Non-singlet structure functions beyond the next-to-next-to leading order

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We study the evolution of the flavour non-singlet deep-inelastic structure functions F2,NS and F₃ at the next-to-next-to-next-to-leading order (N³LO) of massless perturbative QCD. The present information on the corresponding three-loop coefficient functions is used to derive approximate expressions of these quantities which prove completely sufficient for values x > 10⁻² of the Bjorken variable. The inclusion of the N³LO corrections reduces the theoretical uncertainty of alphaₛ determinations from non-singlet scaling violations arising from the truncation of the perturbation series to less than 1%. We also study the predictions of the soft-gluon resummation, of renormalization-scheme optimizations by the principle of minimal sensitivity (PMS) and the effective charge (ECH) method, and of the Pade' summation for the structure-function evolution kernels. The PMS, ECH and Pade' approaches are found to facilitate a reliable estimate of the corrections beyond N³LO.