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Developments in perturbative QCD

Gavin P. Salam

TL;DR

This review surveys developments in perturbative QCD spanning fixed-order and all-order techniques, emphasizing conceptual advances with LHC relevance. It highlights twistor-space methods (CSW/BCFW) that simplify tree-level multi-jet amplitudes, automation of one-loop (NLO) calculations, and NNLO efforts including sector-decomposition and subtraction strategies. The all-order discussion covers modern MC event generators, matching schemes like CKKW and MC@NLO, and analytical resummations up to high logarithmic accuracy, plus small-x saturation physics via BK and related stochastic extensions. Collectively, the work underscores steady progress toward percent-level predictions for complex final states, improved interfacing between fixed-order and resummed approaches, and continued cross-fertilization with theoretical developments, all of which are crucial for robust LHC phenomenology and new physics searches.

Abstract

A brief review of key recent developments and ongoing projects in perturbative QCD theory, with emphasis on conceptual advances that have the potential for impact on LHC studies. Topics covered include: twistors and new recursive calculational techniques; automation of one-loop predictions; developments concerning NNLO calculations; the status of Monte Carlo event generators and progress in matching to fixed order; analytical resummation including the push to NNLL, automation and gap between jets processes; and progress in the understanding of saturation at small x.

Developments in perturbative QCD

TL;DR

This review surveys developments in perturbative QCD spanning fixed-order and all-order techniques, emphasizing conceptual advances with LHC relevance. It highlights twistor-space methods (CSW/BCFW) that simplify tree-level multi-jet amplitudes, automation of one-loop (NLO) calculations, and NNLO efforts including sector-decomposition and subtraction strategies. The all-order discussion covers modern MC event generators, matching schemes like CKKW and MC@NLO, and analytical resummations up to high logarithmic accuracy, plus small-x saturation physics via BK and related stochastic extensions. Collectively, the work underscores steady progress toward percent-level predictions for complex final states, improved interfacing between fixed-order and resummed approaches, and continued cross-fertilization with theoretical developments, all of which are crucial for robust LHC phenomenology and new physics searches.

Abstract

A brief review of key recent developments and ongoing projects in perturbative QCD theory, with emphasis on conceptual advances that have the potential for impact on LHC studies. Topics covered include: twistors and new recursive calculational techniques; automation of one-loop predictions; developments concerning NNLO calculations; the status of Monte Carlo event generators and progress in matching to fixed order; analytical resummation including the push to NNLL, automation and gap between jets processes; and progress in the understanding of saturation at small x.

Paper Structure

This paper contains 13 sections, 8 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Fixed-order calculations
  3. Tree-level amplitudes and twistors
  4. One-loop amplitudes
  5. NNLO jet calculations
  6. NNLO splitting functions
  7. Other accuracy-related issues
  8. All-order calculations
  9. Monte Carlo event generators (MC)
  10. Matching MC & fixed order
  11. Analytical resummations
  12. Small $x$ and saturation
  13. Concluding remarks

Figures (4)

  • Figure 1: Graphical illustration of the CSW rules: by joining together two MHV amplitudes with an off-shell scalar propagator one obtains an amplitude with an extra negative helicity (NMHV).
  • Figure 2: ImpactMoch:2004pa of NNLO DGLAP corrections on the derivative of a toy singlet quark distribution $q_S = \sum_i (q_i + \bar{q}_i)$.
  • Figure 3: Spectrum for $b$-production ($\to J/\Psi$) compared to MC@NLO and an analytical prediction.Cacciari:2003uh
  • Figure 4: Diagram giving NGL: to calculate the probability of there being no emission into the gap, one should resum a large-angle energy-ordered cascade of emissions rather than just direct emission from the original hard partons.