Symbolic Summation and Higher Orders in Perturbation Theory

Abstract

Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms. Examples such as the non-planar vertex at two loops, or integrals from the recent calculation of the three-loop QCD corrections to structure functions in deep-inelastic scattering are given.

5 pages, 2 figures, latex

References in corpus (6)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• The Quark Form Factor at Higher Orders
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• Expansion around half-integer values, binomial sums and inverse binomial sums
• Master integrals for massive two-loop Bhabha scattering in QED

Cited by in corpus (3)

• QCD Corrections to Semi-Inclusive Hadron Production in Electron-Positron Annihilation at Two Loops
• Master Integrals for Massless Three-Loop Form Factors: One-Loop and Two-Loop Insertions
• On a two-loop crossed six-line master integral with two massive lines