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Parton Distribution Functions at the LHC - what are the issues?

Parton Distribution Functions at the LHC - what are the issues?. with Alan Martin, Dick Roberts & Robert Thorne. James Stirling (IPPP Durham) Oxford, 4 May 2004. pdfs at LHC. high precision (SM and BSM) cross section predictions require precision pdfs:  th =  pdf + …

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Parton Distribution Functions at the LHC - what are the issues?

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  1. Parton Distribution Functions at the LHC- what are the issues? with Alan Martin, Dick Roberts & Robert Thorne James Stirling (IPPP Durham) Oxford, 4 May 2004 Oxford, 4 May 2004

  2. pdfs at LHC • high precision (SM and BSM) cross section predictions require precision pdfs: th = pdf + … • ‘standard candle’ processes (e.g. Z) to • check formalism • measure machine luminosity? • learning more about pdfs from LHC measurements (e.g. high-ET jets → gluon, W+/W–→ sea quarks) Oxford, 4 May 2004

  3. where X=W, Z, H, high-ET jets, … and  known • to some fixed order in pQCD and EW • in some leading logarithm approximation (LL, NLL, …) to all orders via resummation ^ QCD factorization theorem for short-distance inclusive processes now: NLO pQCD verysoon: NNLO Oxford, 4 May 2004

  4. DGLAP evolution Q. is NLO (or NNLO) DGLAP sufficient at small x? Are higher-orders ~ αSn logm x important? momentum fractions x1 and x2determined by mass and rapidity of X xdependence of f(x,Q2) determined by fit to data, Q2 dependence determined by DGLAP equations: Oxford, 4 May 2004

  5. new Full 3-loop (NNLO) DGLAP splitting functions! Moch, Vermaseren and Vogt, hep-ph/0403192, hep-ph/0404111 Oxford, 4 May 2004

  6. new comparison with existing approx. 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 Oxford, 4 May 2004

  7. summary of NNLO collider calculations • p + p → jet + X *; in progress • p + p → γ + X; in principle, subset of the jet calculation but issues regarding photon fragmentation, isolation etc • p + p → QQbar + X; requires extension of above to non-zero fermion masses • p + p → (γ*, W, Z) + X *; van Neerven et al, Harlander and Kilgore corrected (2002) • p + p → (γ*, W, Z) + X differential rapidity distribution *; Anastasiou, Dixon, Melnikov (2003) • p + p → H + X; Harlander and Kilgore, Anastasiou and Melnikov(2002-3) Note: knowledge of processes * needed for a full NNLO global parton distribution fit Oxford, 4 May 2004

  8. 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. Oxford, 4 May 2004

  9. (MRST) parton distributions in the proton Martin, Roberts, S, Thorne Oxford, 4 May 2004

  10. examples of ‘precision’ phenomenology jet production W, Z production NNLO QCD NLO QCD Oxford, 4 May 2004

  11. Djouadi & Ferrag, hep-ph/0310209 Oxford, 4 May 2004

  12. Djouadi & Ferrag, hep-ph/0310209 Oxford, 4 May 2004

  13. pdf uncertainties encoded in parton-parton luminosity functions solid = LHC dashed = Tevatron Alekhin 2002 Oxford, 4 May 2004

  14. Note: CTEQ gluon ‘more or less’ consistent with MRST gluon Note:high-x gluon should become better determined from Run 2 Tevatron data Q. by how much? Oxford, 4 May 2004

  15. 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!) → see talks in PDF Working Group! Oxford, 4 May 2004

  16. Djouadi & Ferrag, hep-ph/0310209 Oxford, 4 May 2004

  17. 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 Oxford, 4 May 2004

  18. tensions within the global fit? • 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 Oxford, 4 May 2004

  19. CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100 Oxford, 4 May 2004

  20. 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 Oxford, 4 May 2004

  21. 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 Oxford, 4 May 2004

  22. extrapolation errors theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x–0.5 as x → 0 Oxford, 4 May 2004

  23. ubar=dbar differences between the MRST and Alekhin u and d sea quarks near the starting scale Oxford, 4 May 2004

  24. Oxford, 4 May 2004

  25. how can LHC improve knowledge of pdfs? • test DGLAP evolution at small x by forward hard scattering processes • precision W, Z cross sections for learning more about sea quark asymmetries • improve information of high x gluon distribution? Oxford, 4 May 2004

  26. DGLAP evolution momentum fractions x1 and x2determined by mass and rapidity of X xdependence of f(x,Q2) determined by fit to data, Q2 dependence determined by DGLAP equations: Oxford, 4 May 2004

  27.  forward W, Z, dijet… production samples small x Oxford, 4 May 2004

  28. different partons 4% total error (MRST 2002) similar partons different Δχ2 σ(W) and σ(Z) : precision predictions and measurements at the LHC Oxford, 4 May 2004

  29. x1=0.006 x2=0.006 – x1=0.52 x2=0.000064 ratio close to 1 because u  u etc. (note: MRST error = ±1½%) sensitive to large-x d/u and small x u/d ratios Q. What will be the experimental precision? – – ratio of W–and W+ rapidity distributions Oxford, 4 May 2004

  30. high ET jet cross section at the LHC MRST2001E pdf error band (TeV) Q. What will be the experimental precision? Oxford, 4 May 2004

  31. summary and outlook • need a better understanding of differences between pdf sets (central values and errors): 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 data from HERA revealing breakdown of fixed-order DGLAP? If so, what are implications for LHC? • FL ?! – direct information on the small-x gluon • the impact of a full NNLO pdf fit? Oxford, 4 May 2004

  32. summary and outlook contd. • impact on global fits of HERA jet data? (e.g. γ*g→jets) • current interest in flavour structure of sea: e.g. ubar  dbar ands  sbar (NuTeV). Can LHC provide information? (e.g. s g → W c ) • moving beyond inclusive regime – the role of unintegrated (in kT) parton distributions? • improvements expected by LHC start-up? (i.e. from theory + new HERA, Tevatron data) Oxford, 4 May 2004

  33. extra slides Oxford, 4 May 2004

  34. ±3% ±2% contours correspond to ‘ experimental’ pdf errors only; shift of prediction using CTEQ6 pdfs shows effect of ‘theoretical’ pdf errors Oxford, 4 May 2004

  35. Oxford, 4 May 2004

  36. Oxford, 4 May 2004

  37. Oxford, 4 May 2004

  38. (LO) W cross sections at the Tevatron and LHC using (NLO) partons from MRST, CTEQ and Alekhin Oxford, 4 May 2004

  39. flavour decomposition of W cross sections at hadron colliders recall that the only constraint on very small x quarks from inclusive DIS (F2ep) data is on the combination 4/9 [u+c+ubar+cbar] + 1/9 [d+s+dbar+sbar] Oxford, 4 May 2004

  40. differences between the MRST, CTEQ and Alekhin strange quarks near the starting scale Oxford, 4 May 2004

  41. the ‘conservative’ pdfs (blue lines) do not describe the very lowx DIS data not included in the fit MRST, hep-ph/0308087 Oxford, 4 May 2004

  42. the change in the NLO and NNLO gluons when DIS data with x < 0.005 are removed from the global fit MRST, hep-ph/0308087 Oxford, 4 May 2004

  43. no data in fit no data in fit comparison of the standard MRST and ‘conservative’ NNLO pdfs MRST, hep-ph/0308087 Oxford, 4 May 2004

  44. Oxford, 4 May 2004

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