2006/04/30 by Carola F. Berger, Zvi Bern, Lance J. Dixon +3 · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.74.036009
published as Phys.Rev.D74:036009,2006 · 77 pages, 17 figures; v2, corrected minor typos in text and small equations
arxiv created 2006/08/31 · openalex publication_date 2006/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The recently developed on-shell bootstrap for computing one-loop amplitudes in nonsupersymmetric theories such as QCD combines the unitarity method with loop-level on-shell recursion. For generic helicity configurations, the recursion relations may involve undetermined contributions from nonstandard complex singularities or from large values of the shift parameter. Here we develop a strategy for sidestepping difficulties through the use of pairs of recursion relations. To illustrate the strategy, we present sets of recursion relations needed for obtaining n-gluon amplitudes in QCD. We give a recursive solution for the one-loop n-gluon QCD amplitudes with three or four color-adjacent gluons of negative helicity and the remaining ones of positive helicity. We provide an explicit analytic formula for the QCD amplitude A6;1(1^\ensuremath-,2^\ensuremath-,3^\ensuremath-,4+,5+,6+), as well as numerical results for A7;1(1^\ensuremath-,2^\ensuremath-,3^\ensuremath-,4+,5+,6+,7+), A8;1(1^\ensuremath-,2^\ensuremath-,3^\ensuremath-,4+,5+,6+,7+,8+), and A8;1(1^\ensuremath-,2^\ensuremath-,3^\ensuremath-,4^\ensuremath-,5+,6+,7+,8+). We expect the on-shell bootstrap approach to have widespread applications to phenomenological studies at colliders.