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

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Forum042 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- E T 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 Calculate, Predict & TestModel, Fit, Extrapolate & Pray!

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Forum043 the QCD factorization theorem for hard-scattering (short-distance) inclusive processes ^ proton jet antiproton Px1Px1P x2Px2PP where X=W, Z, H, high-E T jets, SUSY sparticles, black hole, …, and Q is the hard scale (e.g. = M X ), 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

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Forum044 DGLAP evolution momentum fractions x 1 and x 2 determined by mass and rapidity of X x dependence of f i (x,Q 2 ) determined by global fit (MRST, CTEQ, …) to deep inelastic scattering (H1, ZEUS, …) data*, Q 2 dependence determined by DGLAP equations: * F 2 (x,Q 2 ) = q e q 2 x q(x,Q 2 ) etc

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Forum045 examples of precision phenomenology W, Z productionjet production NNLO QCD NLO QCD

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Forum046 what limits the precision of the predictions? the order of the perturbative expansion the uncertainty in the input parton distribution functions example: LHC σ pdf ±3%, σ pt ± 2% σ theory ± 4% whereas for ggH : σ pdf << σ pt 4% total error (MRST 2002)

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Forum047 t t b b Nikitenko, Binn 2003 not all NLO corrections are known! the more external coloured particles, the more difficult the NLO pQCD calculation Example: pp ttbb + X bkgd. to ttH

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Forum048 John Campbell, Collider Physics Workshop, KITP, January 2004

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Forum049 NNLO: the perturbative frontier The NNLO coefficient C is not yet known, the curves show guesses C=0 (solid), C=±B 2 /A (dashed) the scale dependence and hence σ th is significantly reduced Other advantages of NNLO: better matching of partons hadrons reduced power corrections better description of final state kinematics (e.g. transverse momentum) Glover Tevatron jet inclusive cross section at E T = 100 GeV

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Forum0410 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 parton final states or parton final state rapid progress in last two years [many authors] many 22 scattering processes with up to one off-shell leg now calculated at two loops … to be combined with the tree-level 24, the one-loop 23 and the self- interference of the one-loop 22 to yield physical NNLO cross sections this is still some way away but lots of ideas so expect progress soon! soft, collinear

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Forum0411 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

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Forum interfacing N n LO and parton showers Benefits of both: N n LOcorrect overall rate, hard scattering kinematics, reduced scale, dependence, … PScomplete event picture, correct treatment of collinear logarithms to all orders, … see talk by Bryan Webber

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Forum0413 HO corrections to Higgs cross section Catani et al, hep-ph/ the HO pQCD corrections to (ggH) are large (more diagrams, more colour) can improve NNLO precision slightly by resumming additional soft/collinear higher-order logarithms example: σ(M H =120 LHC σ pdf ±3%, σ ptNNL0 ± 10%, σ ptNNLL ± 8%, σ theory ± 9% H t g g

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Forum0414 top quark production awaits full NNLO pQCD calculation; NNLO & N n LL soft+virtual approximations exist (Cacciari et al, Kidonakis et al), probably OK for Tevatron at ~ 10% level (> σ pdf ) Kidonakis and Vogt, hep-ph/ LO NNLO(S+V) NLO Tevatron … but such approximations work less well at LHC energies

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Forum0415 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. – parton shower (e.g. HERWIG) HEPCODE : a comprehensive list of publicly available cross-section codes for high-energy collider processes, with links to source or contact person

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Forum0416 pdfs from global fits Formalism NLO DGLAP MSbar factorisation Q 0 2 functional Q 0 2 sea quark (a)symmetry etc. Who? Alekhin, CTEQ, MRST, GKK, Botje, H1, ZEUS, GRV, BFP, … Data DIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … ) Drell-Yan (E605, E772, E866, …) High E T jets (CDF, D0) W rapidity asymmetry (CDF) N dimuon (CCFR, NuTeV) etc. f i (x,Q 2 ) α S (M Z )

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Forum0417 (MRST) parton distributions in the proton Martin, Roberts, S, Thorne

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Forum0418 uncertainty in gluon distribution (CTEQ) then f g σ ggX etc.

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Forum0419 solid = LHC dashed = Tevatron Alekhin 2002 pdf uncertainties encoded in parton-parton luminosity functions: with = M 2 /s, so that for abX

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Forum0420 longer Q 2 extrapolation smaller x

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Forum0421 Djouadi & Ferrag, hep-ph/ Higgs cross section: dependence on pdfs

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Forum0422 Djouadi & Ferrag, hep-ph/

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Forum0423 Djouadi & Ferrag, hep-ph/ the differences between pdf sets needs to be better understood!

