherwise bias = 1   fractional difference in flux from centre to edge of bin  can be as large as ~15% for bins of  cos  = 0.1)

13. A little history... Before full 3D was tuned to be fast enough: DST method. Based on idea of ‘trigger’ in experiment –Rough calculation done first –Neutrinos which went near detector got repeat full treatment. Speed up by reusing rough calculation at lots of points on Earth (always same θ Z ).

14. A bit more on technique... ‘Plug and play’ modules of code: –Hadron production module Target (different versions) Simple test generators Used Honda_int for tests –Decay generator –Atmospheric model

15. Results

16. dφ/d ln(E) (m -2 s -1 sr -1 )

17. Give fluxes vs E

18. Azimuth angle distribution East-West effect NESWNNESWN E ν >315 MeV

19. Energy dependence of East-West effect

20. Flavour ratios

22. Down/Horizontal Ratios

23. Up/Down asymmetry

24. Some systematics

25. Cross section change Effect of artificial increase in total cross section of 15%

26. Atmospheric Density

27. Associative production Effect of a 15% reduction in ΛK + production

28. Effects not considered: Later talk on hadron model and primary fluxes Effect of mountain at Kamioka. (effects of altitude variation around the earth are in, but no local Kamioka map). Solar wind: Assume it can be lumped in with flux uncertainty. Charm production. Neutral kaon regeneration. Polarisation in 3 body decays.

29. Summary Considered here all systematic errors except hadron production and fluxes (next talk). Most of them are small. 3D effects are not large, but increase in program complexity is large. Cross checks between calculations. Improvements: –Mountain needed ? –Use more information from muon fluxes.