1. Flux calculation results and systematic errors from Bartol calculation presented by Giles Barr, Oxford with considerable help from Simon Robbins ICRR-Kashiwa December 2004

2. Outline Hadron production –Survey of data, model independent error estimates of existing data (by Simon Robbins et. al.) –New error propagation method –Results Warning: Very Preliminary OK to share it in the spirit of a ‘Workshop’

3. Barton et. al. Atherton et. al. SPY Serpukov Allaby et. al. Abbott et. al. Eichten et. al. Cho et. al. 1 GeV101001 TeV Parent energy 10 Population of hadron- production phase-space for pA → πX interactions. ν μ flux (represented by boxes) as a function of the parent and daughter energies. Measurements. 1-2 p T points 3-5 p T points >5 p T points Can attempt fit all the data simultaneously. Antiproton example: Duperray, Huang, Protasov, Buénerd astro-ph/0305274 1 GeV 10 100 1 TeV 10 Daughter energy Hadron production measurements

4. pT range coverage This energy is best situation

5. Proton energy Target 2.4 includes target fragmentation, antibaryon production Dip at high x in Target 2.1 due to implementation detail in leading particle

6. From Gaisser-Honda review

7. π production at 20 GeV

8. K production at 20 GeV

9. Lower energy

10. Proposed total errors PionsKaons x LAB (low edge).0.1.2.3.4.5.6.7.8.9.0.1.2.3.4.5.6.7.8.9 <8 GeV 10%30%40% 8-15 GeV 30%10%30%40% 15-30 GeV 30105%10%302010% 30-500 GeV 3015%4030% >500 GeV 3015%+Energy dep.4030%+Energy dep.

11. Primary cosmic ray N N K π π μ ν Consider chain from primary to neutrino Look for the interaction where baryon → meson Apply weight

12. Linear addition of all errors (overestimate)

13. More sophisticated combination Flaws: No difference pi+pi-, or K+K- Linear combination too pessimistic –Not all uncertainties will be this bad at once. Separate uncertainties – add quadratically How ?

14. More sophisticated combination (1)PionsKaons x LAB (low edge).0.1.2.3.4.5.6.7.8.9.0.1.2.3.4.5.6.7.8.9 <8 GeV 10%40% 8-15 GeV 10%40% 15-30 GeV 5%10% 30-500 GeV 15%30% >500 GeV 15%30% PionsKaons x LAB (low edge).0.1.2.3.4.5.6.7.8.9.0.1.2.3.4.5.6.7.8.9 <8 GeV 10%30%40% 8-15 GeV 30%10%30%40% 15-30 GeV 30105%10%302010% 30-500 GeV 3015%4030% >500 GeV 3015%+Energy dep.4030%+Energy dep.

15. More sophisticated combination (1)PionsKaons x LAB (low edge).0.1.2.3.4.5.6.7.8.9.0.1.2.3.4.5.6.7.8.9 <8 GeV 10%40% 8-15 GeV 10%40% 15-30 GeV 5%10% 30-500 GeV 15%30% >500 GeV 15%30% PionsKaons x LAB (low edge).0.1.2.3.4.5.6.7.8.9.0.1.2.3.4.5.6.7.8.9 <8 GeV 10%30%40% 8-15 GeV 30%10%30%40% 15-30 GeV 30105%10%302010% 30-500 GeV 3015%4030% >500 GeV 3015%+Energy dep.4030%+Energy dep.

16. More sophisticated combination Flaws: No difference pi+pi-, or K+K- (1)PionsKaons x LAB (low edge).0.1.2.3.4.5.6.7.8.9.0.1.2.3.4.5.6.7.8.9 <8 GeV 10%40% 8-15 GeV 10%40% 15-30 GeV 5%10% 30-500 GeV 15%30% >500 GeV 15%30% PionsKaons x LAB (low edge).0.1.2.3.4.5.6.7.8.9.0.1.2.3.4.5.6.7.8.9 <8 GeV 10%30%40% 8-15 GeV 30%10%30%40% 15-30 GeV 30105%10%302010% 30-500 GeV 3015%4030% >500 GeV 3015%+Energy dep.4030%+Energy dep.

17. Results Have used 1D for testing this investigation: Present ν μ /anti-ν μ Then present other ratios

18. ν μ /anti-ν μ Flux & syst errors Flux syst errors Flux ratio & syst errors Flux ratio syst errors

19. Type-ratio uncertainty versus energy

20. Angle-ratio uncertainty versus energy

21. Type-ratio uncertainties – cos θ

24. Summary Still preliminary yet, but this technique looks as if it works. –Depends (subjectively) on how you divide up the uncertainty Lots of bins, independent is not reality Too few bins → approach linear addition. –Probably wrong to have full correlation between π + and π - IMPORTANT: Do not take the values of the errors too seriously in this preliminary presentation. Straightforward to add primary flux errors and other errors.

25. Primary fluxes (Data-Fit)/Fit 100%