1. Status of Recent Parton Distribution Analyses Hung-Liang Lai Department of Science Education Taipei Municipal Teachers College Introduction Time evolution of Parton Distributions Stability studies @Taipei Summer Institute, National Taiwan Univ. July 21, 2005 (Compiled from talks given by W.K.Tung@Beijing and D. Stump@DIS05)

2. universal, extracted by global analysis Theory Input

3. NuTev

4. Experimental input (continued) ( ) (DIS jets, heavy quark prod. …)

5. Kinematics of Parton variables LHC Tevatron QCD (DGLAP) evolution Predictive power of global analysis of PDFs is based on the renormalization group properties of the universal Parton Distributions f(x,Q).

6. Progress in the determination (time evolution) of the u-quark distribution pre-HERA post-HERA

7. The old and the new Does the happy story continue for the other parton flavors? NO ! The d-quark story

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

9. Evolving …

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

11. Gluon consolidation

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

13. Valence and Sea Quark distributions of the Nucleon How about (flavor) SU(3) symmetry (s+sb=ub+db)? Is the strange sea charge symmetric (s = sb)? How does the d(x)/u(x) ratio behave? Low/medium x behavior well determined; Large-x behavior open. Certainly not!  ~0.4 more precise value to come. Jury is still out. Has important implications on the NuTeV anomaly. What about heavy quark distributions?

14. What do we know about heavy quark distributions? There is yet very little direct experimental input. Theory formulation further depends on the “scheme” chosen to handle heavy quark effects in PQCD– fixed-flavor-number (FFN) vs. variable-flavor- number (VFN) schemes, threshold suppression prescriptions, … etc. All c(x,Q) and b(x,Q) found in existing PDF sets are based on “radiatively generated” heavy flavors. Open question: Are there any “intrinsic” heavy quarks?

15. Any non-perturbative (intrinsic) component, if it exists, is expected to be primarily in the large-x region, hence will be distinguishable from the perturbative (radiative) one. Yet unexplored Territories …

16. Standard Candle Processes: W/Z total cross-section predictions; Precision PQCD phenomenological analyses: W/Z rapidity distribution; W/Z transverse momentum distribution; W-mass measurement; W/Z + Jet differential cross sections; … (Echo precision DIS phenomenology of the 1990’s) Precision Top and Higgs Phenomenology: predictions and measurement of SM parameters. Predictions on possible New Physics Discoveries: SUSY, Technicolor and other strong dynamics, Extra Dimensions … Collider Physics Issues related to Global QCD Analysis

17. PDFs, Tevatron and LHC Global analysis of PDFs (fixed-target, Hera, & Hadron Colliders) Tevatron Run II measurements LHC measurements

18. The precision phenomenology issues are intimately tied to: How well do we understand the uncertainties of PDFs? Uncertainties due to exptl input to the global analysis: Have been the focus of much work by several groups (exptl and theory); (Alekhin, GKK, H1, Zeus, Cteq, Mrst) Issues are complex; most recent, practical approaches are: (i) an iterative Hessian method (eigenvector solutions.); (ii) a Lagrange Multiplier method---developed by Stump, Pumplin etal (MSU/CTEQ) (adopted by Mrst) The main difficulty is not with the theory of statistical methods; rather it is with developing sensible ways to treat nominally incompatible experimental data sets used in the global analysis.  There are no rigorous answers; some subjective judgment must be involved.  differences in estimated uncertainties among groups.

19. Uncertainties of PDFs: CTEQ6 by an iterative Hessian method, using orthonormal eigenvector sets Q 2 = 10 GeV 2

20. Stability Studies These issues were studied in CTEQ1,2 analyses. The stable cuts found then have been left unchanged since. (No less difficult to quantify. Studied empirically by varying kinematic cuts used in the global analysis.) Recent study by MRST revived the interest on this issue, particularly because of its findings, that the cuts have an important impact on predictions for the PDFs, and their Tevatron Run II and LHC predictions. EPJ,C35, 325(2004) Important for Tevatron II and LHC physics: Are these indications supported also by current CTEQ analysis?

21. Standard Candle: σ(W) and σ(Z) : precision predictions and measurements at Tevatron Run 2 and the LHC.  4% total error (MRST 2002)

22.  w and  z ranges due to PDF uncertainties Error range: 2 – 5 %; W-, Z- cross sections are highly correlated; Tevatron(CDF)LHC(CTEQ) Use CTEQ eigenvector PDF sets

23. MRST “Theory” Uncertainty (varying cuts in global fits) (EPJ,2004) Are these findings disturbing? Are theory uncertainties really so large at NLO–so much larger than NNLO corrections at LHC? Is stability reached only at NNLO? CTEQ studied this issue … Alarm bell? Instability at NLO !

24.  W at the Tevatron No instability found in the CTEQ NLO analysis. Issue related to compatibility of data sets; parametrization of PDFs; behavior of gluon at large and small x, … etc. The results of applying x cuts to the CTEQ6 data set then performing NLO fits: 20 % 2 %

25. To gain more insight into the results… … probe the uncertainty of a prediction from the global analysis using the Lagrange Multiplier method.

26. MRST paper: Removing the constraints of data with x < 0.005 radically changes the NLO PDF’s and hence the cross section for W production. The differential cross section, d  /dy. [MRST, Eur Phys J C35, 325 (2004)]

27. The effects of the strong cuts:  the central prediction barely moves;  the uncertainty increases significantly. Lagrange Multiplier method  calculate  2 versus  W.  2 versus  W [positive gluon] Black curve: standard cuts (x min =0) Blue curve: strong cuts (x min =0.005)

28. W production at the LHC is sensitive to the gluon distribution function. Tevatron: W production is dominated by a LO process with two valence quarks. LHC: The LO contribution must involve a sea quark; and the NLO contribution from a gluon is significant.

29. Black: CTEQ6.1 Green: CTEQ estimated Range of uncertainty Blue: MRST2002 (“default”) Red: MRST2003c (“conservative”) The Differences in Gluon distributions small x large x

30. The Differences in Gluon distributions – another view

31. Conclusions Much progress has been made over the past two decades on parton distribution analyses. Up and down distributions are well determined. Gluon is in good shape. Strange and heavy flavors are still short of data to qualify. NLO stability is not really of a question. But the drive to NNLO seems natural when ingredients are ready. CTEQ group is working on NNLO implementation.

32. How much do predictions of LHC physics depend on knowledge of PDFs? General observations: Processes that are sensitive to gluons will have large PDF-related uncertainties; Processes that are sensitive to PDFs at very small x, or “large” x will have larger uncertainties; For most processes, uncertainties due to PDFs are much larger than that due to higher-order corrections (generally NNLO). Systematic global QCD analyses to quantify, and to reduce, the uncertainties of PDFs are essential for all aspects of the collider physics programs of Tevatron II, Hera II, and LHC.

33. What can HCP contribute to Global QCD Analysis of nuclear structure (i.e. PDFs) In general: next generation of colliders are W/Z factories; many processes can provide new information on PDFs. More specifically: Many gluon-sensitive processes can help narrow the large uncertainties on g(x,Q 0 ) ; W/Z rapidity distributions, R(W + /W - ), … can provide needed information on SU(2) flavor dependence of partons; New channels to study heavy quark distributions. All these can have significant feedback on precision measurement of m W, and top, Higgs parameters.

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