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QCD: from Tevatron to LHC

QCD: from Tevatron to LHC. QCD at hadron colliders – overview Precision pQCD MHV - a new calculational technique Central exclusive diffractive production Summary. James Stirling IPPP, University of Durham.

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QCD: from Tevatron to LHC

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  1. QCD: from Tevatron to LHC • QCD at hadron colliders – overview • Precision pQCD • MHV - a new calculational technique • Central exclusive diffractive production • Summary James Stirling IPPP, University of Durham

  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. Higgs or high-ET jet production, the rates and event properties can be predicted with good precision using perturbation theory For SOFT processes, e.g. the total cross section, diffractive, etc. processes, the rates and properties are dominated by non-perturbative QCD effects, which are much less well understood IoP HEPP Dublin

  3. IoP HEPP Dublin

  4. g underlying event H t g p parton distribution functions H cf. special kinematics, e.g. pp→ppH p higher-order pQCD corrections, jets parton showering for inclusive production, the basic calculational framework is provided by the QCD FACTORISATION THEOREM

  5. where X=W, Z, H, high-ET jets, SUSY sparticles, graviton, …, 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. high-ET jet prodn. • or in some leading logarithm approximation (LL, NLL, …) where • L =log(Q2/Q02) >> 1 to all orders via resummation the QCD factorization theorem for hard-scattering (short-distance) inclusive processes ^ IoP HEPP Dublin

  6. 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 IoP HEPP Dublin

  7. (MRST) parton distributions in the proton Martin, Roberts, S, Thorne IoP HEPP Dublin

  8. jet production W, Z production NNLO QCD NLO QCD examples of ‘precision’ phenomenology … and many other examples IoP HEPP Dublin

  9. at the Tevatron... • benchmark SM cross sections (W,Z, jets, top, …) • fine-tune pdfs (i.e. Tevatron data in global fits) • more refined tests: resummation, energy flows, jet structure… • tune models for the underlying event • benchmark exclusive processes (see later) NOTE: no competitive S measurements at hadron colliders! then at the LHC... • high-precision predictions for SM and BSM production processes • … for use as luminosity measurement? • extrapolate models for underlying event (?!) • reliable estimates for BSM exclusive production (later) IoP HEPP Dublin

  10. longer Q2 extrapolation smaller x IoP HEPP Dublin

  11. constraining pdfs at the Tevatron CDF W asymmetry D0 high ET jet MRST fits MRST CTEQ → d(x)/u(x) at medium x → g(x) at medium, high x IoP HEPP Dublin

  12. x1=0.006 x2=0.006 – x1=0.52 x2=0.000064 ratio close to 1 because u  u etc. sensitive to large-x d/u and small x u/d ratios Q. What is the experimental precision? – – LHC: ratio of W–and W+ rapidity distributions IoP HEPP Dublin

  13. DGLAP? BFKL? saturation? higher-twist? LHC: small x? e.g. ALICE in pp mode @ 1031 cm-2 s-1 with forward muon detection IoP HEPP Dublin

  14. NNLO: the perturbative frontier • The higher we calculate in fixed-order perturbation theory, the weaker the (renormalisation and factorisation) scale dependence and the smaller the theoretical error σthon the cross section •  = A αS(R)N [1 + C1 (R)αS(R)+ C2 (R)αS(R)2 + …. ] • Other advantages of NNLO: • better matching of partons  hadrons • reduced power corrections • better description of final state kinematics (e.g. transverse momentum) NNLO IoP HEPP Dublin

  15. summary of NNLO calculations (~1990 ) ep • DIS pol. and unpol. structure function coefficient functions • Sum Rules (GLS, Bj, …) • DGLAP splitting functions Moch Vermaseren Vogt (2004) • total hadronic cross section, and Z  hadrons,    + hadrons • heavy quark pair production near threshold • CF3part of (3 jet) Gehrmann-De Ridder, Gehrmann, Glover(2004) • inclusive W,Z,*van Neerven et al, Harlander and Kilgorecorrected(2002) • inclusive * polarised Ravindran, Smith, Van Neerven(2003) • W,Z,*differential rapidity disnAnastasiou, Dixon, Melnikov, Petriello (2003) • H0, A0Harlander and Kilgore; Anastasiou and Melnikov; Ravindran, Smith, Van Neerven(2002-3) • WH, ZHBrein, Djouadi,Harlander (2003) • QQ onium and Qq meson decay rates e+e- pp NNLO correction to large ET jet cross section still missing! HQ + other partial/approximate results (e.g. soft, collinear) and NNLL improvements IoP HEPP Dublin

  16. b 1972-77 1977-80 2004 a Pba = >1991 Note: need to know splitting and coefficient functions to the same perturbative order to ensure that (n)/logF = O(αS(n+1)) The calculation of the complete set of P(2) splitting functions by Moch, Vermaseren and Vogt (hep-ph/0403192,0404111)completes the calculational tools for a consistent NNLO pQCD treatment of Tevatron & LHC hard-scattering cross sections! IoP HEPP Dublin

