Non-singlet structure functions at three loops: Fermionic contributions Original Research Article

We compute the fermionic (nf) contributions to the flavour non-singlet structure functions in unpolarized electromagnetic deep-inelastic scattering at third order of massless perturbative QCD. Complete results are presented for the corresponding nf-parts of the three-loop anomalous dimension and the three-loop coefficient functions for the structure functions F2 and FL. Our results agree with all partial and approximate results available in the literature. The present calculation also facilitates a complete determination of the threshold-resummation parameters B2 and D2DIS of which only the sum was known so far, thus completing the information required for the next-to-next-to-leading logarithmic resummation. We find that D2DIS vanishes in the MS scheme.