Differential equations and high-energy expansion of two--loop diagrams in D dimensions

Abstract

New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an application of this method, we calculate the two--loop master integral for "crossed--triangle" topology which was previously known only up to $O(\ep)$ order. The case when a topology contains several master integrals is also considered. We present an algorithm of the term-by-term calculation of the asymptotical expansion in this case and analyze in detail the "crossed--box" topology with three master integrals.

arXiv comment13 pages,8 figures, uses elsart.cls. Misprints corrected

References in corpus (11)

• Differential Equations for Two-Loop Four-Point Functions
• Differential Equations for Feynman Graph Amplitudes
• Dimensionally Regulated Pentagon Integrals
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• High-precision calculation of multi-loop Feynman integrals by difference equations
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• New results for two-loop off-shell three-point diagrams
• Asymptotics of Feynman Diagrams and The Mellin-Barnes Representation
• Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
• Vertex diagrams for the QED form factors at the 2-loop level

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