Deep-inelastic structure functions: Reconstruction from Mellin moments

We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in perturbative QCD. Our results agree with all partial results available in the literature. We find that the correct leading logarithmic (LL) predictions for small momentum fractions x do not provide a good estimate of the respective complete results. A new, unpredicted LL contribution is found for the colour factor d abc d abc entering at three loops for the first time. We investigate the size of the corrections and the stability of the NNLO evolution under variation of the renormalization scale. Except for very small x the corrections are found to be rather small even for large values of the strong coupling constant, in principle facilitating a perturbative evolution into the sub-GeV regime.

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“…Details have been discussed in Refs. [45,65]. The renormalization is carried out in the MS-scheme [66,67] as described in Ref.…”

Section: Notations and Methodsmentioning

confidence: 99%

The three-loop splitting functions in QCD: the non-singlet case

Vogt¹,

Moch²,

Vermaseren³

2004

Nuclear Physics B

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1,232

1,280

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“…Besides the x −1 contributions, the non-x −1 terms do not seem to be sufficiently suppressed either, at least for a steep gluon distribution. Due to the present large uncertainties [13] on the x −1 terms, however, definite conclusions especially for a flat gluon distribution require the computation [9] of the exact x-dependence of P (2) ij . On the other hand, such conclusions can The convolutions of the leading (and, for P (2) , subleading) small-x terms of (a, b) the NNLO splitting functions P (2) gg and P (2) qg and (c) the NNLO coefficient function c (2) 2,g with two typical 'steep' (upper row) and 'flat' (lower row) gluon distributions, compared with the respective (for P (2) approximate) full results.…”

Section: Singlet Parton Densities and Structure Functions At Nnlomentioning

confidence: 99%

“…The three-loop splitting functions entering the NNLO evolution of the parton distributions have not been completed so far either [9]. However, previous partial results [10,11] have been substantially extended by the calculation of two more Mellin moments [12].…”

Section: Introductionmentioning

confidence: 99%

Parton densities and structure functions at next-to-next-to-leading order and beyond

Neerven

Vogt

2002

J. Phys. G: Nucl. Part. Phys.

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Abstract. We summarize recent results on the evolution of unpolarized parton densities and deep-inelastic structure functions in massless perturbative QCD. Due to last year's extension of the integer-moment calculations of the three-loop splitting functions, the 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 N 3 LO for x >10 −2 . The resulting values for α s do not significantly change beyond NNLO, their renormalization scale dependence reaches about ±1% at N 3 LO.

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