# Presentation: 124176

## 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(M*Z*)  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*) & M*W*
- 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)

## 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

## 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

## Bottom-Quark Production

- Old picture: factor-of-two discrepancy between NLO QCD theory and experimental data
- 1993–2000

- But: fragmentation

- 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)

## 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

## NNLO Corrections to Collider Physics

- Vector boson production — new luminosity standard: 1% attainable
- Semianalytic calculation: analytic + parton distributions
- Anastasiou, Dixon, Melnikov, & Petriello (2003)

## 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

-  known

-  new

-  new

- to be done

- 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)

## 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

## Merging Parton Showers with Leading Order

- 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

- Gleisberg, Höche, Krauss, Schälicke, Schumann, Soff, Winter (SHERPA)

## Merging Parton Showerswith 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

## 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 theory*weak* ↔ *weak* coupling
- Nair (1988); Witten (2003)
- N =4 SUSY: laboratory for techniques

## 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

## Cachazo–Svrček–Witten Construction 

- Cachazo, Svrček, & Witten (2004)

## 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

- 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)

## Revenge of the 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

- Hippies

- ’60s

## 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*)

- Unitarity-based method

- On-shell recursion

- − Overlap Terms

## A 2→4 QCD Amplitude

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

## 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