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

We calculate the unpolarized and polarized three–loop anomalous dimensions and splitting functions $P_{\mathrm{N}\mathrm{S}}^{+},P_{\mathrm{N}\mathrm{S}}^{-}$ and $P_{\mathrm{N}\mathrm{S}}^{\mathrm{s}}$ in QCD in the $\overline{\mathsf{M}\mathsf{S}}$ scheme by using the traditional method of space–like off shell massless operator matrix elements. This is a gauge–dependent framework. For the first time we also calculate the three–loop anomalous dimensions $P_{\mathrm{N}\mathrm{S}}^{\pm \mathrm{t}\mathrm{r}}$ for transversity directly. We compare our results to the literature.