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Forum0424 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 f i (CTEQ: Δχ 2 =100, Alekhin: Δχ 2 =1) – factorisation/renormalisation scheme/scale – Q 0 2 – parametric form Ax a (1-x) b [..] etc – α S – treatment of heavy flavours – theoretical assumptions about x0,1 behaviour – theoretical assumptions about sea flavour symmetry – evolution and cross section codes (removable differences!) see ongoing HERA-LHC Workshop PDF Working Group

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Forum0425 resummation 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 α S n log(M 2 /q T 2 ) m is necessary at small q T, to be matched with fixed-order QCD at large q T Bozzi Catani de Florian Grazzini q T (GeV) Kulesza Sterman Vogelsang Z

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Forum0426 comparison of resummed / fixed-order calculations for Higgs (M H = 125 GeV) q T distribution at LHC Balazs et al, hep-ph/ differences due mainly to different N n LO and N n LL contributions included Tevatron d (Z)/dq T provides good test of calculations

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Forum0427 α S measurements at hadron colliders in principle, from an absolute cross section measurement… α S n but problems with exp. normalisation uncertainties, pdf uncertainties, etc. or from a relative rate of jet production (X + jet) / (X) α S but problems with jet energy measurement, non- cancellation of pdfs, etc. or, equivalently, from shape variables (cf. thrust in e + e - )

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Forum0428 inclusive b cross section UA1, 1996 prompt photon production UA6, 1996 inclusive jet cross section CDF, 2002 S. Bethke hadron collider measurements {

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Forum0429

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Forum0430 D0 (1997): R 10 = (W + 1 jet) / (W + 0 jet)

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Forum0431 BFKL at hadron colliders Andersen, WJS jet Production of jet pairs with equal and opposite large rapidity (Mueller-Navelet jets) as a test of QCD BFKL physics cf. F 2 ~ 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

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Forum0432 forward physics classical forward physics – σ tot, σ el, σ SD, σ DD, 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 ~ N tot 2 /N el ) new forward physics – a potentially important tool for precision QCD and New Physics Studies at Tevatron and LHC p + p p X p or p + p M X M where = rapidity gap = hadron-free zone, and X = χ c, H, tt, SUSY particles, etc etc advantages? good M X resolution from M miss (~ 1 GeV?) (CMS-TOTEM) disadvantages?low event rate – the price to pay for gaps to survive the hostile QCD environment

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Forum0433 Typical event Hard single diffraction Hard double pomeron Hard color singlet rapidity gap collision events

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Forum0434 For example: Higgs at LHC (Khoze, Martin, Ryskin hep-ph/ ) M H = 120 GeV, L = 30 fb -1, M miss = 1 GeV N sig = 11, N bkgd = 4 3σ effect ?! Note: calibration possible via X = quarkonia or large E T jet pair Observation of p + p p + χ 0 c (J/ γ) + p by CDF? new QCD challenge: to refine and test such models & elevate to precision predictions! selection rules couples to gluons

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Forum0435 summary QCD at hadron colliders means … performing precision calculations (LONLONNLO ) for signals and backgrounds, cross sections and distributions – still much work to do! (cf. 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

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Forum0436 extra slides

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Forum0437 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-E T jets gluon, W + /W – sea quarks)

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Forum0438 Full 3-loop (NNLO) non-singlet DGLAP splitting function! Moch, Vermaseren and Vogt, hep-ph/ new

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Forum0439 MRST: Q 0 2 = 1 GeV 2, Q cut 2 = 2 GeV 2 xg = Ax a (1–x) b (1+Cx 0.5 +Dx) – Ex c (1-x) d CTEQ6: Q 0 2 = 1.69 GeV 2, Q cut 2 = 4 GeV 2 xg = Ax a (1–x) b e cx (1+Cx) d

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Forum0440 with dataset A in fit, Δχ 2 =1 ; with A and B in fit, Δχ 2 =? 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 tensions within the global fit?

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Forum0441 CTEQ α S (M Z ) values from global analysis with Δχ 2 = 1, 100

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Forum0442 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 ~ (MRST hep-ph/ ) Q. Is fixed–order DGLAP insufficient for small-x DIS data?! Δ = improvement in χ 2 to remaining data / # of data points removed

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Forum0443 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

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Forum0444 extrapolation errors theoretical insight/guess: f ~ A x as x 0 theoretical insight/guess: f ~ ± A x –0.5 as x 0

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Forum0445 differences between the MRST and Alekhin u and d sea quarks near the starting scale ubar=dbar

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Forum0446

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Forum0447 LHCσ NLO (W) (nb) MRST ± 4 (expt) CTEQ6205 ± 8 (expt) Alekhin02215 ± 6 (tot) similar partons different Δχ 2 different partons σ(W) and σ(Z) : precision predictions and measurements at the LHC 4% total error (MRST 2002)

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Forum0448 ratio of W – and W + rapidity distributions x 1 =0.52 x 2 = x 1 =0.006 x 2 =0.006 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? ––

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Forum0449 Note: high-x gluon should become better determined from Run 2 Tevatron data Q. by how much? Note: CTEQ gluon more or less consistent with MRST gluon

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