  17. NNLO phenomenology already under way… • σ(W) and σ(Z) : precision predictions and measurements at the Tevatron and LHC • the pQCD series appears to be under control • with sufficient theoretical precision, these ‘standard candle’ processes could be used to measure the machine luminosity IoP HEPP Dublin

  18. 4% total error (MRST 2002) what limits the precisionof 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 IoP HEPP Dublin

  19. g H t • the HO pQCD corrections to (gg→H) are large (more diagrams, more colour) • can improve NNLO precision slightly by resumming additional soft/collinear higher-order logarithms • example: σ(MH=120 GeV) @ LHC σpdf  ±3%, σptNNL0  ± 10% σptNNLL  ± 8%, →σtheory  ± 9% g HO corrections to Higgs cross section Catani et al, hep-ph/0306211 scale variation: MH/2→ 2MH IoP HEPP Dublin

  20. effect of NNLO correction on Higgs production at LHC IoP HEPP Dublin

  21. Tevatron NNLO(S+V) NLO LO Kidonakis and Vogt, hep-ph/0308222 top quark production awaits full NNLO pQCD calculation; NNLO & NnLL “soft+virtual” approximations exist (Cacciari et al, Kidonakis et al), probably OK for Tevatron at ~ 10% level (> σpdf ) … but such approximations work less well at LHC energies IoP HEPP Dublin

  22. +0.7 -0.9 … consistent with SM NNLO prediction  = 6.7 pb IoP HEPP Dublin

  23. Where have all the theorists gone?

  24. + … MHV • consider a n-gluon scattering amplitude with  helicity labels • Parke and Taylor (PRL 56 (1986) 2459) “this result is an educated guess” “we do not expect such a simple expression for the other helicity amplitudes” “we challenge the string theorists to prove more rigorously that [it] is correct” • Witten, December 2003 (hep-th/0312171) “Perturbative gauge theory as a string theory in twistor space” r s Maximum Helicity Violating = (colour factors suppressed) IoP HEPP Dublin

  25. gg  ggg IoP HEPP Dublin

  26. Cachazo, Svrcek, Witten (March 2004,hep-th/0403047): elevate MHV scattering amplitudes to effective vertices in a new scalar graph approach • and use them with scalar propagators to calculate • tree-level non-MHV amplitudes • with both quarks and gluons • … and loop diagrams! • dramatic simplification: compact output in terms of familiar spinor products • phenomenology? tree-level multijet cross sections at LHC etc • latest on LOOPS: obvious MHC constructions OK in SUSY-YM, but non-trivial to extract contribution from gluons-only in loops Cachazo, Svrcek, Witten, Georgiou, Khoze, Zhu, Wu, Zhu, Bena, Bern, Kosower, Glover, Brandhuber, Spence, Travaglini, Bern, del Duca, Dixon, Dunbar, Bidder, Bjerrum-Bohr, Ita, Perkins, … IoP HEPP Dublin

  27.    central exclusive diffractive physics compare … • p + p  H + X • the rate (parton,pdfs, αS) • the kinematic distribtns. (d/dydpT) • the environment (jets, underlying event, backgrounds, …) with … • p + p  p + H + p • a real challenge for theory (pQCD + npQCD) and experiment (tagging forward protons, triggering, …) b b IoP HEPP Dublin

  28. hard single diffraction ‘rapidity gap’ collision events typical jet event hard double pomeron hard color singlet exchange IoP HEPP Dublin

  29. forward proton tagging: the physics case p + p → p  X  p • all objects produced this way must be in a 0++ state → spin-parity filter/analyser • with a mass resolution of ~O(1 GeV) from the proton tagging, the Standard ModelH →bb decay mode opens up, with S/B > 1 • H → WW(*) also looks very promising • in certain regions of MSSM parameter space, S/B > 20, and double proton tagging is THE discovery channel • in other regions of MSSM parameter space, explicit CP violation in the Higgs sector shows up as an azimuthal asymmetry in the tagged protons → direct probe of CP structure of Higgs sector at LHC • any exotic 0++ state, which couples strongly to glue, is a real possibility: radions, gluinoballs, … KMR e.g. mA = 130 GeV, tan  = 50 M = 1 GeV, L = 30 fb-1 S B mh = 124.4 GeV 71 3 mH = 135.5 GeV 124 2 mA = 130 GeV 1 2 e.g. SM Higgs → bb M = 1 GeV, L = 30 fb-1 S B mh = 120 GeV 11 4

  30. gap survival the challenges … Khoze Martin Ryskin Kaidalov WJS de Roeck Cox Forshaw Monk Pilkington Helsinki group Saclay group … theory need to calculate production amplitude and gap Survival Factor: mix of pQCD and npQCD significant uncertainties important checks from Tevatron for X=jets, , quarkonia, … X experiment • tagging the leading protons: Mmiss = O(1 GeV) is crucial • small event rates (price to pay for clean events) • selection of exclusive events & backgrounds • triggering at L1 in the LHC GPDs IoP HEPP Dublin

