1. Global QCD Analysis and Hadron Collider Physics What is the role of QCD and global QCD analysis in Hadron Collider Physics? Review of global QCD analysis: how far have we come; how far do we still have to go? What can global QCD analysis do for hadron collider physics? How can hadron collider physics contribute to global QCD analysis of nucleon structure?

2. Representative Standard Model processes—cross sections and event rates at the Tevatron and LHC  tot HH TT  w/z bb New Physics signals, if present, are generally quite low, and difficult to disentangle from the QCD and EW “backgrounds”. ~10 14

3. The many faces of QCD in Hadron Collider Physics hadrons leptons, hadrons partons, gauge bosons, new particles (universal) parton Distributions SM physics: PQCD & EW jet algorithms hadronization models: MC programs frag. functions New physics scenarios Asymptotic Freedom and Factorization of QCD: L.D. S.D. L.D. QCD enters in all aspects of HCP (red boxes).

4. Significant Recent Progress in PQCD Physics Quantitative (NLO) treatment of general processes: Systematic NLO Calculation of Multi-particle (W/Z, , jets) final states; Development of NLO MC event generators; Better understanding of heavy quark production and decay;…. Precision (NNLO) Study of critical processes: Evolution kernel ; Z, W, , rapidity distributions ; Higgs production;…. Cf. other talks at this conference This talk will be concerned with … Various resummation schemes for multi-scale problems

5. Global QCD Analysis of Parton Structure of the Nucleon Intrinsic interest: QCD dynamics at short distance, PQCD; fundamental structure of the nucleon (non- perturbative) — QCD dynamics at the confinement scale; Practical importance: essential ingredient that connects the hadron world to the parton world for all SM and New physics processes in hadron colliders. (Crucial to understanding both the signal and the background of most processes of interest.) Survey: How far have we come along, 20 years after EHLQ and Duke-Owens (when SSC was the big dream) ? How much more do we have to go (in order to realize the full potential of Tevatron and LHC) ?

6. universal, extracted by global analysis Theory Input

7. NuTev

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

9. 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).

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

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

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

13. Evolving …

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

15. Gluon consolidation

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

17. Uncertainties of PDFs: CTEQ6 by an iterative Hessian method, using orthonormal eigenvector sets Q 2 = 10 GeV 2 Theory uncertainties not explicitly included; but some allowance is made in the tolerance.

18. Valence and Sea Quark distributions of the Nucleon Do the sea quarks observe SU(2) isospin symmetry? Certainly not! Large-x behavior open. 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?

19. 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?

20. 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 …

21. 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

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

23. 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 solu-tions.); (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.

24. Theoretical uncertainties (at small x and low Q): 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. hep-ph/0308087 Important for Tevatron II and LHC physics: Are these indications supported also by current CTEQ analysis?

25. LHCσ NLO (W) (nb) MRST2002204 ± 4 (expt) CTEQ6205 ± 8 (expt) Alekhin02215 ± 6 (tot) similar partons different Δχ 2 different partons Standard Candle: σ(W) and σ(Z) : precision predictions and measurements at Tevatron Run 2 and the LHC.  4% total error (MRST 2002) (Stirling, HeraLhc Workshop 2004) Exptl uncertainties:

26.  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

27. MRST “Theory” Uncertainty (varying cuts in global fits) (2003) 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 !

28.  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 %

29. 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.

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

31. The Differences in Gluon distributions – another view

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. Main Partonic processes for Higgs production:

34. Higgs Production at LHC --- State-of-art calculations (up to NNLO) Harlander,Kilgore(03) Theoretical uncertainties

35. Higgs Physics at the Tevatron and LHC Uncertainties due to PDFs for gg  H --- by comparing different PDF sets Djouadi & Ferrag, hep-ph/0310209

36. Higgs Physics at the Tevatron and LHC Uncertainties due to PDFs for pp  H W Djouadi & Ferrag, hep-ph/0310209

37. Comparing % Uncertainties due to PDFs and due to higher order corrections (as estimated by scale dep.) Belyaev, Pumplin, T, Yuan (Dis2005)

38. How are the uncertainties due to PDFs estimated? Use the Lagrange Multiplier method in global analysis: scan the maximum allowed range of , using “constrained fits”.

39. Top Cross section at the Tevatron M. Cacciari, S. Frixione, M.L. Mangano, P. Nason, G. Ridolfi CTEQ PDF uncertainties MRST PDF uncertainties MRST PDF uncertainties + scale dependence

40. 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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