Factorization in One-Loop Gauge Theory

Abstract

Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared divergences complicate factorization. Here we prove that factorization in such theories is described by a set of universal functions. In particular, a proof of the universality of one-loop splitting functions as the momenta of two particles become collinear is presented. Factorization in multi-particle channels is also given. The discontinuity functions that appear in the splitting functions may also be used to obtain infrared divergent box integral functions from finite ones.

Minor corrections made, 51 pages including figures

References in corpus (23)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Multi-Parton Amplitudes in Gauge Theories
• Dimensionally Regulated Pentagon Integrals
• Higher Order Corrections to Jet Cross Sections in Hadron Colliders
• Field Theory Without Feynman Diagrams: One-Loop Effective Actions
• One-Loop Corrections to Five-Gluon Amplitudes
• Dimensionally Regulated One-Loop Integrals
• One-Loop Corrections to Two-Quark Three-Gluon Amplitudes
• One-Loop N Gluon Amplitudes with Maximal Helicity Violation via Collinear Limits
• On the Calculation of Effective Actions by String Methods
• One-loop helicity amplitudes for all 2 -> 2 processes in QCD and N=1 supersymmetric Yang-Mills theory
• String-Based Methods in Perturbative Gravity
• Calculation of Graviton Scattering Amplitudes using String-Based Methods
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Worldline Green Functions for Multiloop Diagrams
• Multigluon Helicity Amplitudes Involving a Quark Loop
• One-loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon
• One Loop Multiphoton Helicity Amplitudes
• The Higher Derivative Expansion of the Effective Action by the String-Inspired Method, Part I
• Supersymmetry Relations Between Contributions To One-Loop Gauge Boson Amplitudes
• Multiloop String-Like Formulas for QED
• Navigating Around the Algebraic Jungle of QCD: Efficient Evaluation of Loop Helicity Amplitudes

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