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Parton Distribution Functions from Global Fits

Parton Distribution Functions from Global Fits. overview. current issues and questions. James Stirling (IPPP Durham) Hi-X Workshop 2004. some specific high-x issues. All MRST results with Alan Martin, Dick Roberts & Robert Thorne. parton distribution functions f i (x,Q 2 ) ….

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Parton Distribution Functions from Global Fits

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  1. Parton Distribution Functions from Global Fits overview current issues and questions James Stirling (IPPP Durham) Hi-X Workshop 2004 some specific high-x issues All MRST results with Alan Martin, Dick Roberts & Robert Thorne Marseille, 26 July 2004

  2. parton distribution functions fi(x,Q2) … • needed for high precision (SM and BSM) cross section predictions: th = pdf + … at Tevatron, LHC, … • encode important information about the quark, gluon structure of hadrons • are fundamental QCD quantities – calculable in principle from first-principles (e.g. lattice) QCD, in practice obtained from global fits to wide variety of data Marseille, 26 July 2004

  3. ^  • where X=W, Z, H, high-ET jets, SUSY sparticles, black hole, …, and Q is the ‘hard scale’ (e.g. = MX), usuallyF = R = Q, and  is known … • to some fixed order in pQCD and EWpt, e.g. • or in some leading logarithm approximation • (LL, NLL, …) to all orders via resummation the QCD factorization theorem for hard-scattering (short-distance) inclusive processes ^ Marseille, 26 July 2004

  4. DGLAP equations F2(x,Q2) = q eq2 x q(x,Q2)etc xdependence of fi(x,Q2) determined by ‘global fit’ to deep inelastic scattering (H1, ZEUS, NMC, …) and hadron collider data Marseille, 26 July 2004

  5. 1972-77 1977-80 2004 >1991 Need to know splitting and coefficient functions to the same perturbative order to ensure that (n)/logF = O(αS(n+1)) Marseille, 26 July 2004

  6. new Full 3-loop (NNLO) DGLAP splitting functions! previous estimates based on known moments and leading behaviours Moch, Vermaseren and Vogt, hep-ph/0403192, hep-ph/0404111 Marseille, 26 July 2004

  7. comparison with existing approximate NNLO fits? (MRST, Alekhin) • exact NNLO splitting functions are very close to approximate splitting functions (van Neerven, Vogt) based on moments & known small- and large-x behaviours… • … and therefore the corresponding pdfs are almost identical • Note: • the full NNLO pdf fit awaits calculation of the inclusive high ET jet cross section at NNLO • including NNLO (splitting & coefficient functions) gives a slight improvement in overall fit quality, and reduction in αS(MZ) from 0.119 to 0.116 Marseille, 26 July 2004

  8. ratio of MRST2001 NLO and ‘NNLO’ parton distributions Marseille, 26 July 2004

  9. Who? Alekhin, CTEQ, MRST, GGK, Botje, H1, ZEUS, GRV, BFP, … http://durpdg.dur.ac.uk/hepdata/pdf.html pdfs from global fits Formalism LO, NLO, NNLO DGLAP MSbar factorisation Q02 functional form @ Q02 sea quark (a)symmetry etc. fi (x,Q2) fi (x,Q2) αS(MZ ) Data DIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … ) Drell-Yan (E605, E772, E866, …) High ET jets (CDF, D0) W rapidity asymmetry (CDF) N dimuon (CCFR, NuTeV) etc. Marseille, 26 July 2004

  10. summary of DIS data + neutrino FT DIS data Note: must impose cuts on DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically: Q2 > 2 - 4 GeV2 W2 = (1-x)/xQ2 > 10 - 15 GeV2 Marseille, 26 July 2004

  11. typical data ingredients of a global pdf fit Marseille, 26 July 2004

  12. recent global fit work • H1, ZEUS: ongoing fits for pdfs + uncertainties from HERA and other DIS data • Martin, Roberts, WJS, Thorne (MRST): updated `MRST2001' global fit (hep-ph/0110215); LO/NLO/‘NNLO’ comparison (hep-ph/0201127); pdf uncertainties: from experiment (hep-ph/0211080) and theory (hep-ph/0308087) • Pumplin et al. (CTEQ): updated ‘CTEQ6’ global fit (hep-ph/0201195), including uncertainties on pdfs; dedicated study of high ET jet cross sections for the Tevatron (hep-ph/0303013); strangeness asymmetry from neutrino dimuon production (hep-ph/0312323) • Giele, Keller, Kosower (GKK): restricted global fit, focusing on data-driven pdf uncertainties (hep-ph/0104052) • Alekhin: restricted global fit (DIS data only), focusing on effect of both theoretical and experimental uncertainties on pdfs and higher-twist contributions (hep-ph/0011002); updated and including ‘NNLO’ fit (hep-ph/0211096) Marseille, 26 July 2004

