We study the factorization of soft and collinear singularities in dimensionally-regularized fixed-angle scattering amplitudes in massless gauge theories. Lett. Comment: 11 pages; calculation extended to general 5-parton kinematics. Lett. For amplitudes with four or more hard partons we present a minimal solution where the soft anomalous dimension is a sum over colour dipoles, multiplied by the cusp anomalous dimension. decomposition of the scattering according to the possible patterns of hard hep-ph/0508310. The fifth form factor is expressed in terms of the Casimir operators (squared colour charges) of irreducible representations in the crossing $t$- and $u$-channels. In this colour flow basis the amplitude is represented by a vector with components M I . In As an application we revisit the problem of large angle radiation in $gg\to gg$ and give a relatively simple solution and interpretation of the results. We then modify The eight-by-eight anomalous dimension matrix for gluon-gluon scattering shows a simplified structure in the basis corresponding to definite color exchange in the t-channel. This symmetry is broken by cusp singularities in both the soft and the eikonal jet functions. Octet exchange in the hard scattering is associated with the familiar “reggeized”, sαg(t) behavior, which arises from s-dependence in Sudakov suppression. The latter simplifies in the ‘compact pair expansion’ which singles out the global charges (Casimirs) of the pair color states. numerically the gap cross section and gap fraction and compare the results with large class of final-state resummations, in a range of processes. B575 (2003) 268-278, Considering different bases we unveil some interesting properties of this matrix. Once the extent of this parasitic feedforward is highlighted, the topological nature of appropriate feedforward compensation is relatively easy to innovate. currently-used random treatment of radiation in the parton shower is generating gluon exchanges between Wilson lines in configuration space, and explore their structure is written on paper. the parton shower algorithm in order to correct the simulation of QCD It was noticed in Ref. and bases, and special functions such as scalar products are defined for such It describes the coupled seven-channel non-Abelian intranuclear evolution of the four-gluon color-singlet states. We consider the recently developed diagrammatic approach to soft-gluon Nuclear $p_\perp$-broadening of an energetic parton pair, Nuclear effects in high-energy proton-nucleus collisions : transverse momentum broadening of energetic parton systems and soft anomalous dimension matrices, ColorMath - A package for color summed calculations in SU(Nc), On the breaking of collinear factorization in QCD, On the renormalization of multiparton webs, An Overview of Analog Feedback Part II: Amplifier Configurations in Generic Device Technologies, Color structure for soft gluon resummation - A general recipe, The Massive Soft Anomalous Dimension Matrix at Two Loops, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, Nonlinear k ⊥ factorization for gluon-gluon dijets produced off nuclear targets, Sudakov resummation of multiparton QCD cross sections, Soft gluons at large angles in hadron collisions, Hadron collisions and the fifth form factor, Evolution of color exchange in QCD hard scattering, Color exchange in near-forward hard elastic scattering, Dijet Rapidity Gaps in Photoproduction from Perturbative QCD, The colour evolution of the process q q -> q q g, Symmetry of Anomalous Dimension Matrices for Colour Evolution of Hard Scattering Processes, Principles of general final-state resummation and automated A Mathematica package for color summed calculations in QCD (SU(Nc)) is In Ref. It contributes to the logarithmic violation of Bjorken scaling which was one of the great early successes of QCD.

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