Some recent results on evaluating Feynman integrals

Abstract

Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner bases to solve integration by parts relations in an automatic way is described.

5 pages, LaTeX, Conference Proceedings Radcor 2005

References in corpus (25)

• Harmonic Polylogarithms
• Asymptotic expansion of Feynman integrals near threshold
• Differential Equations for Two-Loop Four-Point Functions
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Differential Equations for Feynman Graph Amplitudes
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• Automatic Integral Reduction for Higher Order Perturbative Calculations
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Explicit solutions of the 3--loop vacuum integral recurrence relations
• Problems of the Strategy of Regions
• Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
• The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• The on-shell massless planar double box diagram with an irreducible numerator
• Analytical Evaluation of Dimensionally Regularized Massive On-Shell Double Boxes
• Using differential equations to compute two-loop box integrals
• Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off Shell
• Solving Recurrence Relations for Multi-Loop Feynman Integrals
• The Leading Power Regge Asymptotic Behaviour of Dimensionally Regularized Massless On-Shell Planar Triple Box
• Groebner Bases in Perturbative Calculations
• Evaluating multiloop Feynman integrals by Mellin-Barnes representation
• Progress towards 2 to 2 scattering at two-loops

Cited by in corpus (5)

• Feynman Diagrams and Differential Equations
• Next-to-leading order electroweak corrections to $gg\to HH$ and $gg\to gH$ in the large-$m_t$ limit
• On the reduction of Feynman integrals to master integrals
• Evaluating the three-loop static quark potential
• A new method for finding more symmetry relations of Feynman integrals