2004/12/31 by Ruth Britto, Freddy Cachazo, Bo Feng · 26 citations
Mathematics · Physics and Astronomy · #Algorithm #Amplitude #Black Holes and Theoretical Physics #Factorization #Feynman diagram #Gluon #Mathematical analysis #Mathematical physics #Mathematics #Momentum (technical analysis) #Particle physics #Particle physics theoretical and experimental studies #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Recursion (computer science) #Tree (set theory) #hep-ph #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2005.02.030
published as Nucl.Phys.B715:499-522,2005 · 27 pages, harvmac. 6 figures. v2: Fixed typos in (4.1), added symmetric form of the alternating-helicity eight-gluon amplitude, added references. v3: Fixed typo in (4.1), added reference, added acknowledgment, minor clarifications
arxiv created 2005/02/05 · openalex publication_date 2005/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A(1+,2-,3+,4-,5+,6-,7+,8-). We show how to build any amplitude in terms of three-gluon amplitudes only.