The polarized three-loop anomalous dimensions from on-shell massive operator matrix elements

We calculate all contributions ∝TFto the polarized three–loop anomalous dimensions in the M–scheme using massive operator matrix elements and compare to results in the literature. This includes the com-plete anomalous dimensions γ(2),PSqqand γ(2)qg. We also obtain the complete two–loop polarized anomalous dimensions in an independent calculation. While for most of the anomalous dimensions the usual direct computation methods in Mellin N–space can be applied since all recurrences factorize at first order, this is not the case for γ(2)qg. Due to the necessity of deeper expansions of the master integrals in the dimensional parameter ε=D−4, we had to use the method of arbitrary high moments to eliminate elliptic contributions in intermediate steps. 4000 moments were generated to determine this anomalous dimension and 2640 mo-ments turned out to be sufficient. As an aside, we also recalculate the contributions ∝TFto the three–loop QCD β–function.