Automatic Computation of Feynman Diagrams

Abstract

Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current status of automatic calculation of Feynman diagrams in particle physics. The most important theoretical techniques are introduced and their usefulness is demonstrated with the help of simple examples. A survey over frequently used programs and packages is provided, discussing their abilities and fields of applications. Subsequently, some powerful packages which have already been applied to important physical problems are described in more detail. The review closes with the discussion of a few typical applications for the automated computation of Feynman diagrams, addressing current physical questions like properties of the $Z$ and Higgs boson, four-loop corrections to renormalization group functions and two-loop electroweak corrections.

Latex, 62 pages. Typos corrected, references updated and some comments added. Vertical offset changed. The complete paper is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp98/ttp98-41/ or via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints/

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• The Theory of Deeply Inelastic Scattering
• Second Order QCD Corrections to $\Gamma (t\to Wb)$
• Results and Techniques of Multi-Loop Calculations
• Practical Algebraic Renormalization
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• High-precision e-expansions of massive four-loop vacuum bubbles
• Hadronic Higgs Production and Decay in Supersymmetry at Next-to-Leading Order
• FormTracer - A Mathematica Tracing Package Using FORM
• ep-Finite Basis of Master Integrals for the Integration-By-Parts Method
• Light Hybrid Mesons in QCD
• J/psi plus jet associated production in two-photon collisions at next-to-leading order
• Three-loop non-diagonal current correlators in QCD and NLO corrections to single-top-quark production
• Automatic reduction of four-loop bubbles
• The rational parts of one-loop QCD amplitudes I: The general formalism
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• J/psi plus prompt-photon associated production in two-photon collisions at next-to-leading order
• DoFun 3.0: Functional equations in Mathematica
• A simple way to generate high order vacuum graphs
• Pseudo-scalar Higgs production at next-to-leading order SUSY-QCD
• Calculation of Massless Feynman Integrals using Harmonic Sums
• Corrections of Order $\alpha {\alpha }_s$ to W Boson Decays
• Relation between bottom-quark MS-bar Yukawa coupling and pole mass
• Fast Evaluation of Feynman Diagrams
• On the two-loop contributions to the pion mass
• A note on the rare decay of a Higgs boson into photons and a $Z$ boson
• Recursive Graphical Solution of Closed Schwinger-Dyson Equations in phi^4-Theory -- Part1: Generation of Connected and One-Particle Irreducible Feynman Diagrams
• One-loop vertex integrals in heavy-particle effective theories
• Higgs Decay, Z Decay and the QCD Beta-Function
• A simple algorithm for automatic Feynman diagram generation
• Mixing Renormalization for Scalar Fields
• Applications of QCD
• Evaluating massive planar two-loop tensor vertex integrals
• Scalar and Pseudo-Scalar Higgs Production at Hadron Colliders