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

Abstract

We calculate the unpolarized and polarized three--loop anomalous dimensions and splitting functions $P_{\mathrm{NS}}^{+},P_{\mathrm{NS}}^{-}$ and $P_{\mathrm{NS}}^{\mathrm{s}}$ in QCD in the $\overline{\mathsf{MS}}$ 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 $P_{\mathrm{NS}}^{\pm \mathrm{tr}}$ for transversity directly. We compare our results to the literature.

Comments: 40 pages Latex