QCD at the Dawn of the LHC Era

1
QCD at the Dawn of the LHC Era

• David A. Kosower
• CEASaclay
• PANIC 05, Santa Fe, October 2428, 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)

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

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

5
Bottom-Quark Production

• Old picture factor-of-two discrepancy between
  NLO QCD theory and experimental data
• 19932000

But fragmentation
6

• New picture finally good agreement between
  theory experiment
• Use fragmentation function extracted from ee-
  data
• Consistent theoretical treatment of fragmentation
  matching to resummation
• New small-pT data
• Other small changes (pdfs, as)
• Cacciari, Frixione, Mangano, Nason, Ridolfi (2003)

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

8
NNLO Corrections to Collider Physics

• Vector boson production new luminosity
  standard 1 attainable
• Semianalytic calculation analytic parton
  distributions
• Anastasiou, Dixon, Melnikov, Petriello (2003)

9
NNLO Jet Physics

• Ingredients for n-jet computations
• 2 ? (n2) tree-level amplitudes
• 2 ? (n1) one-loop amplitudes n2 or W1
• Bern, Dixon, DAK, Weinzierl Kunszt, Signer,
  Trocsanyi
• 2 ? n two-loop amplitudes n2 or W1
• 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 34 years
? known
? new
? known
? new
to be done
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• 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)

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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

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Merging Parton Showers with Leading Order
Gleisberg, Höche, Krauss, Schälicke, Schumann,
Soff, Winter (SHERPA)

• If we just start with n-parton configurations
  add showers, wed 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

13
Merging Parton Showerswith Next-to-Leading Order

• If we just add parton showers to an NLO
  calculation, wed double-count virtual
  contributions
• MC_at_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

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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 dualityTopological string theory on CP34 ?
  N 4 supersymmetric gauge theoryweak ? weak
  coupling
• Nair (1988) Witten (2003)
• N 4 SUSY laboratory for techniques

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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

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CachazoSvrcekWitten Construction

• Cachazo, Svrcek, Witten (2004)

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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

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• Proof very general relies only on complex
  analysis factorization
• Applied to gravity
• Bedford, Brandhuber, Spence, Travaglini
  (2/2005)
• Cachazo Svrcek (2/2005)
• Massive amplitudes
• Badger, Glover, Khoze, Svrcek (4/2005, 7/2005)
• Forde DAK (7/2005)
• Integral coefficients
• Bern, Bjerrum-Bohr, Dunbar, Ita (7/2005)
• Connection to CachazoSvrcekWitten construction
• Risager (8/2005)
• CSW construction for gravity ? Twistor string for
  N 8?
• Bjerrum-Bohr, Dunbar, Ita, Perkins, Risager
  (9/2005)

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Revenge of the Hippies
Hippies
60s

• 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

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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
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A 2?4 QCD Amplitude

• Rational terms
  Bern, Dixon, DAK (2005)
• and an all-n form too!

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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