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Hard Q C D Processes at Colliders

Hard Q C D Processes at Colliders. Lance Dixon, SLAC 2007 Lepton-Photon Symposium Daegu, Korea, August 16, 2007. CMS. ATLAS. Theme: LHC is just around the corner. pp collisions at 14 TeV center-of-mass energy, 7 times Tevatron Luminosity (collision rate) 10 – 100 times greater.

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Hard Q C D Processes at Colliders

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  1. Hard QCD Processes at Colliders Lance Dixon, SLAC 2007 Lepton-Photon Symposium Daegu, Korea, August 16, 2007

  2. CMS ATLAS Theme:LHC is just around the corner • pp collisions at 14 TeV center-of-mass energy, 7 times Tevatron • Luminosity (collision rate) 10 – 100 times greater • New window into electroweak-scale physics opening next year L. Dixon, SLAC Hard QCD Processes at Colliders

  3. Are we ready for the LHC? • Physics at the LHC is largely the physics of hard QCD • Will probe QCD in unprecedented regimes, and with unprecedented statistics • QCD governs production of electroweak states • in and beyond the Standard Model • Copious jet production can fake leptons, photons, etc. •  QCD [+ electroweak] hard processes form significant backgrounds to almost all new physics searches at LHC, as well as Tevatron L. Dixon, SLAC Hard QCD Processes at Colliders

  4. Questions to answer • Do we understand hard QCD well at Tevatron/HERA energies? • Do we understand the input parameters well enough? • parton distributions[talks by M. Diehl and C. Gwenlan] • - the strong coupling • Can we compute hard QCD processes theoretically to the accuracy required for LHC experiments? • What new techniques might help in this regard? L. Dixon, SLAC Hard QCD Processes at Colliders

  5. n c c Signals and backgrounds • Newparticles– whether from • supersymmetry • extra dimensions • new forces • Higgs boson(s) typically decay into old particles: quarks, gluons, charged leptons, neutrinos, photons, Ws & Zs (which in turn decay to leptons, …) • Kinematic signatures not always clean (e.g. mass bumps) if neutrinos, or other escaping particles present gluino cascade • Need to quantify Standard Model backgrounds for a variety of multi-particle processes, to maximize potential for new physics discoveries L. Dixon, SLAC Hard QCD Processes at Colliders

  6. Disclaimer • Hard QCD is a vast subject, so I can only scratch the surface • Will say next to nothing about important subjects such as: • High-energy (BFKL) limit [M. Diehl] • Small-x physics and parton saturation [M. Diehl] • (Hard) diffraction [M. Diehl, A. Rostovtsev] • Bottom or top quark production [C. Gwenlan, R. Erbacher] • Multiple parton scattering / underlying event • Matching leading-order predictions with parton showers • Other Monte Carlo developments • Insights from soft collinear effective theory (SCET) • ... L. Dixon, SLAC Hard QCD Processes at Colliders

  7. Outline • Preliminaries & theoretical tools • e+e- application – thrust at NNLO • Higgs at hadron colliders • Jets: substructure and distributions • Vector bosons + jets • Top + jets • New methods for loop amplitudes L. Dixon, SLAC Hard QCD Processes at Colliders

  8. suitable final state Parton distribution function Partonic cross section, computable in perturbative QCD partonic CM energy2 Preliminaries:QCD factorization & parton model mF ~ MZ • Asymptotic freedom guarantees that at short • distances (large transverse momenta), • partons in the proton are almost free. • Sampled “one at a time” in hard collisions. •  QCD-improved parton model: factorization scale (“arbitrary”) renormalization scale (“arbitrary”) L. Dixon, SLAC Hard QCD Processes at Colliders

  9. Parton evolution • parton distributions are nonperturbative • measured experimentally [talks by Diehl, Gwenlan] • most experimental data at much lower mFthan 100-1000 GeV • fortunately, evolution at mF >1-2 GeV is perturbative, • DGLAP equation: LO (1974) NLO (1980) NNLO (Moch, Vermaseren, Vogt, 2004) L. Dixon, SLAC Hard QCD Processes at Colliders

