Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements

Jakob Ablinger; Johannes Blümlein; Alexander Hasselhuhn; Sebastian Klein; Carsten Schneider; Fabian Wißbrock

Paper

Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements

Abstract

3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable

using Appell-function representations and applying modern summation technologies provided by the package {\sf Sigma} and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with

emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of

. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region