The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction

2011/10/02 by Yost, S. A., Bytev, V. V., Kalmykov, M. Yu. +2
#33B06 #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1110.0210

Abstract

Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The hypergeometric representation supplies an analytic framework that is useful for deriving such stable representations. We discuss the reduction of Feynman diagrams to master integrals, and compare integration-by-parts methods to differential reduction of hypergeometric functions. We describe the problem of constructing higher-order terms in the epsilon expansion, and characterize the functions generated in such expansions.

Related

• Hypergeometric functions, their epsilon expansions and Feynman diagrams
• Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions
• Hypergeometric Functions and Feynman Diagrams
• Geometrical approach to loop calculations and the epsilon-expansion of Feynman diagrams
• Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation