1. Sept, 2003PHYSTAT 200331 A study of compatibility

2. Sept, 2003PHYSTAT 200332 The PDF’s are not exactly CTEQ6 but very close – a no-name generic set of PDF’s for illustration purposes. Table of Data Sets 1 BCDMS F2p 339 366.11.08 2 BCDMS F2d 251 273.61.09 3 H1 (a) 104 97.80.94 4 H1 (b) 126 127.31.01 5 H1 (c ) 129 108.90.84 6 ZEUS 229 261.11.14 7 CDHSW F2 85 65.60.77 8 NMC F2p 201 295.51.47 9 NMC d/p 123 115.40.94 10 CCFR F2 69 84.91.23 11E60511994.70.80 12E866 pp184239.21.30 13E866 d/p155.00.33 14D0 jet9062.60.70 15CDF jet3356.11.70 16CDHSW F39676.40.80 17CCFR F38726.80.31 18CDF W Lasy118.70.79 N  2  2 /N N tot = 2291  2 global = 2368.

3. Sept, 2003PHYSTAT 200333 The effect of setting all normalization constants to 1. 1BCDMS F2p186.5 2BCDMS F2d27.6 3H1 (a)7.3 4H1 (b)10.1 5H1 (c )24.0 8NMC F2p4.0 11E60513.3 12E866 pp95.7  2  2 (opt. norm) = 2368.  2 (norm 1) = 2742.  2 = 374.0

4. Sept, 2003PHYSTAT 200334 Example 1. The effect of giving the CCFR F2 data set a heavy weight. By applying weighting factors in the fitting function, we can test the “compatibility” of disparate data sets. 3H1 (a)8.3 7CDHSW F26.3 8NMC F2p18.1 10CCFR F2  19.7 12E866 pp5.5 14D0 jet23.5  2  2 (CCFR) =  19.7  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.

5. Sept, 2003PHYSTAT 200335 Example 1b. The effect of giving the CCFR F2 data weight 0, i.e., removing the data set from the global analysis. 3H1 (a)  8.3 6ZEUS6.9 8NMC F2p  10.1 10CCFR F240.0  2  2 (CCFR) = +40.0  2 (other) =  17.4 Imagine starting with the other data sets, not including CCFR. The result of adding CCFR is that  2 global of the other sets increases by 17.4 ; this must be an acceptable increase of  2.

6. Sept, 2003PHYSTAT 200336 Example 2. ZEUS F2 measurements 2BCDMS F2d5.0 3H1 (a)18.7 6ZEUS  13.7 8NMC F2p26.1 10CCFR F213.8 14D0 jet  10.1 15CDF jet4.3 Heavy weight for ZEUS  2 (zeus) =  13.7  2 (other) = +  Zero weight for ZEUS 3H1 (a)  7.0 6ZEUS18.3 8NMC F2p  4.0  2 (zeus) =   2 (other) =  10.6 (Like fitting ZEUS alone) [removing zeus =>  2 (other) decreases by 10.6]

7. Sept, 2003PHYSTAT 200337 Example 3. H1 data sets Heavy weight for H1 data 1BCDMS p10.2 2BCDMS d10.0 3H1 (a)  13.4 4H1 (b)  7.1 5H1 (c )  6.7 6ZEUS27.5 7CDHSW5.0 10CCFR F237.9 12E866 pp  11.0 14D0 jet27.3  2  2 (H1)  27.2  2 (other) = +106.1 Zero weight for H1 3H1 (a)13.5 6ZEUS  4.6 10CCFR F2  4.1  2  2 (H1)   2 (other)  11.0

8. Sept, 2003PHYSTAT 200338 Example 4. The D0 jet cross section 6ZEUS9.2 10CCFR F27.6 12E866 pp5.5 14D0 jet  7.8 Heavy weight for D0 jet  2 (D0 jet)  7.8  2 (other) = +26.8 Zero weight for D0 jet 5H1 (c )  4.3 6ZEUS6.9 8NMC F2p8.0 10CCFR F2  9.0 14D0 jet64.3 15CDF jet  4.6  2 (D0 jet)   2 (other) =  6.5

9. Sept, 2003PHYSTAT 200339 2BCDMS F2d  15.1 3H1 (a)  12.4 4H1 (b)  4.3 6ZEUS27.5 7CDHSW F219.2 8NMC F2p8.0 10CCFR F254.5 14D0 jet22.0 16CDHSW F311.0 17CCFR F35.9 Example 5. Giving heavy weight to H1 and BCDMS  2 for all data sets  2  2 ( H & B ) =  38.7  2 ( other ) = +149.9

10. Sept, 2003PHYSTAT 200340 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  2 must be large. Adding a new data set and refitting may increase the  2 ‘s of other data sets by amounts >> 1.

11. Sept, 2003PHYSTAT 200341 Clever ways to test the compatibility of disparate data sets Plot  2 versus  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)