Iterative and iterative-noniterative integral solutions in 3-loop massive QCD calculations
13th International Symposium on Radiative Corrections, RADCOR 2017, St. Gilgen, Avusturya, 25 - 29 Eylül 2017, cilt.290, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 290
- Basıldığı Şehir: St. Gilgen
- Basıldığı Ülke: Avusturya
- Kırklareli Üniversitesi Adresli: Hayır
Özet
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 γqg (2) and the structure of the principle solution in the iterative non-interative case of the 3-loop QCD corrections to the ρ-parameter.