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Imamoglu, Erdal ; Kaltofen, Erich L. ( , Journal of Symbolic Computation)
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Imamoglu, Erdal ; Kaltofen, Erich L. ; Yang, Zhengfeng ( , Proc. 2018 ACM International Symposium on Symbolic and Algebraic Computation)
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Ablinger, Jakob ; Behring, Arnd ; Bluemlein, Johannes ; De Freitas, Abilio ; Imamoglu, Erdal ; van Hoeij, Mark ; von Manteuffel, Andreas ; Radu, Cristian-Silviu ; Schneider, Carsten ( , Proceedings of RADCOR 2017)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 $\gamma^{(2)}_{qg}$ and the structure of the principle solution in the iterative non-interative case of the 3-loop QCD corrections to the $\rho$-parameter.more » « less