Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/Nf)

Bennett, J.F.; Gracey, J.A.

doi:10.1016/s0550-3213(98)00021-2

Cited by 36 publications

(39 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The same holds for the N 2 f terms at third order [6,8]. Assuming that this relation holds generally for P (2) gg , the results given below Eq.…”

Section: Introductionmentioning

confidence: 67%

“…For processes with initial-state hadrons, the next-to-next-to-leading order (NNLO) expressions include the three-loop splitting functions. The computation of these functions is under way [1], but will not be completed in the near future [2].Partial results have already been obtained [3][4][5][6][7][8][9], however, most notably the five lowest even-integer moments for the flavour non-singlet combination entering electromagnetic deep-inelastic scattering (DIS) [3], and four moments for the singlet splitting functions [4]. In refs.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Improved approximations for the three-loop splitting functions in QCD

2000

View full text Add to dashboard Cite

We update our approximate parametrizations of the three-loop splitting functions for the evolution of unpolarized parton densities in perturbative QCD. The new information taken into account is given by the additional Mellin moments recently calculated by Retey and Vermaseren. The inclusion of these constraints reduces the uncertainties of our approximations considerably and extends their region of applicability by about one order of magnitude to lower momentum fractions x.PACS: 12.38. Bx, 13.60.Hb In order to achieve a high accuracy of the predictions of perturbative QCD for hard processes, the calculations need to transcend the standard next-to-leading order (NLO) approximation. For processes with initial-state hadrons, the next-to-next-to-leading order (NNLO) expressions include the three-loop splitting functions. The computation of these functions is under way [1], but will not be completed in the near future [2].Partial results have already been obtained [3][4][5][6][7][8][9], however, most notably the five lowest even-integer moments for the flavour non-singlet combination entering electromagnetic deep-inelastic scattering (DIS) [3], and four moments for the singlet splitting functions [4]. In refs. [10,11] we have demonstrated that this information -due to the smoothening effect of the ubiquitous convolution with the initial parton densities and the small size of the corrections -is fully sufficient for momentum fractions x > ∼ 0.1 and leaves only small uncertainties down to x ≃ 10 −3 at scales above about 10 GeV 2 . We have provided approximate parametrizations for the three-loop splitting functions, including quantitative estimates of their residual uncertainties. These results have already been applied [12] to structure functions in DIS and Drell-Yan cross sections at hadron colliders, for which the subprocess cross sections have been computed up to NNLO [13,14].Very recently the fixed-moment calculations of refs. [3,4] have been extended, using improved computing resources, up to the twelfth moment [2]. For the first time also (odd) moments of the three-loop valence splitting functions have been obtained there. These results provide a severe check of our approximation procedure, as the latter led to rather tight predictions for the (tenth and) twelfth moments. This test is passed by the results of refs. [10,11]. In this letter we update these parametrizations by including the moments of ref.[2] in the derivation. As a result the residual uncertainties are greatly reduced, and the region of safe applicability is extended by about one order of magnitude in x, an improvement most relevant for applications to structure functions at HERA [12].Our notations for the parton densities and splitting functions are as follows: the nonsinglet combinations of quark and antiquark densities, q i andq i , are given byN f stands for the number of effectively massless flavours. The corresponding splitting functions are denoted by P ± NS and P V NS ≡ P − NS + P S NS . The latter function, P S NS , occurs for t...

show abstract

“…The same holds for the N 2 f terms at third order [6,8]. Assuming that this relation holds generally for P (2) gg , the results given below Eq.…”

Section: Introductionmentioning

confidence: 67%

mentioning

confidence: 99%

Improved approximations for the three-loop splitting functions in QCD

2000

View full text Add to dashboard Cite

show abstract

“…[8] via integer Mellin-N techniques. However, these techniques lack some flexibility, e.g., they cannot incorporate additional information on the x-dependence of the two-loop coefficient functions [6,7] and of the three-loop splitting functions [15,16,17,18,19]. Hence we pursue an alternative approach which allows for incorporating the NNLO corrections into programs using standard x-space [10,11] or equivalent complex-N techniques [12,20].…”

Section: Introductionmentioning

confidence: 99%

NNLO evolution of deep-inelastic structure functions: the non-singlet case

Neerven¹,

Vogt²

2000

Nuclear Physics B

171

201

View full text Add to dashboard Cite

We study the next-to-next-to-leading order (NNLO) evolution of flavour non-singlet quark densities and structure functions in massless perturbative QCD. Present information on the corresponding three-loop splitting functions is used to derive parametrizations of these quantities, including Bjorken-x dependent estimates of their residual uncertainties. Compact expressions are also provided for the exactly known, but rather involved twoloop coefficient functions. The size of the NNLO corrections and their effect on the stability under variations of the renormalization scale are investigated. The residual uncertainty of the three-loop splitting functions does not lead to appreciable effects for x > 10 −2 . Inclusion of the NNLO contributions reduces the main theoretical uncertainty of α s determinations from non-singlet scaling violations by more than a factor of two.

show abstract

“…Moreover a prediction made in [39] has been confirmed. The gluonic OMEs A gg,Q and A gq,Q are needed for correct flavor matching in case of the transition of a single heavy quark becoming light, cf.…”

Section: Three-loop Contributions To the Gluonic Massive Omesmentioning

confidence: 56%

Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N

Bluemlein¹

2013

Proceedings of “Loops and Legs in Quantum Field Theory ” 11th DESY Workshop on Elementary Particle Physics — PoS(LL2012)

View full text Add to dashboard Cite

Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/Nf)

Cited by 36 publications

References 40 publications

Improved approximations for the three-loop splitting functions in QCD

Improved approximations for the three-loop splitting functions in QCD

NNLO evolution of deep-inelastic structure functions: the non-singlet case

Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N

Contact Info

Product

Resources

About