James Stirling IPPP, University of Durham

1. Thanks to QCD-Hard and QCD-Soft parallel session organisers and speakers! QCD Theory – a status report and review of some developments in the past year James Stirling IPPP, University of Durham

2. more QCD? … see also QCD @ HERA: Klein QCD @ Tevatron: Lucchesi QCD and hadron spectroscopy: Close, Shan Jin QCD and heavy quarks: Ali, Shipsey QCD on the Lattice: Hashimoto QCD - ICHEP04

3. an essential and established* part of the toolkit for discovering physics beyond the standard model, e.g. at Tevatron and LHC a Yang-Mills gauge field theory with a very rich structure (asymptotic freedom  confinement), much of which is not yet fully understood in a quantitative way * we no longer “test QCD”! QCD is … QCD - ICHEP04

4. αS(E) non-perturbative approaches: lattice, Regge theory, skyrmions, large-Nc,… 1 perturbative field theory calculations 0 E for ‘hard’ processes (i.e. suitably inclusive, with at least one large momentum transfer scale), QCD is a precision tool – calculations and phenomenology aiming at the per-cent level for semi-hard, exclusive and soft processes, we need to extend and test calculational techniques experiment and theory working together QCD in 2004 compare tot(pp) andtot(e+e-hadrons) QCD - ICHEP04

5. 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 • New at this conference: • ZEUS DIS + jets pdf fit • HERA jet cross sections and shape variables • JADE 4-jet rate and jet shape moments • LEP 1,2 jet shape observables, 4-jet rate • All NLO and all consistent with world average

6. jet production W, Z production NNLO QCD NLO QCD examples of ‘precision’ phenomenology … and many other examples presented at this Conference QCD - ICHEP04

7. LO automated codes for arbitrary matrix element generation (MADGRAPH, COMPHEP, HELAC, …) jet = parton, but ‘easy’ to interface to hadronisation MCs large scale dependence αS()N therefore not good for precision analyses NLO now known for ‘most’ processes of interest dV(N) + dR(N+1) reduced scale dependence (but can still dominate αSmeasurement) jet structure begins to emerge no automation yet, but many ideas now can interface with PS 1 status of pQCD calculations fixed order:d = A αSN [1 + C1αS+ C2αS2 + …. ] thus LO, NLO, NNLO, etc, or resummed to all orders using a leading log approximation, e.g. d = A αSN [1 + (c11L + c10 ) αS+ (c22L2+c21L + c20 ) αS2 + …. ] whereL = log(M/qT), log(1/x), log(1-T), … >> 1thus LL, NLL, NNLL, etc. current frontier QCD - ICHEP04

8. 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/ pT distribution of tt at Tevatron

9. 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! QCD - ICHEP04

10. Too many calculations, too few people! John Campbell, Collider Physics Workshop, KITP, January 2004 QCD - ICHEP04

11. Glover 2 NNLO: the perturbative frontier Example: jet cross section at hadron colliders • The NNLO coefficient C is not yet known, the curves show guessesC=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) (also e+e- 3 jets) Tevatron jet inclusive cross section at ET = 100 GeV QCD - ICHEP04

12. 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

13. 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! QCD - ICHEP04

14. 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 HQ + other partial/approximate results (e.g. soft, collinear) and NNLL improvements QCD - ICHEP04

15. 1972-77 1977-80 2004 new >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 completes the calculational tools for a consistent NNLO pQCD treatment of Tevatron & LHC hard-scattering cross sections! QCD - ICHEP04

16. b a Full 3-loop (NNLO) DGLAP splitting functions! Pba = previous estimates based on known moments and leading behaviours Moch, Vermaseren and Vogt, hep-ph/0403192, hep-ph/0404111 Moch QCD - ICHEP04

17. Moch, Vermaseren and Vogt, hep-ph/0403192, hep-ph/0404111 7 pages later… …then 8 pages of the same quantities expressed in x-space! QCD - ICHEP04

18. 4% total error (MRST 2002) 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

19. Kulesza Sterman Vogelsang qT (GeV) Bozzi Catani de Florian Grazzini 3 resummation Z Work continues to refine the predictions for ‘Sudakov’ processes, e.g. for the Higgs or Z transverse momentum distribution, where resummation of large logarithms of the form n,m αSn log(M2/qT2)m is necessary at small qT, to be matched with fixed-order QCD at large qT (also: event shapes, heavy quark prodn.) De Florian Marchesini QCD - ICHEP04

20. g H t g g threshold logs logN(1-M2/sgg) H g resummation contd. - HO corrections to (Higgs) • 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% Catani et al, hep-ph/0306211 QCD - ICHEP04

21. 4 dawn of a new calculational era? • (numerical) calculation of QCD tree-level scattering amplitudes can be automated … but method is “brute force”, and multiparton complexity soon saturates computer capability • no automation in sight for loop amplitudes • analytic expressions are very lengthy (recall P(2)) • a recent paper by Cachazo, Svrcek and Witten may be the long-awaited breakthrough … Bern QCD - ICHEP04

22. slide from Zvi Bern gg  ggg QCD - ICHEP04

23. the Parke-Taylor amplitude mystery • 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) true! QCD - ICHEP04