  31. For heavier Higgs (> 135 GeV) H →WW(*) has lower rate but • higher branching rate • higher detection efficiency • easier to trigger than H → bb IoP HEPP Dublin

  32. FP420 a request for funds for • R&D for cryostat development (to be able to instrument the ~420m region) • R&D for detectors (e.g. edgeless 3D silicon technology) • Studies for trigger/acceptance/resolution IoP HEPP Dublin

  33. summary ‘QCD at hadron colliders’ means … • learning more about proton structure • performing precision calculations (LO→NLO→NNLO ) for signals and backgrounds, cross sections and distributions – still much work to do! (cf. EWPT @ LEP) • refining event simulation tools (e.g. PS+NLO) • extending the calculational frontiers, e.g. • MHV for tree-level and (hopefully) loops • hard + diffractive/forward processes • particularly important and interesting is p + p → p  X  p – challenge for experiment and theory

  34. finally … • UK phenomenologists are world-leading in this area: • HERWIG (Cambridge-Manchester-Durham) • CEDAR (UCL-Durham) • MRST (Cambridge-Durham-RAL) • MHV (Queen Mary-Durham-Swansea) • CEDP (Manchester-Durham) • …

  35. extra slides IoP HEPP Dublin

  36. IoP HEPP Dublin

  37. gap survival anything that couples to gluons p + p → p  H  p at LHC • For example:Khoze, Martin, Ryskin • (hep-ph/0210094) • MH = 120 GeV, L = 30 fb-1 , Mmiss = 1 GeV • Nsig = 11, Nbkgd = 4  3σ effect ?! Need to calculate production amplitude and gap Survival Factor: mix of pQCD and npQCD significant uncertainties • BUTcalibration possible via X = quarkonia, large ET jet pair, , etc. at Tevatron • (Khoze, Martin, Ryskin,WJS) X selection rules mass resolution is crucial! Royon et al S/B QCD challenge: to refine and test calculations & elevate to precision predictions! mass resolution IoP HEPP Dublin

  38. soft, collinear anatomy of a NNLO calculation: p + p  jet + X • 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 the collinear and soft singularities exactly cancel between the N +1 and N + 1-loop contributions IoP HEPP Dublin

  39. 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 • the key is to identify and calculate the ‘subtraction terms’ which add and subtract to render the loop (analytically) and real emission (numerically) contributions finite • this is still some way away but lots of ideas so expect progress soon! IoP HEPP Dublin

  40. world average (MSbar, NNLO) αS(MZ) = 0.1182  0.0027 cf. (2002) 0.1183  0.0027 World Summary of αS(MZ) – July 2004 from S. Bethke, hep-ex/0407021 IoP HEPP Dublin

  41. αS measurements at hadron colliders • in principle, from an absolute cross section measurement…   αSn but problems with exp. normalisation uncertainties, pdf uncertainties, etc. • or from a relative rate of jet production (X + jet) / (X)  αS but problems with jet energy measurement, non-cancellation of pdfs, etc. • or, equivalently, from ‘shape variables’ (cf. thrust in e+e-) IoP HEPP Dublin

  42. hadron collider measurements { S. Bethke inclusive b cross section UA1, 1996 prompt photon production UA6, 1996 inclusive jet cross section CDF, 2002 IoP HEPP Dublin

  43. IoP HEPP Dublin

  44. D0 (1997): R10= (W + 1 jet) / (W + 0 jet) IoP HEPP Dublin

  45. pdf uncertainties encoded in parton-parton luminosity functions: with  = M2/s, so that for ab→X IoP HEPP Dublin

  46. 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, WJS jet jet BFKL at hadron colliders IoP HEPP Dublin

  47. 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 the leading order O(αS4) cross section has a large renormalisation scale dependence! IoP HEPP Dublin

  48. Too many calculations, too few people! John Campbell, Collider Physics Workshop, KITP, January 2004 IoP HEPP Dublin

  49. HEPCODE: a comprehensive list of publicly available cross-section codes for high-energy collider processes, with links to source or contact person • Different code types, e.g.: • tree-level generic (e.g. MADEVENT) • NLO in QCD for specific processes (e.g. MCFM) • fixed-order/PS hybrids (e.g. MC@NLO) • parton shower (e.g. HERWIG) www.ippp.dur.ac.uk/HEPCODE/ IoP HEPP Dublin

  50. interfacing NnLO and parton showers new + Benefits of both: NnLOcorrect overall rate, hard scattering kinematics, reduced scale dep. PScomplete event picture, correct treatment of collinear logs to all orders Example: MC@NLO Frixione, Webber, Nason, www.hep.phy.cam.ac.uk/theory/webber/MCatNLO/ processes included so far … pp  WW,WZ,ZZ,bb,tt,H0,W,Z/ IoP HEPP Dublin pT distribution of tt at Tevatron

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