Automatic Computation of Feynman Diagrams

TL;DR

<3-5 sentence high-level summary>

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.

Figures (25)

• Figure 1: Two-loop master diagram. The arrows denote the direction of momentum flow.
• Figure 2: Symbolic equation resulting from Eq. (\ref{['eqrecI']}) applied to the diagram $I(1,1,1,1,1)$. The dot indicates that the respective denominator appears twice.
• Figure 3: Three-loop topology for which the system of recurrence relations was explicitely solved. Solid lines carry a common mass $M$, dashed lines are massless.
• Figure 4: Two-loop propagator-type diagram. The momenta $k_i$ are linear combinations of the loop momenta $l,k$ and the external momentum $p$.
• Figure 5: Large-momentum procedure for the one-loop photon polarization function.