Parton distribution uncertainty and W and Z production at hadron colliders

1. Parton distribution uncertainty and W and Z production at hadron colliders Dan Stump Department of Physics and Astronomy Michigan State University CTEQ Meeting

2. PDF uncertainty and inclusive jet production CTEQ Meeting

3. PDF uncertainty and the cross section for inclusive jet production at the Tevatron. Run 1: CTEQ6.1, central fit and 40 Eigenvector Basis Sets CTEQ Meeting

4. Comparing the CDF data (Run 1) and the NLO calculation with CTEQ6.1 Green: 1 + 40 alternative sets; Red: full uncertainty range CTEQ Meeting

5. The “master equation” for the Hessian method asymmetric errors, or one could use the Sullivan-Nadolsky formula CTEQ Meeting

6. Inclusive jet cross section for Run 2, in 5 rapidity bins, predicted by CTEQ6.1. Red: central prediction; Blue: full uncertainty range CTEQ Meeting

7. Inclusive jet cross section for the LHC, predicted by CTEQ6.1. central prediction + 40 alternatives CTEQ Meeting

8. PDF uncertainty — the method CTEQ Meeting

9. Uncertainties of Parton Distribution Functions —a major challenge for global analysis The total cross sections for W and Z production were among the first examples to which we applied the new methods of uncertainty analysis. sW and sZ were good test cases. CTEQ Meeting

10. Estimate the uncertainty on the predicted cross section for ppbar W+X at the Tevatron collider. global c2 local c2’s CTEQ Meeting

11. Each experiment defines a “prediction” and a “range”. This figure shows the Dc2 = 1 ranges. CTEQ Meeting

12. This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled c2). CTEQ Meeting

13. The final result is an uncertainty range for the prediction of sW. Survey of swBln predictions (by R. Thorne, 2002) CTEQ Meeting

14. Each experiment defines a “prediction” and a “range”. This figure shows the Dc2 = 1 ranges for the value of aS. Particle data group (shaded strip) is 0.1170.002. The fluctuations are larger than expected for normal statistics. The vertical lines have Dc2global=100; as(MZ)=0.11650.0065. CTEQ Meeting

15. How well can we determine the value of aS( MZ ) from Global Analysis? For each value of aS, find the best global fit. Then look at the c2 value for each experiment as a function of aS. CTEQ Meeting

16. PDF uncertainty for W/Z production CTEQ Meeting

17. Inclusive Z production at the Tevatron, Run 2 (K factor for NNLO/NLO = 1.045 has been applied) Red: 1 + 40 alternativesBlue: full uncertainty range 0.258  0.008 nb Green: Latest CDF value Purple: Latest D0 value 0.25390.00330.00460.0152 nb 0.26490.00390.00990.0172 nb CTEQ Meeting

18. Inclusive W production at the Tevatron, Run 2 (K factor for NNLO/NLO = 1.037 has been applied) Red: 1 + 40 e.v. basis setsBlue: 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 CTEQ Meeting

19. The error ellipse for W and Z production at the Tevatron, Run 2 Red: 1 + 40 e.v. basis sets Purple: Full uncertainty range (error ellipse) Blue: Uncorrelated ranges, roughly 3% each CTEQ Meeting

20. Are the “up” and “down” displacements along the eigenvector directions symmetric? CTEQ Meeting

21. Z production at the LHC Red: 1 + 40 e.v. basis setsBlue: Full uncertainty range 1.95  0.07 nb CTEQ Meeting

22. W production at the LHC Red: 1 + 40 e.v. basis setsBlue: Full uncertainty range 19.5  0.8 nb Orange: MRST prediction 20.00.8 nb CTEQ Meeting

23. Error ellipse for W and Z production at the LHC Red: 1 + 40 e.v. basis sets Blue: uncorrelated ranges Purple: Full uncertainty range (error ellipse) CTEQ Meeting

24. The PDF uncertainty in the ratiosZ/sW is very small possible test for new physics. CTEQ Meeting

25. Why calculations don’t agree CTEQ Meeting

26. W production at the Tevatron; MRST calculations from their paper on Theoretical Errors CTEQ 2.630.09 nb CTEQ Meeting

27. W production at the LHC; MRST calculations from their paper on Theoretical Errors CTEQ 19.50.8 nb CTEQ Meeting

28. Other theoretical uncertainties • Branching ratio • Treatment of W width (off shell W) • EW parameter values, e.g., CKM matrix • Treatment of heavy quark mass effects • may lead to differences of order 1 % CTEQ Meeting

29. A survey of results from different programs (Pavel Nadolsky, C P Yuan) s = 1.96 TeV s = 14 TeV CTEQ Meeting

30. PT dependence of vector boson production Collins, Soper and Sterman (CSS) formalism for pT resummation, schematically, BLNY parametrization (Brock, Landry, Nadolsky, Yuan) i.e., 4 N.P. parameters (g1,g2,g3,bmax) CTEQ Meeting

31. The BLNY fit to E288, E605, CDF Z, and D0 Z data CTEQ Meeting

32. Standard Dc2 = 1 parameter errors … but are such small uncertainties realistic? CTEQ Meeting

33. Reassess the parameter uncertainties, using the methods that we have used for PDF uncertainties. The most interesting parameter, and which should have the largest uncertainty, is g2. • Method • Scan the BLNY fit versus g2 values. • For a range of g2 values, construct the best fit to g1 and g3. • Then look how c2 varies with g2. CTEQ Meeting

34. A c2 “parabola” for each experiment… … implies an allowed range for the value of g2 for each experiment. bmax = 0.5 GeV-1 CTEQ Meeting

35. A c2 “parabola” for each experiment… … implies an allowed range for the value of g2 for each experiment. bmax = 1.12 GeV-1 CTEQ Meeting

36. Comparison of CDF Z and D0 Z data (Run 1) to resummation calculation with BLNY parametrization CTEQ Meeting

37. More work needs to be done to obtain a final uncertainty range for g2. Our larger goal is to include pT cross sections in the global analysis; i.e., simultaneously to fit PDF parameters and resummation parameters, for both W and Z production. CTEQ Meeting