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QCD at the Dawn of the LHC Era

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  1. QCD at the Dawn of the LHC Era David A. Kosower CEA–Saclay PANIC ’05, Santa Fe, October 24–28, 2005

  2. The Challenge • Everything at a hadron collider (signals, backgrounds, luminosity measurement) involves QCD • Strong coupling is not small: s(MZ)  0.12 and running is important • events have high multiplicity of hard clusters (jets) • each jet has a high multiplicity of hadrons • higher-order perturbative corrections are important • Processes can involve multiple scales: pT(W) & MW • need resummation of logarithms • Confinement introduces further issues of mapping partons to hadrons, but for suitably-averaged quantities (infrared-safe) avoiding small E scales, this is not a problem (power corrections) PANIC ’05, Santa Fe, Oct 24–28,2005

  3. Approaches • General parton-level fixed-order calculations • Numerical jet programs: general observables • Systematic to higher order/high multiplicity in perturbation theory • Parton-level, approximate jet algorithm; match detector events only statistically • Parton showers • General observables • Leading- or next-to-leading logs only, approximate for higher order/high multiplicity • Can hadronize & look at detector response event-by-event • Semi-analytic calculations/resummations • Specific observable, for high-value targets • Checks on general fixed-order calculations PANIC ’05, Santa Fe, Oct 24–28,2005

  4. General Fixed-Order Programs • LO: Basic shapes of distributionsbut: no quantitative prediction — large scale dependence missing sensitivity to jet structure & energy flow • NLO: First quantitative prediction improved scale dependence — inclusion of virtual corrections basic approximation to jet structure — jet = 2 partons • NNLO: Precision predictions small scale dependence better correspondence to experimental jet algorithms understanding of theoretical uncertainties Anastasiou, Dixon, Melnikov, & Petriello PANIC ’05, Santa Fe, Oct 24–28,2005

  5. Bottom-Quark Production • Old picture: factor-of-two discrepancy between NLO QCD theory and experimental data 1993–2000 But: fragmentation PANIC ’05, Santa Fe, Oct 24–28,2005

  6. New picture: finally good agreement between theory & experiment • Use fragmentation function extracted from e+e− data • Consistent theoretical treatment of fragmentation & matching to resummation • New small-pT data • Other small changes (pdfs, αs) Cacciari, Frixione, Mangano, Nason, Ridolfi (2003) PANIC ’05, Santa Fe, Oct 24–28,2005

  7. NNLO Splitting Function Moch, Vermaseren, & Vogt (2004) • Stability of perturbative expansion confirmed • Essential ingredient for 1% precision physics at hadron colliders • Incorporated into momentum evolution of parton distributions • Landmark computation • Also of interest to string theorists — anomalous dimensions in N =4 supersymmetric gauge theories PANIC ’05, Santa Fe, Oct 24–28,2005

  8. NNLO Corrections to Collider Physics • Vector boson production — new luminosity standard: 1% attainable • Semianalytic calculation: analytic + parton distributions Anastasiou, Dixon, Melnikov, & Petriello (2003) PANIC ’05, Santa Fe, Oct 24–28,2005

  9. NNLO Jet Physics • Ingredients for n-jet computations • 2 → (n+2) tree-level amplitudes • 2 → (n+1) one-loop amplitudes n=2 or W+1 Bern, Dixon, DAK, Weinzierl; Kunszt, Signer, Trocsanyi • 2 → n two-loop amplitudes n=2 or W+1 Anastasiou, Bern, Chetyrkin, De Freitas, Dixon, Garland, Gehrmann, Glover, Laporta, Moch, Oleari, Remiddi, Smirnov, Tausk, Tejeda-Yeomans, Tkachov, Uwer, Veretin, Weinzierl • Doubly-singular (double-soft, soft-collinear, triply-collinear, double collinear) behavior of tree-level amplitudes • & their integrals over phase space • Singular (soft & collinear) behavior of one-loop amplitudes • & integrals over phase space • Initial state double and lone singular behavior known since the ’80s known for 10 years known for 3–4 years known new known new to be done PANIC ’05, Santa Fe, Oct 24–28,2005

  10. Formalism for NNLO jet corrections • Dipole subtraction method (cf. Catani & Seymour at NLO) Weinzierl; Grazzini & Frixione (2004) • Sector decomposition (automation of Ellis, Ross, & Terrano (1980)) Binoth & Heinrich; Anastasiou, Melnikov, & Petriello (2003) • Antenna subtraction DAK;Gehrmann, Gehrmann-De Ridder, Glover • Complete ingredients now available for e+e− → 3 jets, using antenna method Gehrmann, Gehrmann-De Ridder, Glover (2005) PANIC ’05, Santa Fe, Oct 24–28,2005

