A study of compatibility Sept 2003 PHYSTAT 2003

A study of compatibility Sept, 2003 PHYSTAT 2003 31

Table of Data Sets The PDF’s are not exactly CTEQ 6 but very close – a no-name generic set of PDF’s for illustration purposes. Ntot = 2291 c 2 global = 2368. Sept, 2003 1 2 3 4 5 6 7 8 9 10 BCDMS F 2 p BCDMS F 2 d H 1 (a) H 1 (b) H 1 (c ) ZEUS CDHSW F 2 NMC F 2 p NMC d/p CCFR F 2 11 12 13 14 15 16 17 18 E 605 E 866 pp E 866 d/p D 0 jet CDF jet CDHSW F 3 CCFR F 3 CDF W Lasy PHYSTAT 2003 N c 2 339 251 104 126 129 229 85 201 123 69 366. 1 273. 6 97. 8 127. 3 108. 9 261. 1 65. 6 295. 5 115. 4 84. 9 119 184 15 90 33 96 87 11 94. 7 239. 2 5. 0 62. 6 56. 1 76. 4 26. 8 8. 7 c 2/N 1. 08 1. 09 0. 94 1. 01 0. 84 1. 14 0. 77 1. 47 0. 94 1. 23 0. 80 1. 30 0. 33 0. 70 1. 70 0. 80 0. 31 0. 79 32

The effect of setting all normalization constants to 1. Dc 2 1 2 3 4 5 8 11 12 BCDMS F 2 p BCDMS F 2 d H 1 (a) H 1 (b) H 1 (c ) NMC F 2 p E 605 E 866 pp 186. 5 27. 6 7. 3 10. 1 24. 0 13. 3 95. 7 c 2 (opt. norm) = 2368. c 2 (norm 1) = 2742. Dc 2 = 374. 0 Sept, 2003 PHYSTAT 2003 33

By applying weighting factors in the fitting function, we can test the “compatibility” of disparate data sets. Example 1. The effect of giving the CCFR F 2 data set a heavy weight. Dc 2 3 H 1 (a) 8. 3 7 CDHSW F 2 6. 3 8 NMC F 2 p 18. 1 10 CCFR F 2 -19. 7 12 E 866 pp 14 D 0 jet 5. 5 23. 5 Dc 2 (CCFR) = -19. 7 Dc 2 (other) = +63. 3 Giving a single data set a large weight is tantamount to determining the PDF’s from that data set alone. The result is a significant improvement for that data set but which does not fit the others. Sept, 2003 PHYSTAT 2003 34

Example 1 b. The effect of giving the CCFR F 2 data weight 0, i. e. , removing the data set from the global analysis. Dc 2 3 H 1 (a) -8. 3 6 ZEUS 6. 9 8 NMC F 2 p -10. 1 10 CCFR F 2 40. 0 Dc 2 (CCFR) = +40. 0 Dc 2 (other) = -17. 4 Imagine starting with the other data sets, not including CCFR. The result of adding CCFR is that c 2 global of the other sets increases by 17. 4 ; this must be an acceptable increase of c 2. Sept, 2003 PHYSTAT 2003 35

Example 2. ZEUS F 2 measurements Heavy weight for ZEUS 2 3 6 8 10 14 15 BCDMS F 2 d H 1 (a) ZEUS NMC F 2 p CCFR F 2 D 0 jet CDF jet (Like fitting ZEUS alone) 5. 0 18. 7 -13. 7 26. 1 13. 8 -10. 1 4. 3 Dc 2 (zeus) = -13. 7 Dc 2 (other) = +64. 6 Zero weight for ZEUS 3 H 1 (a) 6 ZEUS 8 NMC F 2 p Dc 2 (zeus) = +18. 3 Dc 2 (other) = -10. 6 Sept, 2003 PHYSTAT 2003 -7. 0 18. 3 -4. 0 [removing zeus => c 2 (other) decreases by 10. 6] 36

Example 3. H 1 data sets Heavy weight for H 1 data 1 2 3 4 5 6 7 10 12 14 BCDMS p BCDMS d H 1 (a) H 1 (b) H 1 (c ) ZEUS CDHSW CCFR F 2 E 866 pp D 0 jet 10. 2 10. 0 -13. 4 -7. 1 -6. 7 27. 5 5. 0 37. 9 -11. 0 27. 3 Dc 2 (H 1) = -27. 2 Dc 2 (other) = +106. 1 Zero weight for H 1 3 6 10 H 1 (a) ZEUS CCFR F 2 13. 5 -4. 6 -4. 1 Dc 2 (H 1) = +18. 1 Dc 2 (other) = -11. 0 Sept, 2003 PHYSTAT 2003 37 Dc 2

Example 4. The D 0 jet cross section Heavy weight for D 0 jet 6 10 12 14 ZEUS CCFR F 2 E 866 pp D 0 jet 9. 2 7. 6 5. 5 -7. 8 Dc 2 (D 0 jet) = -7. 8 Dc 2 (other) = +26. 8 Zero weight for D 0 jet 5 6 8 10 14 15 H 1 (c ) ZEUS NMC F 2 p CCFR F 2 D 0 jet CDF jet -4. 3 6. 9 8. 0 -9. 0 64. 3 -4. 6 Dc 2 (D 0 jet) = +64. 3 Dc 2 (other) = -6. 5 Sept, 2003 PHYSTAT 2003 38

Example 5. Giving heavy weight to H 1 and BCDMS Dc 2 for all data sets 2 3 4 6 7 8 10 14 16 17 BCDMS F 2 d H 1 (a) H 1 (b) ZEUS CDHSW F 2 NMC F 2 p CCFR F 2 D 0 jet CDHSW F 3 CCFR F 3 -15. 1 -12. 4 -4. 3 27. 5 19. 2 8. 0 54. 5 22. 0 11. 0 5. 9 Dc 2(H & B) = -38. 7 Dc 2(other) = +149. 9 Sept, 2003 PHYSTAT 2003 39

Lessons from these reweighting studies • Global analysis requires compromises – the PDF model that gives the best fit to one set of data does not give the best fit to others. This is not surprising because there are systematic differences between the experiments. • The scale of acceptable changes of c 2 must be large. Adding a new data set and refitting may increase the c 2‘s of other data sets by amounts >> 1. Sept, 2003 PHYSTAT 2003 40

Clever ways to test the compatibility of disparate data sets • Plot c 2 versus c 2 J Collins and J Pumplin (hep-ph/0201195) • The Bootstrap Method Efron and Tibshirani, Introduction to the Bootstrap (Chapman&Hall) Chernick, Bootstrap Methods (Wiley) Sept, 2003 PHYSTAT 2003 41