Quark and gluon form factors to four loop order in QCD: the $N_f^3$   contributions
  We calculate the four-loop massless QCD corrections with three closed quark lines to quark and gluon form factors. We apply a novel integration by parts algorithm based on modular arithmetic and compute all relevant master integrals for arbitrary values of the space-time dimension. This is the first calculation of a gluon form factor at this perturbative order in QCD. 
Andreas von Manteuffel, Robert M. Schabinger
hep-ph hep-th