James Stirling IPPP, University of Durham 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

J Stirling QCD - ICHEP042 more QCD? … see also HERA: Klein Tevatron: Lucchesi QCD and hadron spectroscopy: Close, Shan Jin QCD and heavy quarks: Ali, Shipsey QCD on the Lattice: Hashimoto

J Stirling QCD - ICHEP043 QCD is … 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”!

J Stirling QCD - ICHEP044 QCD in 2004 compare  tot (pp) and  tot (e + e -  hadrons ) 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 E 0 1 α S (E) non-perturbative approaches: lattice, Regge theory, skyrmions, large-N c,… perturbative field theory calculations

World Summary of α S (M Z ) – July 2004 from S. Bethke, hep-ex/ world average (MSbar, NNLO) α S (M Z ) =  cf. (2002)  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

J Stirling QCD - ICHEP046 examples of ‘precision’ phenomenology W, Z productionjet production NNLO QCD NLO QCD … and many other examples presented at this Conference

J Stirling QCD - ICHEP047 status of pQCD calculations LO –automated codes for arbitrary matrix element generation (MADGRAPH, COMPHEP, HELAC, …) –jet = parton, but ‘easy’ to interface to hadronisation MCs –large scale dependence α S (  ) 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 α S measurement) –jet structure begins to emerge –no automation yet, but many ideas –now can interface with PS fixed order: d  = A α S N [ 1 + C 1 α S + C 2 α S 2 + …. ] thus LO, NLO, NNLO, etc, or resummed to all orders using a leading log approximation, e.g. d  = A α S N [ 1 + (c 11 L + c 10 ) α S + (c 22 L 2 + c 21 L + c 20 ) α S 2 + …. ] where L = log(M/q T ), log(1/x), log(1-T), … >> 1 thus LL, NLL, NNLL, etc. current frontier 1

+ interfacing N n LO and parton showers Benefits of both: N n LOcorrect overall rate, hard scattering kinematics, reduced scale dep. PScomplete event picture, correct treatment of collinear logs to all orders Example: Frixione, Webber, Nason, processes included so far … pp  WW,WZ,ZZ,bb,tt,H 0,W,Z/  p T distribution of tt at Tevatron new

J Stirling QCD - ICHEP049 t t b b 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 the leading order O(α S 4 ) cross section has a large renormalisation scale dependence!

J Stirling QCD - ICHEP0410 John Campbell, Collider Physics Workshop, KITP, January 2004 Too many calculations, too few people!

J Stirling QCD - ICHEP0411 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 Example: jet cross section at hadron colliders 2 (also e + e -  3 jets)

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 parton final states or parton final state soft, collinear the collinear and soft singularities exactly cancel between the N +1 and N + 1-loop contributions

J Stirling QCD - ICHEP0413 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!

J Stirling QCD - ICHEP0414 summary of NNLO calculations (~1990  ) 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 C F 3 part of  (3 jet) Gehrmann-De Ridder, Gehrmann, Glover(2004) inclusive W,Z,  * van Neerven et al, Harlander and Kilgore corrected (2002) inclusive  * polarised Ravindran, Smith, Van Neerven (2003) W,Z,  * differential rapidity dis n Anastasiou, Dixon, Melnikov, Petriello (2003) H 0, A 0 Harlander and Kilgore; Anastasiou and Melnikov; Ravindran, Smith, Van Neerven (2002-3) WH, ZH Brein, Djouadi, Harlander (2003) QQ onium and Qq meson decay rates + other partial/approximate results (e.g. soft, collinear) and NNLL improvements ep e+e-e+e- pp HQ

J Stirling QCD - ICHEP Note: need to know splitting and coefficient functions to the same perturbative order to ensure that  (n) /  log  F = O(α S (n+1) ) >1991 new 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!

