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## QCD at the Dawn of the LHC Era

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**QCD at the Dawn of the LHC Era**David A. Kosower CEA–Saclay PANIC ’05, Santa Fe, October 24–28, 2005**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**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**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**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**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**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**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**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**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**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**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**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**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**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**Cachazo–Svrček–Witten Construction**Cachazo, Svrček, & Witten (2004) PANIC ’05, Santa Fe, Oct 24–28,2005**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**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**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**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**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**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