4/ Examples of PDF Uncertainty. May 2005 CTEQ Summer School 25

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1 4/ Examples of PDF Uncertainty May 2005 CTEQ Summer School 25

2 Estimate the uncertainty on the predicted cross section for pp bar W+X at the Tevatron collider. global χ 2 local χ 2 s May 2005 CTEQ Summer School 26

3 Each experiment defines a prediction and a range. This figure shows the χ 2 = 1 ranges. May 2005 CTEQ Summer School 27

4 This figure shows broader ranges for each experiment based on the 90% confidence level (cumulative distribution function of the rescaled χ 2 ). May 2005 CTEQ Summer School 28

5 The final result is an uncertainty range for the prediction of σ W. Survey of σ w B lν predictions (by R. Thorne) PDF set energy s w B ln [nb] PDF uncert Alekhin Tevatron 2.73 ± 0.05 MRST2002 Tevatron 2.59 ± 0.03 CTEQ6 Tevatron 2.54 ± 0.10 Alekhin LHC 21.5 ± 0.6 MRST2002 LHC 20.4 ± 0.4 CTEQ6 LHC 20.5 ± 0.8 May 2005 CTEQ Summer School 29

6 Inclusive W production at the Tevatron, Run 2 (K factor for NNLO/NLO = has been applied) Red: e.v. basis sets Blue: full uncertainty range 2.63 ± 0.09 nb Orange: MRST prediction 2.69±0.11 nb Green: Latest CDF value 2.780±0.014±0.060±0.167 nb Purple: Latest D0 value 2.865±0.008±0.075±0.186 nb May 2005 CTEQ Summer School 30

7 The error ellipse for W and Z production at the Tevatron, Run 2 Red: e.v. basis sets Purple: Full uncertainty range (error ellipse) Blue: Uncorrelated ranges, roughly ±3% each May 2005 CTEQ Summer School 31

8 Error ellipse for W and Z production at the LHC Red: e.v. basis sets Blue: uncorrelated ranges Purple: Full uncertainty range (error ellipse) May 2005 CTEQ Summer School 32

9 W production at the LHC is sensitive to the gluon distribution function. Tevatron: W production can occur by a LO process with valence quarks. LHC: The LO contribution must involve a sea quark; and there is an NLO contribution from a gluon. May 2005 CTEQ Summer School 33

10 How well can we determine the value of α S ( M Z ) from Global Analysis? For each value of α S, find the best global fit. Then look at the χ 2 value for each experiment as a function of α S. May 2005 CTEQ Summer School 34

11 Each experiment defines a prediction and a range. This figure shows the χ 2 = 1 ranges. Particle data group (shaded strip) is 0.117± The fluctuations are larger than expected for normal statistics. The vertical lines have χ 2 global=100, α s (MZ)=0.1165± May 2005 CTEQ Summer School 35

12 May 2005 CTEQ Summer School 36

13 Uncertainties of LHC parton-parton luminosities Lum(ˆ) s = C i, j ij fi ( x1) f j( x2) δ s x1x2s) dx1dx2 Provides simple estimates of PDF uncertainties at the LHC. May 2005 CTEQ Summer School 37 (ˆ

14 PDF uncertainty for inclusive jet production at CDF and D0 Run 1 data CTEQ6.1 the 40 eigenvector basis sets May 2005 CTEQ Summer School 38

15 (D-T)/T for Run 1 data CTEQ6.1: the 40 eigenvector basis sets May 2005 CTEQ Summer School 39

16 The 40 eigenvector basis sets used to calculate PDF uncertainty in the Hessian method May 2005 CTEQ Summer School 40

17 Predictions for Run 2 at CDF and D0 The boundaries are the full uncertainty range from the Master Formula. May 2005 CTEQ Summer School 41

18 CTEQ6.1 The u-quark PDf and its full uncertainty band. (This representation is potentially misleading because low-x and high-x are correlated!) May 2005 CTEQ Summer School 42

19 Comparison of MRST and CTEQ6 u-quark May 2005 CTEQ Summer School 43

20 Comparison of MRST and CTEQ6 u-quark May 2005 CTEQ Summer School 44

21 CTEQ6.1 The gluon PDf and its full uncertainty band. (This representation is potentially misleading because low-x and high-x are correlated!) May 2005 CTEQ Summer School 45

22 Comparison of MRST and CTEQ6 gluon May 2005 CTEQ Summer School 46

23 Comparison of MRST and CTEQ6 gluon May 2005 CTEQ Summer School 47

24 Theoretical uncertainties may also be important, but are more difficult to assess. Parameterization of f(x,q 0 ) at Q 0 =1.3 GeV a nonperturbative function Higher order QCD corrections ( NNLO perturbation theory) May 2005 CTEQ Summer School 48

25 5/ Outlook May 2005 CTEQ Summer School 49

26 Parton distribution functions are a necessary theoretical infrastructure for hadron colliders. Tools now exist to assess the PDF uncertainties. Certain advances will be important for making accurate predictions for the LHC. May 2005 CTEQ Summer School 50

27 HERA2LHC and TEV4LHC New Data to include in the global analysis NuTeV, HERA II, Tevatron Run 2 Extend the accuracy of the global analysis to NNLO perturbation theory. May 2005 CTEQ Summer School 51