Non-planar elliptic vertex

Abstract

We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct integration of parametric representations in terms of iterated integrals. Taking non-planar elliptic vertex as an example we show that in addition to two mentioned methods one can use analytical solution of differential equations in terms of power series. Moreover, in the last case it is possible to obtain the exact in $\epsilon$ results expressible either in terms of generalized hypergeometric or Kampé de Fériet functions

29 pages, 4 figures, representations of the obtained results in the form of hypergeometry were added

References in corpus (20)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Sector Decomposition
• Resolution of singularities for multi-loop integrals
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• The massless higher-loop two-point function
• The kite integral to all orders in terms of elliptic polylogarithms
• Libra: a package for transformation of differential systems for multiloop integrals
• Elliptic polylogarithms and Feynman parameter integrals
• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
• Towards multiple elliptic polylogarithms
• Two-loop $gg\to Hg$ amplitude mediated by a nearly massless quark
• Hypergeometric representation of the two-loop equal mass sunrise diagram
• Modular transformations of elliptic Feynman integrals
• Blowing up Feynman integrals
• Massive kite diagrams with elliptics
• Integral representation for three-loop banana graph

Cited by in corpus (3)

• On series and integral representations of some NRQCD master integrals
• Expansion of hypergeometric functions in terms of polylogarithms with nontrivial variable change
• Sunrise integral in non-relativistic QCD with elliptics