Difference Equations in Massive Higher Order Calculations

Abstract

The calculation of massive 2--loop operator matrix elements, required for the higher order Wilson coefficients for heavy flavor production in deeply inelastic scattering, leads to new types of multiple infinite sums over harmonic sums and related functions, which depend on the Mellin parameter $N$. We report on the solution of these sums through higher order difference equations using the summation package {\tt Sigma}.

15 pages latex, Proceedings ACAT 2007

References in corpus (12)

• New features of FORM
• The third-order QCD corrections to deep-inelastic scattering by photon exchange
• Harmonic Sums and Mellin Transforms up to two-loop Order
• Heavy quark coefficient functions at asymptotic values $Q^2\gg m^2$
• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• Analytic Continuation of Mellin Transforms up to two-loop Order
• The massless two-loop two-point function
• Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions
• Mellin Moments of the Next-to-next-to Leading Order Coefficient Functions for the Drell-Yan Process and Hadronic Higgs-Boson Production
• $O({\alpha }_s^2)$ Timelike Wilson Coefficients for Parton-Fragmentation Functions in Mellin Space
• Calculation of Massive 2-Loop Operator Matrix Elements with Outer Gluon Lines
• Structural Relations between Harmonic Sums up to w=6

Cited by in corpus (7)

• A Refined Difference Field Theory for Symbolic Summation
• Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(ε)
• Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction
• A Symbolic Summation Approach to Feynman Integral Calculus
• A Symbolic Summation Approach to Find Optimal Nested Sum Representations
• Heavy Flavour Production in Deep--Inelastic Scattering - Two--Loop Massive Operator Matrix Elements and Beyond
• Feynman integrals and difference equations