  10. (2007) by NNLO, a precision observable Also expand partonic cross section: Problem:Leading-order, tree-level predictions only qualitative due to poor convergence of expansion in (setting) LO NLO NNLO Example: Z production at Tevatron Distribution in rapidity Y has ADMP (2004) still ~50% corrections, LO  NLO L. Dixon, SLAC Hard QCD Processes at Colliders

  11. convolute with pdfs apply cuts LO tree dim. reg. first, cancel infrared divergences ( ) between virtual & real NLO 1 loop tree + 1 parton NNLO 2 loops 1 loop + 1 parton tree + 2 partons intricate ( ) IR cancellations Primer on higher-order QCD What partonic amplitudes, other ingredients are needed? Example: Z production at hadron colliders L. Dixon, SLAC Hard QCD Processes at Colliders

  12. NNLO = 2-loop x tree* + … n=2 LO = |tree|2 n=8 NLO = loop x tree* + … n=3 all amplitudes known (2000-2004), not yet implemented + 6-gluon amplitude (n=4) (2006) State of the art Example of jet production at hadron colliders For production of W/Z/Higgs + jets, situation is similar or worse if you count the W/Z/Higgs as replacing one jet L. Dixon, SLAC Hard QCD Processes at Colliders

  13. + • collinear singularities when • kg|| kq and kg|| kq • associated with each line • and proportional to _ Integration techniques: • analytic – simplest processes only • slicing – excise singular strips in phase space. Integrate • approximate cross section analytically in strips, rest numerically. • subtraction – subtract function mimicking exact cross section, but • which can be integrated more easily. Integrate difference numerically. • direct numerical integration – after sector decomposition Singular phase-space integration NLO real radiation: • soft singularity when kg 0 • classical radiation from • “accelerating” quark-antiquark pair L. Dixon, SLAC Hard QCD Processes at Colliders

  14. 1) Start with collinear approximation, add “half of soft behavior” on each side. “Dipole” subtraction [N.B.: not the dipole used in MC community] Catani, Seymour (1996) 2) Start with soft radiation pattern, add “half of collinear behavior” on each side. “Antenna” subtraction Kosower (1997,2003) Two types of subtraction methods Ellis, Ross, Terrano (1980) Frixione, Kunszt, Signer (1995) Long history of developments, including: • More recently, Lorentz-invariant subtraction terms • built up for general processes in 2 different ways: L. Dixon, SLAC Hard QCD Processes at Colliders

  15. To improve accuracy of MC’s, • incorporate NLO corrections into them. • MC@NLO, POWHEG do this, • but adding new processes is nontrivial. Frixione, Webber (2002), Nason, Frixione, Webber (2003),...; Nason, Ridolfi (2006), Frixione, Nason, Ridolfi (2007) If the first step of the shower were the same as the NLO subtraction term, this procedure would be greatly simplified. E.g. use Catani-Seymour functions to shower Nagy, Soper (2005); S. Schumann, to appear • Or, base shower on “antenna” functions VINCIA: Giele, Kosower, Skands (2007) NLO-aware parton showers are coming • Parton showers a key part • of Monte Carlo simulation programs • such as PYTHIA and HERWIG • – produce hadron-level events, • are essential to experimental analysis L. Dixon, SLAC Hard QCD Processes at Colliders

  16. At NLO, Catani-Seymour subtraction now implemented • in a wide variety of processes (limited largely by availability • of 1 loop amplitudes). • E.g., MCFM • NLOJET++ Campbell, Ellis, http://mcfm.fnal.gov/ Nagy, http://nagyz.web.cern.ch/nagyz/Site/NLOJET++/NLOJET++.html • NNLO generalizations of the CS method under development for specific applications: • e+e- n jets • pp  [H, W, Z, WZ, ...] + X Weinzierl (2003); Frixione, Grazzini (2005); Somogyi, Trócsányi, Del Duca (2005,2006) Catani, Grazzini (2007) • Antenna-based subtractions also developed at NNLO Gehrmann, Gehrmann-de Ridder, Heinrich (2003); Gehrmann, Gehrmann-de Ridder, Glover (2004,2005,2006) culminating recently in computation of the NNLO thrust distribution Subtraction: from NLO to NNLO L. Dixon, SLAC Hard QCD Processes at Colliders

