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

The third-order QCD corrections to deep-inelastic scattering by photon exchange

“…An idealized fit to d ln F 2,ns /d ln Q 2 at Q 2 0 ≈ 40 GeV 2 , as described in more detail in Ref. [19], yields the following order-dependence of the central values: 10) where the N 4 LO kernel has been estimated by the Padé summation. Thus, even if the idealized fit underestimates the shifts by a factor of two, an α s -uncertainty of 1% or less from the truncation of the perturbation series has been reached by the calculation of the N 3 LO coefficient functions.…”

“…Thus the extraction of α s from the scaling violations of structure functions can be effectively promoted to N 3 LO accuracy, reducing the (formerly dominant) uncertainty due to the truncation of the perturbation series to less than 1%, see, e.g., Refs. [18][19][20][21][22]. The three-loop coefficient functions are also of considerable theoretical interest, for example facilitating the derivation of higher-order results for the resummation of threshold logarithms [23][24][25][26][27][28] and the quark form factor [29,30].…”

Non-singlet structure functions: Combining the leading logarithms resummation at small-x with DGLAP

“…The standard DGLAP -technology of calculating f (x, Q 2 ) corresponds to first calculating Γ n (Q 2 ) and then reconstructing f (x, Q 2 ) from the moments, choosing appropriate forms for ∆q. Presently C(ω) for the non-singlet structure functions are known with two-loop [2] and three-loop [3] accuracy. In order to make the all-order resummation of the double-logarithmic contributions to f N S (x, Q 2 ) and g N S 1 (x, Q 2 ), i.e.…”

The interplay between Sudakov resummation, renormalons and higher twist in deep inelastic scattering

“…Note that both r m (λ) andr m (λ) are free of a linear term: their expansions start at order λ 2 . These functions have two generic properties [21,22,40] associated with their origin in an integral over the running coupling: they increase factorially with m due to infrared renormalons and posses an increasing singularity at λ = 1, corresponding to Q 2 /N ≃ Λ 2 , where the perturbative treatment looses its validity. Terms with δ 2 enter first at NNLL accuracy (m = 2):…”

“…Section 3 is devoted to data analysis. Matching the DGE exponent into the known [35]- [40] next-to-next-to-leading order (NNLO) result we obtain an improved perturbative prediction for the scaling violation at large N, which we use as a baseline for the study of power corrections. The experimental moments N = 4 -11 of F 2 for the proton are calculated based on SLAC and BCDMS data.…”