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Future high luminosity polarized deep--inelastic scattering experiments willimprove both the knowledge of the spin sub--structure of the nucleons andcontribute further to the precision determination of the strong couplingconstant, as well as, reveal currently yet unknown higher twist contributionsin the polarized sector. For all these tasks to be performed, it is necessaryto know the QCD leading twist scaling violations of the measured structurefunctions. Here an important ingredient consists in the polarized singletanomalous dimensions and splitting functions in QCD. We recalculate thesequantities to three--loop order in the M--scheme by using the traditionalmethod of space--like off--shell massless operator matrix elements, being agauge--dependent framework. Here one obtains the anomalous dimensions withoutreferring to gravitational currents, needed when calculating them using theforward Compton amplitude. We also calculate the non--singlet splittingfunction $\Delta P_{\rm qq}^{(2), \rm s, NS}$ and compare the final results tothe literature, also including predictions for the region of small values ofBjorken $x$.

The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements