Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation

Abstract

We describe the application of differential reduction algorithms for Feynman Diagram calculation. We illustrate the procedure in the context of generalized hypergeometric functions, and give an example for a type of q-loop bubble diagram.

6 pages, LaTeX, one eps figure, conference style file included. Related to a talk given by S.A. Yost at LCWS08/ILC08, Chicago, Nov. 16-20, 2008. [v1=v2]

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• On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory
• Hypergeometric functions, their epsilon expansions and Feynman diagrams
• Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions
• Feynman Diagrams, Differential Reduction, and Hypergeometric Functions
• Representation of solutions of the Gauss hypergeometric equation by the multiple polylogarithms, functional relations of the multiple polylogarithms and relations of the multiple zeta values

Cited by in corpus (17)

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• Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions
• Evaluation of the general 3-loop vacuum Feynman integral
• Differential reduction of generalized hypergeometric functions from Feynman diagrams: One-variable case
• Simultaneous decoupling of bottom and charm quarks
• Effective potential at three loops
• Three-loop on-shell Feynman integrals with two masses
• Counting the number of master integrals for sunrise-type Feynman diagrams via Mellin-Barnes representation
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• Counting master integrals: integration by parts vs. differential reduction
• HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables
• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction
• Feynman Diagrams, Differential Reduction, and Hypergeometric Functions
• Renormalized $\epsilon$-finite master integrals and their virtues: the three-loop self energy case
• Counting master integrals: Integration by parts vs. functional equations
• Chinese Magic in Loop Integrals