  17. Iterated sector decomposition Binoth, Heinrich (2000-2004) Anastasiou, Melnikov, Petriello (2003,2004) Partition integration region and remap to make divergences 1-dimensional Example from NNLO Z production • Arbitrary observables (parton-level cuts) can be integrated • Several iterations, many sectors required for state-of-the-art NNLO L. Dixon, SLAC Hard QCD Processes at Colliders

  18. transverse momentum resummation needed for + ... threshold resummation needed if steeply falling parton distributions + ... LL, NLL, NNLL resummations Soft-gluon resummation: when fixed-order is not enough • Mismatch between kinematics of virtual and real corrections proportional to color charge of incoming partons much bigger for incoming gluons L. Dixon, SLAC Hard QCD Processes at Colliders

  19. wealth of data to measure ... Kluth (2006) e+e- application:The thrust distribution at NNLO Classic infrared-safe event-shape variable in e+e- annihilation: Brandt et al (1964); Farhi (1977) L. Dixon, SLAC Hard QCD Processes at Colliders

  20. NLO predictions, even with resummed improvements, • when fit to e+e- data, lead to • depending on observable • depending on fit range • error dominated by NLO truncation Need for NNLO predictions ALEPH (2004) L. Dixon, SLAC Hard QCD Processes at Colliders

  21. First NNLO results Gehrmann-De Ridder, Gehrmann, Glover, Heinrich, 0707.1285 [hep-ph] • 15-20% increase for 0.03 < 1-T < 0.33 • somewhat smaller – but NLO T previously gave larger than average value, 0.126 Pert. uncertainty reduced by ~30-40% • Precise value of • will require experimental reanalysis, • incorporating: • resummation for 1-T  0 • power correction analysis • other observables computed at NNLO •  Results eagerly awaited! L. Dixon, SLAC Hard QCD Processes at Colliders

  22. Hadron collider applications Begin with Higgs boson production and decay • Of great phenomenological importance • Gluon-fusion channel, • represents one of the simplest processes, • apart from W or Z production • So theory has already been pushed to high order • Illustrates methods of analysis that should eventually be applied to more complex final states L. Dixon, SLAC Hard QCD Processes at Colliders

  23. Higgs production and decay Focus on most likely mass range: ~ 100  200 GeV gluon fusion dominates, large QCD corrections weak boson fusion tagging jets, small QCD corrections L. Dixon, SLAC Hard QCD Processes at Colliders

  24. Gluon fusion total cross section Series for spoorly behaved: NLO correction +80% ! Dawson; Djouadi, Graudenz, Spira, Zerwas (1991) NNLO computations used large mtapproximation to reduce number of loops by 1 Catani, de Florian, Grazzini; Harlander, Kilgore; Anastasiou, Melnikov; Ravindran, Smith, van Neerven (2001 – 2003) effective vertex • Also resum threshold logarithms • to NNLL accuracy Catani, DeFlorian, Grazzini (2003) L. Dixon, SLAC Hard QCD Processes at Colliders

  25. As spinoff from computation of • NNLO parton evolution • it was possible to extract at N3LO • all with k = 0,1,2,3,4,5 • Missing + nonsingular terms  N3LOapprox Moch, Vermaseren, Vogt (2004) Moch, Vogt (2005) resummation analysis  N4LOapprox (within 2%) Ravindran; Ravindran, Smith, van Neerven (2006) now under good control: Gluon fusion beyond NNLO/NNLL • Even at NNLO, sizable uncertainty remains • (renormalization/factorization scale dependence) L. Dixon, SLAC Hard QCD Processes at Colliders

  26. CMS First computed with sector decomposition Recently also with subtraction method based on universal qT(H) properties Catani, Grazzini (2007) FEHiP Anastasiou Melnikov Petriello (2004,2005) photon rapidity difference photon min/max transverse momentum with cuts at NNLO Smooth background but S/B ~ 1/20 Access to arbitrary distributions at NNLO  improve signal extraction & Higgs coupling extraction good stability from NLO to NNLO, away from kinematic boundaries L. Dixon, SLAC Hard QCD Processes at Colliders

