1. 1984 – 2004: 20 Years of Global QCD Analysis of the Parton Structure of Nucleon – A survey of open issues through the historical perspective DIS04Strbske PlesoTung

2. The two Topcite papers that started this journey in 1984: Q**2 DEPENDENT PARAMETRIZATIONS OF PARTON DISTRIBUTION FUNCTIONS.1092 citations By D.W. Duke, J.F. Owens (Florida State U.),. FSU- HEP-831115, Nov 1983. Phys.Rev.D30:49,1984D.W. DukeJ.F. OwensFlorida State U. SUPER COLLIDER PHYSICS. By E. Eichten, I. Hinchliffe, Kenneth D. Lane, C. Quigg,. Feb 1984. 550pp. 1667 citations Rev.Mod.Phys.56:579,1984E. EichtenI. HinchliffeKenneth D. LaneC. Quigg

3. How far have we come along? What still remains unclear? How far do we still to go?

4. Agenda The Valence quarks The Gluon The Sea quarks  Breaking of Iso-spin Symmetry  Breaking of flavor SU(3)  Strangeness Asymmetry?  Iso-spin Violation?  Heavy Quark Parton Distributions Uncertainties of  Parton Distributions, and  Their Physical Predictions

5. The Valence u Quark: progression of improvements LO fits to early fixed-target DIS data To view small and large x in one plot To reveal the difference in both large and small x regions

6. NLO fits to more fixed- target DIS data sets

7. The beginning of the Hera era ….

8. Refinements …

9. All in the details now? Time to move on to something else?

10. D quark, the other twin: Early LO fits

11. NLO, no dramatic changes

12. The impact of Hera

13. The old and the new Does the happy story continue?

14. The story about the gluon is more interesting, and not as happy …

15. Evolving …

16. Hera again … Small-x ’ s gain is large-x ’ s loss!

17. consolidation

18. What goes up must come down? Does gluon go negative at small x and low Q?(MRST)

19. Uncertainties of PDFs: CTEQ6 Theory un- certainties not included Thus, only lower bounds on the uncertainties

20. Two potential Direct Measurements of the Gluon Distribution Measurement of the longitudinal Structure Function in DIS. Crucial. Still possible at Hera? Direct Photon Production in Hadron Collisions  Data exist–but not always consistent with each other (WA70 and E706);  Theoretical uncertainties in NLO QCD overwhelming; Resummed QCD promising, but has not delivered so far.

21. The non-strange sea quarks: do they observe isospin symmetry? Theorists: Sure, why not ? Isn’t the gluon flavor neutral?

22. Experiments: Let Nature speaks for him/her self! Surprised, you theorists? No, there is no physics reason for db=ub ! Measurement of F 2 n -F 2 p in NC DIS experiments

23. More experimental inputs: (mostly DY asymmetry)

24. Caution: “Modern fit” without DY and Collider input: New DY data (E866) have raised new questions about the large x region

25. Comparing the Valence Quarks of the Nucleon:

29. Odd man out?

31. Strange Content of the Nucleon Structure SU(3) flavor symmetric sea quarks? Why not?

32. Experimental input: (low statistics) data on Dimuon (charm) production in Neutrino-Nucleus scattering.

33. No qualitatively new development

34. CCFR-NuTeV (high statistics) data for dimuon production from  N and anti-  N scattering. Odd man out?

35. All together:

36. Issue: Uncertainties on PDFs The statistical principles and methods for uncertainty analyses are well established: Likelihood,  2, … etc.---all textbook stuff, nothing extraordinary in principle. The devil is, not mainly in the details, rather:  Unknown theoretical uncertainties  Unknown experimental uncertainties What’s needed?

37. Reality #1 : compatibility of experiments (Giele etal, 2001)

38. Basic dilemma: What is the real uncertainty on a measured quantity due to incompatible experimental results? Imagine that two experimental groups have measured a quantity , with the results shown. What is the value of  ? (This is common occurrence in the real world.)   2 L -1 Are all experimental errors understood? Should the errors be taken at face value? What do confidence levels mean?

39. Case study: consequences on  s analysis in the GKK approach (likelihood)

40. Uncertainties of Physical Predictions: What is the true uncertainty? (GKK)  ~ 0.4  ~ 0.1

41. Estimate the uncertainty on the predicted cross section for pp bar  W+X at the Tevatron collider. global  2 local  2 ’s Case study: CTEQ global analysis of  W (  2 method)

42. Each experiment defines a “prediction” and a “range”. This figure shows the  2 = 1 ranges.

43. This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled  2 ).

44. “Uncertainty” in 3 scenarios  Only case I is textbook safe; but II and III are “real”.  There are commonly used prescriptions for dealing with II and III; but none can be rigorously justified.  Over time, inconsistencies are eliminated by refined experiments and analyses (either directly measured or indirectly inferred physical quantity  ) Uncertainty dominated by:  2 L -1     2 L -1         This is the Source of large “tolerance”,  2

45. Mimi-Summary The important issue is not about methodology: likelihood vs.  2 ; or Monte Carlo sampling or Hessian approximation, …  They are essentially equivalent, given consistent theoretical and experimental input. The challenges concern:  Catalog, define, and quantify theoretical uncertainties;  Learn to live and work with imperfect and incompatible data sets---there is no unique procedure, only intuition;  Learn to “agree to disagree”;  Learn to compromise, forge consensus (e.g. choice of sensible schemes), while also emphasize distinctiveness, hence diversity and integrity of the physics results.

46. “Tension” between different physical processes and experiments? Intra-process tension:  BCDMS / NMC / HERA ? (cf. GKK;  s analyses)  CC (CCFR) / NC ? (nuclear vs. nucleon targets,..)  CDF / D0 (both prefer large-x gluons; but there are more subtle tensions) Inter-process tension:  DIS / Jets ? (MRST2003)  DY / Jets ? (MRST2001 ?) How do we systematically address these potential incompatibilities? Likelihood method of GKK; Collins and Pumplin

47. Tension between CDF/D0 data sets? CTEQ6 Analysis: Eigenvector 15 in the Hessian approach is particularly sensitive to jet data: + direction: D0=1.24 CDF=1.60 - direction: 0.435 2.04

48. Collins and Pumplin Study - hep-ph/0106173, and … Pumplin – Ringberg03:

50. Lessons learned, so far, are not surprising: 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. 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. But it provides a systematic way of investigating the relevant problems, and quantifying the “incompatibilities”.

51. A critical technical advance in the Hessian approach which enabled the CTEQ uncertainty studies The Hessian method for  2 analysis has always been the standard, but uncertainty estimates in global QCD analysis by standard tools had been known to be extremely unreliable due to two practical problems:.extreme range of eigenvalues (flat vs. steep) numerical fluctuations of theory predictions An iterative method by Jon Pumplin solved both of these technical difficulties, provided the means to generate reliable eigenvectors in parton parameter space, hence allow the systematic exploration of this space, particularly the a priori unknown “flat directions”

56. CTEQ agenda for studying Nucleon Structure and Collider Physics Large x behavior of G(x,Q), u(x,Q) and d(x,Q); New frontiers on detailed flavor structure of the nucleon: Pinning down the strangeness sector of nucleon structure; Understanding the charm content of the nucleon; Precision W/Z phenomenology at the Tevatron and LHC Predictions by and feedback to global analysis Transverse momentum, resummation and W-mass NNLO analysis Higgs, Top, and Beyond SM Phenomenology