QCD in the Color-Flow Representation

Abstract

For many practical purposes, it is convenient to formulate unbroken non-abelian gauge theories like QCD in a color-flow basis. We present a new derivation of SU(N) interactions in the color-flow basis by extending the gauge group to U(N)xU(1)' in such a way that the two U(1) factors cancel each other. We use the quantum action principles to show the equivalence to the usual basis to all orders in perturbation theory. We extend the known Feynman rules to exotic color representations (e.g. sextets) and interactions (e.g. ${\epsilon }_{ijk}$). We discuss practical applications as they occur in automatic computation programs.

37 pages

References in corpus (7)

• WHIZARD: Simulating Multi-Particle Processes at LHC and ILC
• A standard format for Les Houches Event Files
• HELAC: a package to compute electroweak helicity amplitudes
• Helac-Phegas: a generator for all parton level processes
• An Algorithm to Compute Born Scattering Amplitudes without Feynman Graphs
• An Analytic Initial-State Parton Shower
• Generating QCD amplitudes in the color-flow basis with MadGraph

Cited by in corpus (25)

• Event Generators for High-Energy Physics Experiments
• Precise predictions for same-sign W-boson scattering at the LHC
• Parton branching at amplitude level
• Transversal Modes and Higgs Bosons in Electroweak Vector-Boson Scattering at the LHC
• Resonances at the LHC beyond the Higgs: The Scalar/Tensor Case
• NLO QCD Predictions for off-shell $t\bar{t}$ and $t\bar{t}H$ Production and Decay at a Linear Collider
• Fully-differential Top-Pair Production at a Lepton Collider: From Threshold to Continuum
• Decomposition of one-loop QCD amplitudes into primitive amplitudes based on shuffle relations
• The role of colour flows in matrix element computations and Monte Carlo simulations
• NLO Electroweak Corrections to Multi-Boson Processes at a Muon Collider
• Parallel Adaptive Monte Carlo Integration with the Event Generator WHIZARD
• Scattering of W and Z Bosons at High-Energy Lepton Colliders
• Simple, Parallel, High-Performance Virtual Machines for Extreme Computations
• The Color Discriminant Variable and Scalar Diquarks at the LHC
• Search for Mono-Higgs Signals in $b\bar{b}$ Final States Using Deep Neural Networks
• The chirality-flow formalism
• Automation of NLO processes and decays and POWHEG matching in WHIZARD
• Boosting Vector Calculus with the Graphical Notation
• Functional Directed Acyclical Graphs for Scattering Amplitudes in Perturbation Theory
• New developments in the Whizard event generator
• On long-lived electroweak-singlet coloured scalars
• Determination of the first-generation quark couplings at the Z-pole
• Monte Carlo Event Generators
• Challenges for Monte Carlo generators
• Making extreme computations possible with virtual machines