QCD: from the Tevatron to the LHC

1. QCD: from the Tevatron to the LHC James Stirling IPPP, University of Durham • Overview • Perturbative QCD – precision physics • ‘Forward’ (non-perturbative) processes • Summary

2. Calculate, Predict & Test Model, Fit, Extrapolate & Pray! 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 Forum04

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 Forum04

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 Forum04

5. examples of ‘precision’ phenomenology jet production W, Z production NNLO QCD NLO QCD Forum04

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 Forum04

7. 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 Forum04

8. John Campbell, Collider Physics Workshop, KITP, January 2004 Forum04

9. 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 Forum04

10. 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! Forum04

11. 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 Forum04

12. + interfacing NnLO and parton showers Benefits of both: NnLOcorrect overall rate, hard scattering kinematics, reduced scale, dependence, … PScomplete event picture, correct treatment of collinear logarithms to all orders, … → see talk by Bryan Webber Forum04

13. g H t g HO corrections to Higgs cross section • 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 Forum04

14. 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 Forum04

15. 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/ Forum04

16. 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. Forum04

17. (MRST) parton distributions in the proton Martin, Roberts, S, Thorne Forum04

18. uncertainty in gluon distribution (CTEQ) thenfg→σgg→X etc. Forum04

19. pdf uncertainties encoded in parton-parton luminosity functions: with  = M2/s, so that for ab→X solid = LHC dashed = Tevatron Alekhin 2002 Forum04

20. longer Q2 extrapolation smaller x Forum04

21. Higgs cross section: dependence on pdfs Djouadi & Ferrag, hep-ph/0310209 Forum04

22. Djouadi & Ferrag, hep-ph/0310209 Forum04

23. the differences between pdf sets needs to be better understood! Djouadi & Ferrag, hep-ph/0310209 Forum04

24. 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 Forum04

25. Kulesza Sterman Vogelsang qT (GeV) Bozzi Catani de Florian Grazzini 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 Forum04

26. 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 Forum04

27. 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-) Forum04

28. hadron collider measurements { S. Bethke inclusive b cross section UA1, 1996 prompt photon production UA6, 1996 inclusive jet cross section CDF, 2002 Forum04

29. Forum04

30. D0 (1997): R10= (W + 1 jet) / (W + 0 jet) Forum04

31. 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 Forum04

32. 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 orp + p → M  X  M where  = rapidity gap = hadron-free zone, and X = χc, H, tt, SUSY particles, etc 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’ Forum04

33. ‘rapidity gap’ collision events Typical event Hard single diffraction Hard double pomeron Hard color singlet Forum04

34. 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 ?! 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! Forum04

35. summary ‘QCD at hadron colliders’ means … • 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. to hard + diffractive/forward processes, multiple scattering, particle distributions and correlations etc. etc. • particularly important and interesting is p + p → p  X  p – challenge for experiment and theory Forum04

36. extra slides Forum04

37. 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) Forum04

38. new Full 3-loop (NNLO) non-singlet DGLAP splitting function! Moch, Vermaseren and Vogt, hep-ph/0403192 Forum04

39. 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 Forum04

40. 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 Forum04

41. CTEQ αS(MZ) values from global analysis with Δχ2 = 1, 100 Forum04

42. 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 Forum04

43. 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 Forum04

44. extrapolation errors theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x–0.5 as x → 0 Forum04

45. ubar=dbar differences between the MRST and Alekhin u and d sea quarks near the starting scale Forum04

46. Forum04

47. different partons 4% total error (MRST 2002) similar partons different Δχ2 σ(W) and σ(Z) : precision predictions and measurements at the LHC Forum04

48. 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 Forum04

49. 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? Forum04