AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

Abstract

The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4-2eps dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. AMBRE uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version of AMBRE works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in eps. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops.

26 pages, 10 figures, 1 table, in v2 typos in Eqn. 48 and Eqn. 57 corrected; the corresponding sample files are unchanged

Cited by in corpus (14)

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• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• The QCD form factor of heavy quarks at NNLO
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Analytic integration of real-virtual counterterms in NNLO jet cross sections II
• A complete reduction of one-loop tensor 5- and 6-point integrals
• Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering
• On the tensor reduction of one-loop pentagons and hexagons
• $\mathcal{O}(\alpha {\alpha }_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold
• Hypergeometric functions with rational arguments
• Threshold corrections to the gamma t anti-t vertex at O(alpha alpha(s))