  27. QCD hard radiation: • LO • NLO, enhanced by g(x), FS singularity • NNLO, but enhanced by g(x) Balazs, Berger, Mrenna, Yuan (1997); DIPHOX: Binoth, Guillet, Pilon, Werlen (1999) + NLO corrections to : Bern, LD, Schmidt (2002) g + analogous term for (smaller): Balazs, Berger, Nadolsky, Yuan (2007) g Irreducible background to • Multi-component background: • e±, hadrons faking g , p0 gg , e± bremsstrahlung • fragmentation – radiation inside jet, pTg, jet < 1 GeV • Much removed by isolation cuts L. Dixon, SLAC Hard QCD Processes at Colliders

  28. g g _ In good shape for LHC [NNLO qqgg would be nice] Irreducible gg background (cont.) + NNLL resummation of qT(gg) RESBOS: Balazs, Berger, Nadolsky, Yuan (2007) Comparison with CDF gg data (2005) very instructive, because: Generally good agreement with pQCD predictions Except: Large twin fragmentation contribution (?) for large qT &small Dfgg L. Dixon, SLAC Hard QCD Processes at Colliders

  29. with cuts at NNLO FEHiP: Anastasiou, Dissertori, Stöckli (2007) Critical channel for • Requires jet veto [pTveto] to suppress top-quark background • Cut on lepton-pair azimuthal separation to suppress Can now assess efficiency of these cuts at NNLO • NNLO scale variation much smaller with typical cuts than without. • However, because , resummation investigation desirable L. Dixon, SLAC Hard QCD Processes at Colliders

  30. Weak boson fusion – NLO electroweak NLO QCD corrections to t-channel exchange WBF known for a while to be small, only ~ 5-10% Han, Valencia, Willenbrock (1992); Figy, Oleari, Zeppenfeld (2003,2004) Recent computation adds: Ciccolini, Denner, Dittmaier (2007) QCD corrections to s- and u-channel interferences (small) Electroweak corrections to all channels (sizable, ~ 7%) L. Dixon, SLAC Hard QCD Processes at Colliders

  31. NLO corrections to H + 2 jets • with WBF cuts are +30% • smaller corrections than for • but still significant Gluon fusion as background to WBF NLO QCD corrections to gluon fusion large – what about its contribution to H + 2 forward jets? Recent computation employs “semi-numerical” method for evaluating 1-loop amplitudes for H + 4 partons Campbell, Ellis, Zanderighi (2006) Ellis, Giele, Zanderighi (2005) azimuthal separation of tagging jets for gluon fusion background – probe of WBF production mechanism L. Dixon, SLAC Hard QCD Processes at Colliders

  32. See also http://www.pa.msu.edu/~huston/SpartyJet/SpartyJet.html for a package giving the user flexibility to reconstruct jets with a variety of algorithms/parameters and do comparisons. In use in CDF, ATLAS and CMS. Jets: Jets & infrared safety • Typical e+e- jet algorithm clusters • particles/towers (bottom up) • Typicalhadron collider algorithms use cones • – for seeded cones there is a danger of • infrared unsafety: jet configuration can depend • on arbitrarily soft gluons • Practical seedless cone (SIScone) • now available Salam, Soyez (2007) L. Dixon, SLAC Hard QCD Processes at Colliders

  33. Jet substructure • Can we tell light quark jets from gluon jets? • Not event by event, but statistically, using • different amount of radiation inside the jet • Use kinematics to • select gluon-rich or gluon-depleted samples • Then compare distributions of “jet shape” • – fraction of energy in a smaller cone with g* Works in pp using pTjet as tag And in ep at fixed pTjet using pT order of jet as tag (2007) kT algorithm DISENT CDF (2005) L. Dixon, SLAC Hard QCD Processes at Colliders

  34. Inclusive jets at the Tevatron Test QCD interactions directly at the shortest distances CDF: midpoint cone algorithm good agreement with NLO, central + forward D0: iterative cone algorithm – comparison with NNLL threshold-correcteds Kidonakis, Owens (2001) L. Dixon, SLAC Hard QCD Processes at Colliders