  11. Parton Showers • PYTHIA & HERWIG; SHERPA Marchesini, Webber, & Seymour; Bengtsson, Lönnblad, Sjöstrand; Krauss et al • Basic ideas date from ’80s • Start with simple 2 → 2 process, add more partons using collinear approximation • Leading-log + part of next-to-leading log accuracy: • Can we improve the accuracy: • At higher multiplicity, for wide-angle emission? • At fixed jet multiplicity, for scale stability and higher-order precision? • Burst of theoretical activity in recent years PANIC ’05, Santa Fe, Oct 24–28,2005

  12. Merging Parton Showers with Leading Order Gleisberg, Höche, Krauss, Schälicke, Schumann, Soff, Winter (SHERPA) • If we just start with n-parton configurations & add showers, we’d double-count contributions in near-collinear configurations • Integrations over real emissions alone are IR divergent • Basic approach Catani, Krauss, Kuhn, & Webber(2001) • Generate fixed order configuration • Require separation in kT — eliminate IR divergences • Assign branching history • Reweight with Sudakov factors • Shower below kT Mangano; Krauss; Lönnblad; Mrenna & Richardson • Residual matching sensitivity to be a subject of further studies PANIC ’05, Santa Fe, Oct 24–28,2005

  13. Merging Parton Showerswith Next-to-Leading Order • If we just add parton showers to an NLO calculation, we’d double-count virtual contributions • MC@NLO: Subtract double-counted terms, generated by first branching Frixione & Webber (2002) • Implemented and applied • Requires specific calculation of terms for each process • More general approach based on dipole subtraction Nagy, Soper, Kramer (2005) • Watch this space for further developments Nason; Webber, Laenen, Motylinski, Oleari, Del Duca, Frixione PANIC ’05, Santa Fe, Oct 24–28,2005

  14. Alternative Representations of Field Theories • AdS/CFT Duality: string theory on AdS5 S5  N =4 supersymmetric gauge theory strong ↔ weak coupling Maldacena (1997); Gubser, Klebanov, & Polyakov; Witten (1998) • New duality:Topological string theory on CP3|4  N =4 supersymmetric gauge theoryweak ↔ weak coupling Nair (1988); Witten (2003) • N =4 SUSY: laboratory for techniques PANIC ’05, Santa Fe, Oct 24–28,2005

  15. Twistor Space Penrose (1974) • Rewrite four-vectors as outer products of spinors • Fourier-transform  twistor space • Analyze previously-known results: simple geometric structure in twistor space • Leads to new representations of amplitudes PANIC ’05, Santa Fe, Oct 24–28,2005

  16. Cachazo–Svrček–Witten Construction Cachazo, Svrček, & Witten (2004) PANIC ’05, Santa Fe, Oct 24–28,2005

  17. On-Shell Recurrence Relations Britto, Cachazo, Feng, Witten (2004/5) • Amplitudes written as sum over ‘factorizations’ into on-shell amplitudes — but evaluated for complex momenta • All momenta on shell, momentum conserved PANIC ’05, Santa Fe, Oct 24–28,2005

  18. Proof very general: relies only on complex analysis + factorization • Applied to gravity Bedford, Brandhuber, Spence, & Travaglini (2/2005) Cachazo & Svrček (2/2005) • Massive amplitudes Badger, Glover, Khoze, Svrček (4/2005, 7/2005) Forde & DAK (7/2005) • Integral coefficients Bern, Bjerrum-Bohr, Dunbar, & Ita(7/2005) • Connection to Cachazo–Svrček–Witten construction Risager (8/2005) • CSW construction for gravity  Twistor string for N =8? Bjerrum-Bohr, Dunbar, Ita, Perkins, & Risager (9/2005) PANIC ’05, Santa Fe, Oct 24–28,2005

  19. Revenge of the Hippies ’60s Hippies • Then: amplitudes determined by factorization & dispersion relations — in principle (no field theory) • Amplitudes computed using unitarity + Feynman-integral representation (existence of field theory) + complex factorization • Unitarity-based method: sew amplitudes not diagrams Bern, Dixon, Dunbar, DAK (1994); Britto, Cachazo, Feng (2004) • Lots of explicit results • Fixed order • All-n • Factorization functions PANIC ’05, Santa Fe, Oct 24–28,2005

  20. On-Shell Recursion Relations for Loops • Loop Amplitude = Cut Terms + Rational Terms Bern, Dixon, DAK (2005) • Opens door to many new calculations: time to do them! • Approach already includes external massive particles (H, W, Z) − Overlap Terms Unitarity-based method On-shell recursion PANIC ’05, Santa Fe, Oct 24–28,2005

  21. A 2→4 QCD Amplitude Rational terms Bern, Dixon, DAK (2005) …and an all-n form too! PANIC ’05, Santa Fe, Oct 24–28,2005

  22. Summary • Precision QCD crucial to accomplishing the physics goals of the LHC • Progress on many fronts: NLO, NNLO, parton showers; resummation, uncertainty evaluation in PDFs • Look forward to a significant increase in our capabilities between now & LHC turn on PANIC ’05, Santa Fe, Oct 24–28,2005