On the numerical evaluation of one-loop amplitudes: the gluonic case

2008/05/31 by W. T. Giele, W.T Giele, G. Zanderighi +1 · 4 citations
Physics and Astronomy · #Amplitude #Dimension (graph theory) #Feynman diagram #Gluon #Helicity #High-Energy Particle Collisions Research #Integer (computer science) #Particle physics theoretical and experimental studies #Phase space #Quantum Chromodynamics and Particle Interactions #Tree (set theory) #hep-ph

paper · pdf · doi:10.1088/1126-6708/2008/06/038

published as JHEP 0806:038,2008 · 22 pages, 9 figures; v2: references added, version accepted for publication

openalex publication_date 2008/06/13 · arxiv created 2008/06/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules, tree amplitudes are constructed using recursive relations. The tree amplitudes are then used to build one-loop amplitudes using an integer dimension on-shell cut method. As a first application we considered only three and four gluon vertices calculating the pure gluonic one-loop amplitudes for arbitrary external helicity or polarization states. We compare our numerical results to analytical results in the literature, analyze the time behavior of the algorithm and the accuracy of the results, and give explicit results for fixed phase space points for up to twenty external gluons.

Citations

• CompHEP 4.4—automatic computations from Lagrangians to events
• Bootstrapping one-loop QCD amplitudes with general helicities
• One-loop self-dual and N = 4 super Yang-Mills
• Direct extraction of one-loop integral coefficients
• Computing one-loop amplitudes from the holomorphic anomaly of unitarity cuts
• New recursion relations for tree amplitudes of gluons
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Seminumerical evaluation of one-loop corrections
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Unitarity cuts with massive propagators and algebraic expressions for coefficients
• Regularization and renormalization of gauge fields
• ALPGEN, a generator for hard multiparton processes in hadronic collisions

Cited by

• Automated one-loop calculations: a proof of concept
• Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level
• Color-kinematics duality for QCD amplitudes
• Tensorial reconstruction at the integrand level