Non-Singlet Structure Functions at Three Loops: Fermionic Contributions

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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 MSbar scheme.