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QCD at Hadron Colliders - a theory perspective

QCD at Hadron Colliders - a theory perspective. James Stirling IPPP, University of Durham. Overview Perturbative QCD – precision physics ‘Forward’ (non-perturbative) processes Summary. Scattering processes at high energy hadron colliders can be classified as either HARD or SOFT

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QCD at Hadron Colliders - a theory perspective

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  1. QCD at Hadron Colliders- a theory perspective James Stirling IPPP, University of Durham • Overview • Perturbative QCD – precision physics • ‘Forward’ (non-perturbative) processes • Summary

  2. Scattering processes at high energy hadron colliders can be classified as either HARD or SOFT Quantum Chromodynamics (QCD) is the underlying theory for all such processes, but the approach (and the level of understanding) is very different for the two cases For HARD processes, e.g. W or high-ET jet production, the rates and event properties can be predicted with some precision using perturbation theory For SOFT processes, e.g. the total cross section or diffractive processes, the rates and properties are dominated by non-perturbative QCD effects, which are much less well understood this talk: unpolarised only Chios 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 jet P x1P x2P P antiproton jet the QCD factorization theorem for hard-scattering (short-distance) inclusive processes ^ proton Chios 2004

  4. DGLAP evolution momentum fractions x1 and x2determined by mass and rapidity of X xdependence of fi(x,Q2) determined by ‘global fit’ (MRST, CTEQ, …) to deep inelastic scattering (H1, ZEUS, …) data*, Q2 dependence determined by DGLAP equations: *F2(x,Q2) = q eq2 x q(x,Q2)etc Chios 2004

  5. examples of ‘precision’ phenomenology jet production W, Z production NNLO QCD NLO QCD Chios 2004

  6. 4% total error (MRST 2002) what limits the precision of the predictions? • the order of the perturbative expansion • the uncertainty in the input parton distribution functions • example: σ(Z) @ LHC σpdf  ±3%, σpt  ± 2% →σtheory  ± 4% whereas for gg→H : σpdf << σpt Chios 2004

  7. Glover NNLO: the perturbative frontier • The NNLO coefficient C is not yet known, the curves show guesses C=0 (solid), C=±B2/A (dashed) → the scale dependence and hence  σthis significantly reduced • Other advantages of NNLO: • better matching of partons hadrons • reduced power corrections • better description of final state kinematics (e.g. transverse momentum) Tevatron jet inclusive cross section at ET = 100 GeV Chios 2004

  8. not all NLO corrections are known! t b t b the more external coloured particles, the more difficult the NLO pQCD calculation Example: pp →ttbb + X bkgd. to ttH Nikitenko, Binn 2003 Chios 2004

  9. soft, collinear jets at NNLO • 2 loop, 2 parton final state • | 1 loop |2, 2 parton final state • 1 loop, 3 parton final states • or 2 +1 final state • tree, 4 parton final states • or 3 + 1 parton final states • or 2 + 2 parton final state  rapid progress in last two years [many authors] • many 2→2 scattering processes with up to one off-shell leg now calculated at two loops • … to be combined with the tree-level 2→4, the one-loop 2→3 and the self-interference of the one-loop 2→2 to yield physical NNLO cross sections • this is still some way away but lots of ideas so expect progress soon! Chios 2004

  10. summary of NNLO calculations • p + p → jet + X *; in progress, see previous • 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 Chios 2004

  11. Who? Alekhin, CTEQ, MRST, GKK, Botje, H1, ZEUS, GRV, BFP, … http://durpdg.dur.ac.uk/hepdata/pdf.html pdfs from global fits Formalism NLO 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. Chios 2004

  12. (MRST) parton distributions in the proton Martin, Roberts, S, Thorne Chios 2004

  13. Higgs cross section: dependence on pdfs Djouadi & Ferrag, hep-ph/0310209 Chios 2004

  14. Djouadi & Ferrag, hep-ph/0310209 Chios 2004

  15. the differences between pdf sets needs to be better understood! Djouadi & Ferrag, hep-ph/0310209 Chios 2004

  16. 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 ongoing HERA-LHC Workshop PDF Working Group Chios 2004

  17. pdf uncertainties encoded in parton-parton luminosity functions: with  = M2/s, so that for ab→X solid = LHC dashed = Tevatron Alekhin 2002 Chios 2004

  18. Kulesza Sterman Vogelsang qT (GeV) Bozzi Catani de Florian Grazzini resummation Work continues to refine the predictions for ‘Sudakov’ processes, e.g. for the Higgs or Z transverse momentum distribution, where resummations of large logarithms of the form n,m αSn log(M2/qT2)m is necessary at small qT, and matching with fixed-order QCD at large qT Chios 2004

  19. Production of jet pairs with equal and opposite large rapidity (‘Mueller-Navelet’ jets) as a test of QCD BFKL physics • cf. F2 ~ x as x →0 at HERA • many tests: • y dependence, azimuthal angle decorrelation, accompanying minjets etc • replace forward jets by forward W, b-quarks etc Andersen, S jet jet BFKL at hadron colliders Chios 2004

  20. forward physics • ‘classical’ forward physics – σtot ,σel ,σSD,σDD, etc– a challenge for non-perturbative QCD models. Vast amount of low-energy data (ISR, Tevatron, …) to test and refine such models • output → deeper understanding of QCD, precision luminosity measurement (from optical theorem L ~ Ntot2/Nel) • ‘new’ forward physics – a potentially important tool for precision QCD and New Physics Studies at Tevatron and LHC p + p → p  X  p where  = rapidity gap = hadron-free zone, and X = χc, H, ttbar, SUSY particles, etc advantages? good MX resolution from Mmiss (~ 1 GeV?) (CMS-TOTEM) disadvantages? low event rate – the price to pay for gaps to survive the ‘hostile QCD environment’ Chios 2004

  21. ‘rapidity gap’ collision events Typical event Hard single diffraction Hard double pomeron Hard color singlet Chios 2004

  22. new • For example: Higgs at LHC (Khoze, Martin, Ryskin hep-ph/0210094) • MH = 120 GeV, L = 30 fb-1 , Mmiss = 1 GeV • Nsig = 11, Nbkgd = 4  3σ effect Note:calibration possible via X = quarkonia or large ET jet pair Observation of p + p → p + χ0c (→J/ γ) + p by CDF? QCD challenge: to refine and test such models & elevate to precision predictions! Chios 2004

  23. summary Hadron colliders (like e+e- and ep colliders) provide a rich source of information on both the perturbative and non-perturbative sectors of QCD, some parts of which are well-known and well-understood, others not… ‘standard’ QCD: precision cross section calculations and event simulations [NNLO pQCD, resummation, αS measurements, pdfs, MEPS interface, …] ‘non-standard’ QCD: beyond leading-twist, inclusive quantities [multiple scattering, particle distns and correlns, rapidity gaps, diffractive & exclusive processes, …]  still a very lively and interesting subject! Chios 2004

  24. 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) Chios 2004

  25. new Full 3-loop (NNLO) non-singlet DGLAP splitting function! Moch, Vermaseren and Vogt, hep-ph/0403192 Chios 2004

  26. 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 Chios 2004

  27. 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 Chios 2004

  28. CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100 Chios 2004

  29. 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 Chios 2004

  30. 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 Chios 2004

  31. extrapolation errors theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x–0.5 as x → 0 Chios 2004

  32. ubar=dbar differences between the MRST and Alekhin u and d sea quarks near the starting scale Chios 2004

  33. Chios 2004

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

  35. 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 is the experimental precision? – – ratio of W–and W+ rapidity distributions Chios 2004

  36. 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? Chios 2004

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