Abstract
We summarize recent results on the evolution of unpolarized parton densities and deep-inelastic structure functions in massless perturbative QCD. Due to the last year's extension of the integer-moment calculations of the three-loop splitting functions, the next-to-next-to-leading order (NNLO) evolution of the parton distributions can now be performed reliably at momentum fractions x ≳ 10−4, facilitating a considerably improved theoretical accuracy of their extraction from data on deep-inelastic scattering. The NNLO corrections are not dominated, at relevant values of x, by their leading small-x terms. At large x the splitting-function series converges very rapidly; hence, employing results on the three-loop coefficient functions, the structure functions can be analysed at next-to-next-to-next-to-leading order (N3LO) for x > 10−2. The resulting values for αs do not significantly change beyond the NNLO, their renormalization scale dependence reaches about ±1% at N3LO.
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