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Multi-Parton Amplitudes in Gauge Theories

Michelangelo L. Mangano, Stephen J. Parke

TL;DR

This work presents a comprehensive framework for calculating multi-parton amplitudes in gauge theories by combining a gauge-invariant color-ordered (dual) expansion with helicity amplitudes, supersymmetry relations, and recursion. It demonstrates how to obtain compact analytic expressions for many-parton processes, analyzes their soft and collinear factorization, and develops recursive and exact results (including MHV structures) that illuminate the coherence of non-Abelian radiation. The authors also introduce practical approximations (KS and infrared reduction) to enable fast, reliable event-generation for multi-jet backgrounds in collider environments, and extend the formalism to multiple gauge groups and broken symmetries. Collectively, these methods provide powerful tools for precise background predictions and pave the way toward loop-level extensions and deeper theoretical insights into perturbative gauge theories.

Abstract

In this report we review recent developments in perturbation theory methods for gauge theories. We present techniques and results that are useful in the calculation of cross sections for processes with many final state partons which have applications in the study of multi-jet phenomena in high-energy Colliders.

Multi-Parton Amplitudes in Gauge Theories

TL;DR

This work presents a comprehensive framework for calculating multi-parton amplitudes in gauge theories by combining a gauge-invariant color-ordered (dual) expansion with helicity amplitudes, supersymmetry relations, and recursion. It demonstrates how to obtain compact analytic expressions for many-parton processes, analyzes their soft and collinear factorization, and develops recursive and exact results (including MHV structures) that illuminate the coherence of non-Abelian radiation. The authors also introduce practical approximations (KS and infrared reduction) to enable fast, reliable event-generation for multi-jet backgrounds in collider environments, and extend the formalism to multiple gauge groups and broken symmetries. Collectively, these methods provide powerful tools for precise background predictions and pave the way toward loop-level extensions and deeper theoretical insights into perturbative gauge theories.

Abstract

In this report we review recent developments in perturbation theory methods for gauge theories. We present techniques and results that are useful in the calculation of cross sections for processes with many final state partons which have applications in the study of multi-jet phenomena in high-energy Colliders.

Paper Structure

This paper contains 35 sections, 225 equations, 12 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Helicity Amplitudes
  3. The Color Form Factors
  4. Gluonic Amplitudes: Duality and Gauge Invariance
  5. Quark-Gluon Amplitudes
  6. Supersymmetry Relations among Amplitudes
  7. Explicit Results
  8. Four Partons
  9. Five Partons
  10. Six Partons
  11. Factorization Properties of Dual Amplitudes
  12. Soft Gluon Factorization
  13. Factorization of Collinear Poles
  14. Recursive Relations
  15. Color Ordered Gluon Currents
  16. ...and 20 more sections

Figures (12)

  • Figure 1: The zero-slope limit of the four gluon string diagram in terms of Feynman diagrams.
  • Figure 2: QED-type diagrams.
  • Figure 3: Gluon tree off a quark line.
  • Figure 4: The color flows for quark-antiquark scattering.
  • Figure 5: The color flows for quark-antiquark scattering with emission of two gluons.
  • ...and 7 more figures