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arXiv · 1711.09742

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

J. Ablinger·A. Behring·J. Blümlein·A. De Freitas·E. Imamoglu·M. van Hoeij A. von Manteuffel·C. G. Raab·C. -S. Radu·C. Schneider
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Abstract

Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples are the anomalous dimensions to 3-loop order, the massless Wilson coefficients and also different massive operator matrix elements. Starting at 3-loop order, however, also other letters appear in the case of massive operator matrix elements, the so called iterative non-iterative integrals, which are related to solutions based on complete elliptic integrals or any other special function with an integral representation that is definite but not a Volterra-type integral. After outlining the formalism leading to iterative non-iterative integrals,we present examples for both of these cases with the 3-loop anomalous dimension $γ_{qg}^{(2)}$ and the structure of the principle solution in the iterative non-interative case of the 3-loop QCD corrections to the $ρ$-parameter.

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J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij A. von Manteuffel, C. G. Raab, C. -S. Radu, C. Schneider. 2017-11-27. Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations. https://arxiv.org/abs/1711.09742

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