  35. _ Agreement with NLO is excellent in pp Df or g * Di-jet azimuthal distributions (2004) Complex hadronic final states: 3-4 hard partons poor in ep Is small x or BFKL physics responsible for disagreement? All models tested were too low... H1 (2007); NLOJET++ L. Dixon, SLAC Hard QCD Processes at Colliders

  36. Excellent absolute agreement with NLO prediction (MCFM) for Highlights need for NLO computations beyond Vector bosons + jets Production of with is a background to SUSY searches in CDF data on new Midpoint cone L. Dixon, SLAC Hard QCD Processes at Colliders

  37. _ t t + jet at NLO _ _ • At Tevatron, pp  t t is forward-backward symmetric at LO. • Forward-backward asymmetry develops at NLO, • and is also present in t t jet at LO. Halzen, Hoyer, Kim (1987), Kühn, Rodrigo (1998); Bowen, Ellis, Rainwater (2005) _ • DUWfind astriking reductionin the predicted • forward-backward asymmetry in t t jet at NLO _ % what does this portend for NNLO t t inclusive? _ at NNLO DUW at NLO pTjet > 20 GeV (uncorrected for reconstr.) Very interesting in light of new measurements in t t: D0 _ CDF(corr.) Important background to SUSY at LHC NLO corrections greatly reduce LHC cross section uncertainty Dittmaier, Uwer, Weinzierl (2007) L. Dixon, SLAC Hard QCD Processes at Colliders

  38. Feynman rulesnot optimized for QCD with massless quarks (for example) Motivation: Make computations of QCD trees and loops more efficient “Twistor-inspired” perturbative QCD by unveiling hidden analytic structure L. Dixon, SLAC Hard QCD Processes at Colliders

  39. QCD (twistor space) (momentum space) lines appear Penrose (1967); Witten (2003); Cachazo, Svrček, Witten (2004) Simplicity in Fourier space atomic spectroscopy lines appear L. Dixon, SLAC Hard QCD Processes at Colliders

  40. Back to the 1960’s What are the basic analytic properties of scattering amplitudes? • Branch cuts • Poles • Using inspiration and techniques (special complex momenta) • coming from the twistor approach, one can • reconstruct scattering amplitudes directly from this information • - in general at tree level • - and increasingly at one-loop level • These techniques show a lot of promise for efficiently computing one-loop QCD amplitudes for a variety of important multi-parton processes, such as W, Z + n jets. Britto, Cachazo, Feng, Witten (2004,2005) many authors (2004 – 2007) L. Dixon, SLAC Hard QCD Processes at Colliders

  41. Conclusions • An increasing number of hard QCD processes at colliders are now known quantitatively, i.e. at NLO • For a few benchmark processes, NNLO precision is available • Experiments at the Tevatron and HERA test QCD predictions over a wide range of kinematics • Agreement is generally very good, except near “kinematic boundaries” such as small pT, small x, etc., where resummations/reorganizations must be performed • Still need to push the “loops and legs” frontier to bring NLO/NNLO to more LHC processes • But we are “virtually” ready for LHC turn-on next year! L. Dixon, SLAC Hard QCD Processes at Colliders

  42. Thanks to Zvi Bern, Duncan Brown, Markus Diehl, Robin Erbacher, Claire Gwenlan, Joey Huston, Michael Peskin and Kirsten Tollefson for assistance in preparing this talk – but of course all errors and omissions are mine L. Dixon, SLAC Hard QCD Processes at Colliders

  43. Extra slides L. Dixon, SLAC Hard QCD Processes at Colliders

  44. D0 triply differential g + jet data High statistics data systematically a bit softer than NLO predictions JETPHOX: Aurenche, Fontannez, Guillet, Werlen, ... (1988,1989,...)  Keep an eye on Tevatron di-photon data too as statistics mount L. Dixon, SLAC Hard QCD Processes at Colliders

  45. _ _ qqW,Z at Tevatron qqW,Z at LHC Besides color factors, fast falling pdfs  threshold resummation more important for incoming gluons than quarks gg light Higgs at LHC L. Dixon, SLAC Hard QCD Processes at Colliders

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