Complete $$ {N}_f^2 $$ contributions to four-loop pure-singlet splitting functions
Thomas Gehrmann (Physik-Institut, Universität Zürich, Winterthurerstrasse 190, Zürich, 8057, Switzerland); Andreas Manteuffel (Institut für Theoretische Physik, Universität Regensburg, Regensburg, 93040, Germany, Physik-Institut, Universität Zürich, Winterthurerstrasse 190, Zürich, 8057, Switzerland); Vasily Sotnikov (Physik-Institut, Universität Zürich, Winterthurerstrasse 190, Zürich, 8057, Switzerland); Tong-Zhi Yang (Department of Physics and Astronomy, Michigan State University, East Lansing, MI, 48824, USA, Physik-Institut, Universität Zürich, Winterthurerstrasse 190, Zürich, 8057, Switzerland)
The scale evolution of parton distributions is determined by universal splitting functions. As a milestone towards the computation of these functions to four-loop order in QCD, we compute all contributions to the pure-singlet quark-quark splitting functions that involve two closed fermion loops. The splitting functions are extracted from the pole terms of off-shell operator matrix elements, and the workflow for their calculation is outlined. We reproduce known results for the non-singlet four-loop splitting functions and validate our new pure-singlet results against fixed Mellin moments.
