1. The energy spectrum from the KASCADE- Grande muon data (Update) Juan Carlos Arteaga-Velázquez for the KASCADE-Grande Collaboration Institute of Physics and Mathematics Universidad Michoacana Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

2. Outline Structure of the talk 1)Quality cuts 2)Efficiency studies 3)Muon correction functions 4)The muon spectra 5)The Integral flux 6)Attenuation curves 7)Adding muon data with the CIC method 8)Conversion into Energy 9)Energy spectrum 10) Systematic uncertainties 11) Summary Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

3. Data sets: MC data: Kreta v1.18.05 KG data: Kreta v1.18.05 Quality cuts:  < 40 o Rectangle: A  1.924 x 10 5 m 2 N dtg > 19 Successfully reconstructed N ctot log 10 (N ctot /8.5) > 2.9 log 10 (N e /4.2) -8.4/4.2 -0.385 < s <1.485 N  ≥ 1.25  10 5 N e ≥ 10 5 Sven´s data quality base - standard() - require_clusters(18) - not ankaevent() Iact & 1 Hit7 > 0 Fanka < 4 1) Quality cuts Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

4. 2) Efficiency studies Working in region of maximum efficiency (N   1.25  10 5 ) Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

5. 2) Efficiency studies Working in region of maximum efficiency (N   1.25  10 5 ) Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

6. 2) Efficiency studies Working in region of maximum efficiency (N   1.25  10 5 ) Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

7. 3) Muon correction functions N  corrected for systematic effects with a correction function (CF): Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Main contributions to the CF separated in four different terms: The superscript represents the order in which a given term was calculated. Each term calculated iteratively by fitting versus x, where

8. 3) Muon correction functions N  corrected N  no corrected Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Mixed

9. 3) Muon correction functions N  corrected N  no corrected Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Mixed

10. 3) Muon correction functions N  corrected N  no corrected Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Mixed

11. 3) Muon correction functions N  corrected N  no corrected Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Mixed

12. 3) Muon correction functions No clear correlation between the contributions to the CF Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

13. 3) Muon correction functions No clear correlation between the contributions to the CF Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

14. 3) Muon correction functions Distribution of systematic error of the corrected N  Half width ~ 0.08  Use bin  log 10 (N  ) = 0.1 Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

15. 3) Muon correction functions Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Magnitude of correction σ (i) relative to N  Azimuthal contribution to CF is the smallest one

16. 3) Muon correction functions Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Average contribution of correction function to N 

17. 4) The muon spectra  t eff = 754.1 days Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

18. 4) The muon spectra Importance of the N  correction function p 1 = -2.21  0.02 p 1 = -2.47  0.02 p 1 = -2.18  0.02 p 1 = -2.41  0.02 Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

19. 4) The muon spectra Importance of the N  correction function p 1 = -2.14  0.02 p 1 = -2.39  0.02 p 1 = -2.19  0.02 p 1 = -2.37  0.02 Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

20. 4) The muon spectra Importance of the N  correction function p 1 = -2.20  0.02 p 1 = -2.36  0.02 Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

21. 5) The integral flux Apply cut at constant J(> N  ) For a given J, get N  (  ) Work in region of maximum efficiency and statistics Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

22. 6) Attenuation curves Get attenuation curves Choose the closest curve to N  (  ) Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

23. 6) Attenuation curves Get attenuation curves Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

24. 6) Attenuation curves Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

25. 6) Attenuation curves  2 per degree of freedom (N) and  2 probability P(  2, N) when using a polynomial of 2 nd and 1 st degree in sec  for the fit of attenuation curves More plausible that 2 nd degree polynomial describes the data Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

26. 7) Adding muon data with CIC method Find reference angle  ref for normalization:  ref =  mean = 23.1 o Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

27. 7) Adding muon data with CIC method Muon spectra after applying CIC method Good agreement between the spectra Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

28. 7) Adding muon data with CIC method Muon spectra after applying CIC method Good agreement between the spectra Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

29. 7) Adding muon data with CIC method Muon spectra after applying CIC method Good agreement between the spectra Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

30. 8) Conversion into Energy Fit in region of maximum efficiency and statistics FLUKA/QGSJET II Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

31. 8) Conversion into Energy Systematic error in reconstruction of energy: Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

32. 9) Energy spectrum Assuming mixed composition Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

33. 9) Energy spectrum Assuming mixed composition Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

34. 9) Energy spectrum Assuming mixed composition Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

35. 9) Energy spectrum Assuming mixed composition Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

36. 9) Energy spectrum Assuming mixed composition Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

37. 9) Energy spectrum Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

38. 10) Systematic uncertainties Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Energy-conversion relation:  = 33 o (upper limit) and  = 13 o (lower limit)

39. 10) Systematic uncertainties Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Composition: Pure protons (upper limit) and pure iron nuclei (lower limit)

40. 10) Systematic uncertainties Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009 Systematic error due to composition and energy-conversion relation

41. 11) Summary Energy spectrum from muon data – J.C. Arteaga Karlsruhe, December 2008 A preliminary all-particle primary energy spectrum was obtained from the muon data of KASCADE-Grande using the CIC method. Agreement between results from Kascade and KASCADE-Grande. According to CIC method, muon spectra corresponding to different   are in good agreement. By taking into account muon correction functions a change in slope of muon spectra is observed. Calculation of systematics with new Kreta version are under way.