2003/03/31 by G. Duplancic, G. Duplančić, B. Nizic +1 · 103 citations
Mathematics · Physics and Astronomy · #Algebraic number #Black Holes and Theoretical Physics #Classical mechanics #Dimensional regularization #Feynman diagram #Feynman integral #Geometry #Integral equation #Kinematics #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Parametric statistics #Particle physics theoretical and experimental studies #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scalar (mathematics) #Scattering #Scattering amplitude #Volume integral #hep-ph
paper · pdf · doi:10.1140/epjc/s2004-01723-7
published in The European Physical Journal C 35(1), 105-118 (Springer Science+Business Media) · 22 pages, 2 figures; one appendix added, discussions clarified, version to appear in Eur. Phys. J. C
arxiv created 2004/02/05 · openalex publication_date 2004/04/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral in D=4, and a general two-point integral in D space time dimensions. All the divergences present in the original integral are contained in the general two-point integral and associated coefficients. The problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner. Being derived with no restrictions regarding the external momenta, the method is completely general and applicable for arbitrary kinematics. In particular, it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta, which are unavoidable when calculating one-loop contributions to the hard-scattering amplitude for exclusive hadronic processes at large momentum transfer in PQCD. The iterative structure makes it easy to implement the formalism in an algebraic computer program.