Hypergeometric Feynman Integrals

Klausen, René Pascal

doi:10.48550/arxiv.2302.13184

Cited by 1 publication

(1 citation statement)

References 226 publications

(562 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example Regge, in ref. [16], argues, on the basis of homology arguments, that all Feynman integrals must belong to a suitably generalised class of hypergeometric functions, an insight that was sharpened much more recently with the introduction of the Lee-Pomeransky representation [20] of Feynman integrals and the application of the GKZ theory of hypergeometric functions [21][22][23][24][25][26][27][28]. Regge further argues that such functions obey sets of (possibly) high-order differential equations, which he describes as 'a slight generalisation of the well-known Picard-Fuchs equations', also a recurrent theme [29].…”

Section: Jhep03(2024)096mentioning

confidence: 99%

Integration-by-parts identities and differential equations for parametrised Feynman integrals

Artico,

Magnea

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a different viewpoint on these important tools by working in Feynman-parameter space, and using its projective geometry. Our work is based upon little-known results pre-dating the modern era of loop calculations [16–19, 30, 31]: we adapt and generalise these results, deriving a very general expression for sets of IBP identities in parameter space, associated with a generic Feynman diagram, and valid to any loop order, relying on the characterisation of Feynman-parameter integrands as projective forms. We validate our method by deriving and solving systems of differential equations for several simple diagrams at one and two loops, providing a unified perspective on a number of existing results.

show abstract