Sept, 2003PHYSTAT A study of compatibility

Sept, 2003PHYSTAT 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 BCDMS F2d H1 (a) H1 (b) H1 (c ) ZEUS CDHSW F NMC F2p NMC d/p CCFR F E E866 pp E866 d/p D0 jet CDF jet CDHSW F CCFR F CDF W Lasy N  2  2 /N N tot = 2291  2 global = 2368.

Sept, 2003PHYSTAT The effect of setting all normalization constants to 1. 1BCDMS F2p BCDMS F2d27.6 3H1 (a)7.3 4H1 (b)10.1 5H1 (c )24.0 8NMC F2p4.0 11E E866 pp95.7  2  2 (opt. norm) =  2 (norm 1) =  2 = 374.0

Sept, 2003PHYSTAT 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 F2p CCFR F2  E866 pp5.5 14D0 jet23.5  2  2 (CCFR) =  19.7  2 (other) = 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, 2003PHYSTAT 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  CCFR F240.0  2  2 (CCFR) =  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.

Sept, 2003PHYSTAT Example 2. ZEUS F2 measurements 2BCDMS F2d5.0 3H1 (a)18.7 6ZEUS  NMC F2p CCFR F D0 jet  CDF 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]

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

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

Sept, 2003PHYSTAT BCDMS F2d  H1 (a)  H1 (b)  4.3 6ZEUS27.5 7CDHSW F NMC F2p8.0 10CCFR F D0 jet CDHSW F CCFR F35.9 Example 5. Giving heavy weight to H1 and BCDMS  2 for all data sets  2  2 ( H & B ) =  38.7  2 ( other ) =

Sept, 2003PHYSTAT 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.

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