The energy spectrum from the KASCADE-Grande muon data (Update)

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 • Quality cuts • Efficiency studies • Muon correction functions • The muon spectra • The Integral flux • Attenuation curves • Adding muon data with the CIC method • Conversion into Energy • Energy spectrum • Systematic uncertainties • Summary Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

3. 1) Quality cuts • Data sets: • MC data: Kreta v1.18.05 • KG data: Kreta v1.18.05 • Quality cuts: •  < 40o • Rectangle: A  1.924 x 105 m2 • Ndtg > 19 • Successfully reconstructed • Nctot • log10(Nctot/8.5) > 2.9 log10(Ne/4.2) -8.4/4.2 • -0.385 < s <1.485 • N ≥ 1.25  105 • Ne ≥ 105 • Sven´s data quality base • - standard() • - require_clusters(18) • - not ankaevent() • Iact & 1 • Hit7 > 0 • Fanka < 4 Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

4. 2) Efficiency studies Working in region of maximum efficiency (N 1.25  105) Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

5. 2) Efficiency studies Working in region of maximum efficiency (N 1.25  105) Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

6. 2) Efficiency studies Working in region of maximum efficiency (N 1.25  105) 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): Main contributions to the CF separated in four different terms: Each term calculated iteratively by fitting versus x, where The superscript represents the order in which a given term was calculated. Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

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

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

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

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

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 log10(N) = 0.1 Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

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

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

17. 4) The muon spectra teff = 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 p1 = -2.21 0.02 p1 = -2.18 0.02 p1 = -2.47 0.02 p1 = -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 p1 = -2.14 0.02 p1 = -2.19 0.02 p1 = -2.39 0.02 p1 = -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 p1 = -2.20 0.02 p1 = -2.36 0.02 Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

21. 5) The integral flux Work in region of maximum efficiency and statistics Apply cut at constant J(>N) For a given J, get N() 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 2nd and 1st degree in sec for the fit of attenuation curves More plausible that 2nd 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 = 23.1o 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 FLUKA/QGSJET II Fit in region of maximum efficiency and statistics 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-conversion relation:  = 33o (upper limit) and  = 13o (lower limit) Energy spectrum from muon data – J.C. Arteaga Karlsruhe, February 2009

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

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

41. 11) Summary • 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. Energy spectrum from muon data – J.C. Arteaga Karlsruhe, December 2008