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

Understand

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