Evaluation of Multi-Sums for Large Scale Problems

Abstract

A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products. In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion. The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme.

9 pages Latex, Contr. Proc. RADCOR 2011

References in corpus (6)

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Cited by in corpus (11)

• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• Iterated Binomial Sums and their Associated Iterated Integrals
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• Advanced Computer Algebra Algorithms for the Expansion of Feynman Integrals
• Recent Symbolic Summation Methods to Solve Coupled Systems of Differential and Difference Equations
• Higher Order Heavy Quark Corrections to Deep-Inelastic Scattering
• 3-Loop Heavy Flavor Corrections in Deep-Inelastic Scattering with Two Heavy Quark Lines
• Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
• 3-loop Massive $O(T_F^2)$ Contributions to the DIS Operator Matrix Element $A_{gg}$
• Recent progress on the calculation of three-loop heavy flavor Wilson coefficients in deep-inelastic scattering
• 3-loop heavy flavor Wilson coefficients in deep-inelastic scattering