  13. HEPDATA pdf server Comprehensive repository of past and present polarised and unpolarised pdf codes (with online plotting facility) can be found at the HEPDATA pdf server web site: http://durpdg.dur.ac.uk/hepdata/pdf.html … this is also the home of the LHAPDF project Marseille, 26 July 2004

  14. (MRST) parton distributions in the proton Martin, Roberts, S, Thorne Marseille, 26 July 2004

  15. pdfs with errors…. CTEQ gluon distribution uncertainty using Hessian Method output = best fit set + 2Np error sets Hessian Matrix “best fit” parameters Marseille, 26 July 2004

  16. some current issues… • need a better understanding of differences between pdf sets (central values and error bands): not just ‘experimental errors’ (easier) but theoretical errors too (harder). • are apparent ‘tensions’ between data sets caused by experiment or theory? • is high-precision F2 small-x data from HERA revealing breakdown of fixed-order DGLAP? If so, what are implications for LHC? • the impact of a full NNLO pdf fit? (needs NNLO jet ) Marseille, 26 July 2004

  17. current issues contd. • impact on global fits of forthcoming new Tevatron jet data, also HERA jet data? (via γ*g→jets) • flavour structure of sea: e.g. ubar  dbar ands  sbar (NuTeV) • relative behaviour of u and d at large x • QED effects in pdfs (via O(α) corrections to DGLAP) • pdfs @ LHC • FL direct information on the small-x gluon. Will this ever be measured at HERA?! Marseille, 26 July 2004

  18. Djouadi & Ferrag, hep-ph/0310209 Marseille, 26 July 2004

  19. Djouadi & Ferrag, hep-ph/0310209 Marseille, 26 July 2004

  20. Djouadi & Ferrag, hep-ph/0310209 Marseille, 26 July 2004

  21. why do ‘best fit’ pdfs and errors differ? • different data sets in fit • different subselection of data • different treatment of exp. sys. errors • different choice of • tolerance to define  fi(CTEQ: Δχ2=100, Alekhin: Δχ2=1) • factorisation/renormalisation scheme/scale • Q02 • parametric form Axa(1-x)b[..] etc • αS • treatment of heavy flavours • theoretical assumptions about x→0,1 behaviour • theoretical assumptions about sea flavour symmetry • evolution and cross section codes (removable differences!) Marseille, 26 July 2004

  22. small MRST and CTEQ differences largely understood, see hep-ph/0211080 mainly: CTEQ gluon at Q02 required to be positive at small x means gCTEQ > gMRST there, also 2 = 50 (MRST), 100 (CTEQ) • ALEKHIN gluon smaller at high x (no Tevatron jet data in fit) and different content of sea at small x from different assumptions about ubar-dbar as x  0 and (ii) ratio of strange to non-strange pdfs. Also 2 = 1 allowed by use of smaller overall data set. Marseille, 26 July 2004

  23. MRST: Q02 = 1 GeV2,Qcut2 = 2 GeV2 xg = Axa(1–x)b(1+Cx0.5+Dx) – Exc(1-x)d • CTEQ6: Q02 = 1.69 GeV2,Qcut2 = 4 GeV2 xg = Axa(1–x)becx(1+Cx)d Marseille, 26 July 2004

  24. tensions within the global fit? pictures from W-K Tung • with dataset A in fit, Δχ2=1 ; with A and B in fit, Δχ2=? • ‘tensions’ between data sets arise, for example, • between DIS data sets (e.g. H and N data) • when jet and Drell-Yan data are combined with DIS data Marseille, 26 July 2004

  25. CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100 Marseille, 26 July 2004

  26. as small x data are systematically removed from the MRST global fit, the quality of the fit improves until stability is reached at around x ~0.005 (MRST hep-ph/0308087) Q. Is fixed–order DGLAP insufficient for small-x DIS data?! Δ = improvement in χ2 to remaining data / # of data points removed Marseille, 26 July 2004

  27. the stability of the small-x fit can be recovered by adding to the fit empirical contributions of the form ... with coefficients A, B found to be O(1) (and different for the NLO, NNLO fits); the starting gluon is still very negative at small x however Marseille, 26 July 2004