24. Cachazo, Svrcek, Witten (CSW) April 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? multijet cross sections at LHC etc Georgiou, Khoze; Zhu; Wu, Zhu; Bena, Bern, Kosower; Georgiou, Khoze, Glover; Kosower; Brandhuber, Spence, Travaglini; Bern, del Duca, Dixon, Kosower; … QCD - ICHEP04

25.     5 the ‘other frontier’… 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 (rapidity gaps, forward protons, ..) b b The most sophisticated calculations and input from many other experiments are needed to properly address these issues! QCD - ICHEP04

26. hard single diffraction ‘rapidity gap’ collision events typical jet event hard double pomeron hard color singlet exchange

27. 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 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 Gallinaro Royon QCD - ICHEP04

28. summary QCD theory – major advances in the past year, with promise of more to come… • pQCD calculations at the NNLO/NNLL frontier (e.g. jet cross sections in pp, e+e-), but many NLO “background” calculations still missing • CSW: a new approach still in its infancy (4 months!), but with major potential • away from “hard inclusive”, there are many calculational challenges (semi-hard, power corrections, exclusive, diffractive, …) – close collaboration with experiment is essential QCD - ICHEP04

29. extra slides QCD - ICHEP04

30. comparison of resummed / fixed-order calculations for Higgs (MH = 125 GeV) qT distribution at LHC • Balazs et al, hep-ph/0403052 • differences due mainly to different NnLO and NnLL contributions included • Tevatron d(Z)/dqTprovides good test of calculations log scale linear scale QCD - ICHEP04

31. technical details b a   g q fictitious scalar-gluon vertex number of diagrams (QGRAF) etc. • L = log(Q2/2) • F = A L3 + B L2 + C L + D • P(2) contained in this term QCD - ICHEP04

32. could well be a missing strong interaction effect World Summary of MW from LEPEWWG, Summer 2004 QCD - ICHEP04

33. 2 the interplay of electroweak and QCD precision physics • role ofαS in global electroweak fit • hadronic contributions to muon g-2 • use of (W)and (Z)as ‘standard candles’ to measure luminosity at LHC • inclusion of O(α) QED effects in DGLAP evolution • effect of hadronic structure on extraction of sin2Wfrom N scattering • … Hoecker Vainshtein Ward QCD - ICHEP04

34. QED effects in pdfs • QED corrections to DIS include:  mass singularity ~αlog(Q2/mq2) when ║q • these 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) included in standard radiative correction packages (HECTOR, HERACLES) QCD - ICHEP04

35. QED-improved DGLAP equations • at leading order in α and αS where • momentum conservation: QCD - ICHEP04

36. 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 isospin violation: up(x) ≠ dn(x) first consistent global pdf fit with QED corrections included (MRST 2004) neutron proton new QCD - ICHEP04

37. new partial explanation of NuTeV sin2W “anomaly”? perturbative generation ofs(x) ≠ s(x) Pus(x) ≠ Pus(x) atO(αS3) • Quantitative study by de Florian et al • hep-ph/0404240 • x(s-s)pQCD < 0.0005 cf. from global pdf fit (Olness et al, hep-ph/0312322,3)  0.001 <x(s-s)fit < +0.004 note! QCD - ICHEP04

38. new sin2W from N 3  difference QCD - ICHEP04

39. Conclusion: uncertainties in detailed parton structure are substantial on the scale of the precision of the NuTeV data – consistency with the Standard Model does not appear to be ruled out at present QCD - ICHEP04

40. couples to gluons new selection rules • 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 ?! need to calculate production amplitude and gap Survival Factor  big uncertainties • BUTcalibration possible via X = quarkonia or large ET jet pair, e.g. CDF ‘observation’ of • p + p → p + χ0c (→J/ γ) + p: • excl(J/ γ) < 49 ± 18 (stat) ± 39 (syst) pb cf.thy ~ 70 pb (Khoze et al 2004) mass resolution is crucial! Royon et al QCD challenge: to refine and test such models & elevate to precision predictions! Gallinaro Royon QCD - ICHEP04

41. NNLO corrections to Drell-Yan cross sections • in DY, sizeable HO pQCD corrections since αS (M) not so small • for σ(W), σ(Z) at Tevatron and LHC, allows QCD prediction to be matched for (finite) experimental acceptance in boson rapidity Anastasiou et al. hep-ph/0306192 hep-ph/0312266 QCD - ICHEP04

42. 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 QCD - ICHEP04

43. 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/ QCD - ICHEP04

44. 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. QCD - ICHEP04

45. (MRST) parton distributions in the proton Martin, Roberts, S, Thorne QCD - ICHEP04

46. uncertainty in gluon distribution (CTEQ) thenfg→σgg→X etc. QCD - ICHEP04

47. pdf uncertainties encoded in parton-parton luminosity functions: with  = M2/s, so that for ab→X solid = LHC dashed = Tevatron Alekhin 2002 QCD - ICHEP04

48. longer Q2 extrapolation smaller x QCD - ICHEP04

49. Higgs cross section: dependence on pdfs Djouadi & Ferrag, hep-ph/0310209 QCD - ICHEP04

50. Djouadi & Ferrag, hep-ph/0310209 QCD - ICHEP04