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 (3)

• Two-Loop Massive Operator Matrix Elements and Unpolarized Heavy Flavor Production at Asymptotic Values Q^2 >> m^2
• 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 (5)

• A Refined Difference Field Theory for Symbolic Summation
• Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(ε)
• 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