Differential Reduction Techniques for the Evaluation of Feynman Diagrams

TL;DR

This paper discusses differential reduction techniques that relate hypergeometric functions to evaluate complex Feynman diagrams, proposing a connection between master integrals and derivatives in the reduction process.

Contribution

It introduces a new proposition linking the number of master integrals to the derivatives used in differential reduction of hypergeometric functions.

Findings

Establishes a relation between master integrals and derivatives in reduction

Enhances methods for evaluating high-order Feynman diagrams

Facilitates more efficient calculations in QCD and electroweak corrections

Abstract

Stable reduction methods will be important in the evaluation of high-order perturbative diagrams appearing in QCD and mixed QCD-electroweak radiative corrections at the LHC. Differential reduction techniques are useful for relating hypergeometric functions with shifted values of the parameters. We present a proposition relating the number of master integrals in the expansion of a Feynman diagram to the number of derivatives in a differential reduction.