J Stirling QCD - ICHEP0416 Full 3-loop (NNLO) DGLAP splitting functions! Moch, Vermaseren and Vogt, hep-ph/ , hep-ph/ previous estimates based on known moments and leading behaviours Moch a b P ba =

J Stirling QCD - ICHEP pages later… …then 8 pages of the same quantities expressed in x-space! Moch, Vermaseren and Vogt, hep-ph/ , hep-ph/

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  4% total error (MRST 2002) NNLO phenomenology already under way…

J Stirling QCD - ICHEP0419 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 (also: event shapes, heavy quark prodn.) Bozzi Catani de Florian Grazzini q T (GeV) Kulesza Sterman Vogelsang Z De Florian Marchesini 3

J Stirling QCD - ICHEP0420 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(M H =120 LHC  σ pdf  ±3%  σ ptNNL0  ± 10%,  σ ptNNLL  ± 8%   σ theory  ± 9% H t g g Catani et al, hep-ph/ H g g threshold logs log N ( 1-M 2 /s gg )

J Stirling QCD - ICHEP0421 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 4

J Stirling QCD - ICHEP0422 slide from Zvi Bern gg  ggg

J Stirling QCD - ICHEP0423 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/ ) “Perturbative gauge theory as a string theory in twistor space” Maximum Helicity Violating true! r s = (colour factors suppressed)

J Stirling QCD - ICHEP0424 Cachazo, Svrcek, Witten (CSW) 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 April 2004, hep-th/ Georgiou, Khoze; Zhu; Wu, Zhu; Bena, Bern, Kosower; Georgiou, Khoze, Glover; Kosower; Brandhuber, Spence, Travaglini; Bern, del Duca, Dixon, Kosower; …

J Stirling QCD - ICHEP0425 the ‘other frontier’… p + p  H + X –the rate (  parton, pdfs, α S ) –the kinematic distribtns. (d  /dydp T ) –the environment (jets, underlying event, backgrounds, …)     p + p  p + H + p –a real challenge for theory (pQCD + npQCD) and experiment (rapidity gaps, forward protons,..) compare … with … b b The most sophisticated calculations and input from many other experiments are needed to properly address these issues! 5

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

J Stirling QCD - ICHEP0427 For example: 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 ?! Need to calculate production amplitude and gap Survival Factor: mix of pQCD and npQCD  significant uncertainties BUT calibration possible via X = quarkonia, large E T jet pair, , etc. at Tevatron QCD challenge: to refine and test calculations & elevate to precision predictions! selection rules anything that couples to gluons Gallinaro Royon mass resolution is crucial! Royon et al p + p → p  H  p at LHC gap survival X S/B mass resolution

J Stirling QCD - ICHEP0428 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

J Stirling QCD - ICHEP0429 extra slides

J Stirling QCD - ICHEP0430 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 linear scale log scale

J Stirling QCD - ICHEP0431 technical details q  g  etc. L = log(Q 2 /  2 ) F = A L 3 + B L 2 + C L + D P (2) contained in this term number of diagrams (Q GRAF ) fictitious scalar- gluon vertex a b

J Stirling QCD - ICHEP0432 World Summary of M W from LEPEWWG, Summer 2004 could well be a missing strong interaction effect

J Stirling QCD - ICHEP0433 the interplay of electroweak and QCD precision physics role of α S 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 sin 2  W from N scattering … 2 Ward Hoecker Vainshtein

J Stirling QCD - ICHEP0434 QED effects in pdfs included in standard radiative correction packages (HECTOR, HERACLES) QED corrections to DIS include:  mass singularity ~α log(Q 2 /m q 2 ) when  ║q these corrections are universal and can be absorbed into pdfs, exactly as for QCD singularities, leaving finite (as m q  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) )

J Stirling QCD - ICHEP0435 QED-improved DGLAP equations at leading order in α and α S where momentum conservation:

J Stirling QCD - ICHEP0436 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 Q 2, where it is equivalent to a shift in α S of  α S  dynamic generation of photon parton distribution isospin violation: u p ( x) ≠ d n ( x) first consistent global pdf fit with QED corrections included (MRST 2004) proton neutron new

J Stirling QCD - ICHEP0437 perturbative generation of s(x) ≠ s(x) P us (x) ≠ P us (x) at O(α S 3 ) Quantitative study by de Florian et al hep-ph/   x(s-s)  pQCD <   cf. from global pdf fit (Olness et al, hep-ph/ ,3)   <  x(s-s)  fit < partial explanation of NuTeV sin 2  W “anomaly”? note! new

