English

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

High Energy Physics - Phenomenology 2015-06-05 v2 High Energy Physics - Theory Mathematical Physics math.MP

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 NN 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 ξ{1,1/2,2}\xi \in \{1,1/2,2\} 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 NN. These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q2m2Q^2 \gg m^2.

Keywords

Cite

@article{arxiv.1206.2252,
  title  = {Massive 3-loop Ladder Diagrams for Quarkonic Local Operator Matrix Elements},
  author = {Jakob Ablinger and Johannes Blümlein and Alexander Hasselhuhn and Sebastian Klein and Carsten Schneider and Fabian Wißbrock},
  journal= {arXiv preprint arXiv:1206.2252},
  year   = {2015}
}

Comments

32 pages, 1 style file, 17 figures

R2 v1 2026-06-21T21:17:26.838Z