  28. extrapolation errors theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x–0.5 as x → 0 Marseille, 26 July 2004

  29. ubar=dbar differences between the MRST and Alekhin u and d sea quarks near the starting scale Marseille, 26 July 2004

  30. Marseille, 26 July 2004

  31. Marseille, 26 July 2004

  32. some specifically high-x issues… • the ratio of d/u as x 1 ? (see next talk) • very little is known about flavour structure of sea at high-x, e.g. ubarvs.dbar, s vs.sbar, … • isospin violation, up≠ dn (Induced by QED corrections to pdf analyses, also partial explanation of NuTeV data?) Future experiments (JLab, HERA, LHC?, new DY?, …) can hopefully shed light on some of these Note: how the above quantities appear at large x in currently available pdfs is very dependent on the input parametrisations used; thus if fi (x,Q02)~(1-x)a is assumed then all parton ratios  0 or  Marseille, 26 July 2004

  33. Q. is NLO (or NNLO) DGLAP sufficient at high x? Are higher-orders ~ αSn logm (1-x) important? Higher-twist ~ 1/[Q2(1-x)]neffects? DGLAP evolution Q. is NLO (or NNLO) DGLAP sufficient at small x? Are higher-orders ~ αSn logm x important? For production of heavy object X at LHC, Tevatron, … the momentum fractions x1 and x2aredetermined by the mass and rapidity of X Marseille, 26 July 2004

  34.  forward W, Z, dijet… production at LHC samples small and high x but no acceptance, no triggers?! Marseille, 26 July 2004

  35. sin2W from N Marseille, 26 July 2004

  36. Conclusion: uncertainties in detailed parton structure are substantial on the scale of the precision of the NuTeV data – consistency with the Standard Model dos not appear to be ruled out at present Marseille, 26 July 2004

  37. effect of NNLO at high x • including NNL0 gives stronger scaling violations at large x, mainly through the coefficient function rather than P(2) • thisgives a slightly smaller value ofαS • …and a slightly smaller empirical higher-twist contribution when the fit is extended to smaller Q2 andW2 Marseille, 26 July 2004

  38. Fitted values of D(x) for a higher-twist contribution of the form F2 (1 + D(x) / Q2) in the global fit [MRST hep-ph/0007099] Marseille, 26 July 2004

  39. QED effects in pdfs QED corrections to DIS include: included in standard radiative correction packages (HECTOR, HERACLES) Marseille, 26 July 2004 Note:Cintfinite asmq 0

  40. above QED corrections are universal and can be absorbed into pdfs, exactly as for QCD singularities, leaving finite (as mq 0) O(α) QED corrections in coefficient functions • relevant for electroweak correction calculations for processes at Tevatron & LHC, e.g. W, Z, WH, … (see e.g. U. Baur et al, PRD 59 (2003) 013002) Marseille, 26 July 2004

  41. QED-improved DGLAP equations • at leading order in α and αS where • momentum conservation: Marseille, 26 July 2004

  42. effect on quark distributions negligible at small x where gluon contribution dominates DGLAP evolution at large x, effect only becomes noticeable (order percent) at very large Q2, where it is equivalent to a shift in αS of αS  0.0003 dynamic generation of photon parton distribution (x,Q2) effect on valence quark evolution: (MRST study in progress) Marseille, 26 July 2004

  43. summary • The refinement of our knowledge of parton distributions continues, we are now moving into the “NNLO” era, in time for LHC where we can expect to make high-precision predictions (Higgs, SUSY, …) • High-X is another interesting frontier for pdfs: • we have only limited knowledge of some parton flavours (antiquarks, strange, charm, …) because of absence of data • “Standard” (fixed-order, leading-twist) theory is clearly inadequate, important to identify and quantify the leading corrections and study their impact on pdf extraction. Marseille, 26 July 2004

  44. extra slides Marseille, 26 July 2004

  45.  bbZ contribution to Z production @ LHC Marseille, 26 July 2004

  46. examples of ‘precision’ phenomenology jet production W, Z production NNLO QCD NLO QCD Marseille, 26 July 2004

  47. ±3% ±2% contours correspond to ‘ experimental’ pdf errors only; shift of prediction using CTEQ6 pdfs shows effect of ‘theoretical’ pdf errors Marseille, 26 July 2004

  48. Marseille, 26 July 2004

  49. Marseille, 26 July 2004

  50. (LO) W cross sections at the Tevatron and LHC using (NLO) partons from MRST, CTEQ and Alekhin Marseille, 26 July 2004

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