J Stirling QCD - ICHEP0438 sin 2  W from N 3  difference new

J Stirling QCD - ICHEP0439 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

J Stirling QCD - ICHEP0440 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 ?! need to calculate production amplitude and gap Survival Factor  big uncertainties BUT calibration possible via X = quarkonia or large E T jet pair, e.g. CDF ‘observation’ of p + p → p + χ 0 c (→J/  γ) + p:   excl (J/  γ) < 49 ± 18 (stat) ± 39 (syst) pb cf.  thy ~ 70 pb (Khoze et al 2004) QCD challenge: to refine and test such models & elevate to precision predictions! selection rules couples to gluons Gallinaro Royon mass resolution is crucial! Royon et al new

J Stirling QCD - ICHEP0441 NNLO corrections to Drell-Yan cross sections Anastasiou et al. hep-ph/ hep-ph/ in DY, sizeable HO pQCD corrections since α S (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

J Stirling QCD - ICHEP0442 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

J Stirling QCD - ICHEP0443 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

J Stirling QCD - ICHEP0444 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 )   f i (x,Q 2 ) α S (M Z )

J Stirling QCD - ICHEP0445 (MRST) parton distributions in the proton Martin, Roberts, S, Thorne

J Stirling QCD - ICHEP0446 uncertainty in gluon distribution (CTEQ) then  f g →  σ gg→X etc.

J Stirling QCD - ICHEP0447 solid = LHC dashed = Tevatron Alekhin 2002 pdf uncertainties encoded in parton-parton luminosity functions: with  = M 2 /s, so that for ab→X

J Stirling QCD - ICHEP0448 longer Q 2 extrapolation smaller x

J Stirling QCD - ICHEP0449 Djouadi & Ferrag, hep-ph/ Higgs cross section: dependence on pdfs

J Stirling QCD - ICHEP0450 Djouadi & Ferrag, hep-ph/

J Stirling QCD - ICHEP0451 Djouadi & Ferrag, hep-ph/ the differences between pdf sets needs to be better understood!

J Stirling QCD - ICHEP0452 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 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

J Stirling QCD - ICHEP0453 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 … the QCD factorization theorem for hard-scattering (short-distance) inclusive processes ^ ^  … at hadron colliders DGLAP equations

J Stirling QCD - ICHEP0454 x dependence of f i (x,Q 2 ) determined by ‘global fit’ to deep inelastic scattering (H1, ZEUS, NMC, …) and hadron collider data F 2 (x,Q 2 ) =  q e q 2 x q(x,Q 2 ) etc DGLAP equations

J Stirling QCD - ICHEP0455 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!

J Stirling QCD - ICHEP0456 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

J Stirling QCD - ICHEP0457 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

J Stirling QCD - ICHEP0458 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 gg→H :  σ pdf <<  σ pt  4% total error (MRST 2002)

J Stirling QCD - ICHEP0459 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)

J Stirling QCD - ICHEP0460 Full 3-loop (NNLO) non-singlet DGLAP splitting function! Moch, Vermaseren and Vogt, hep-ph/ new

J Stirling QCD - ICHEP0461 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)

J Stirling QCD - ICHEP0462 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? ––

J Stirling QCD - ICHEP0463 pdfs from global fits Formalism LO, NLO, NNLO DGLAP MSbar factorisation Q 0 2 functional Q 0 2 sea quark (a)symmetry etc. Who? Alekhin, CTEQ, MRST, GGK, 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 )   f i (x,Q 2 ) α S (M Z )

J Stirling QCD - ICHEP0464 summary of DIS data + neutrino FT DIS data Note: must impose cuts on DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically: Q 2 > GeV 2 W 2 = (1-x)/x Q 2 > GeV 2

J Stirling QCD - ICHEP0465 typical data ingredients of a global pdf fit

J Stirling QCD - ICHEP0466 HEPDATA pdf server Comprehensive repository of past and present polarised and unpolarised pdf codes (with online plotting facility) can be found at the HEPDATA pdf server web site: … this is also the home of the LHAPDF project

J Stirling QCD - ICHEP0467 (MRST) parton distributions in the proton Martin, Roberts, S, Thorne