The αs3 correction to Γ(Z0 → hadrons

Larin, S.A.; Ritbergen, T. van; Vermaseren, J.A.M.

doi:10.1016/0370-2693(94)90840-0

Cited by 172 publications

(334 citation statements)

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“…An approximate result has been derived for the latter [15] from the constraints of refs. [7,8,13]. Within errors that result is consistent with D DIS 2 = 0, but, for instance, also with B 2 = −P (1) q,δ + ξ β 0 C F for ξ ≃ 8 .…”

supporting

confidence: 62%

“…The remaining ambiguity in the DIS case (discussed below eq. (22)) is illustrated by the results for D DIS 2 = 0 and for B 2 = −P (1) q,δ + 13 β 0 C F (denoted by ξ = 13 in the figures), the latter curves indicating the maximal NNLL effects consistent with the available three-loop information [7,8,13,15]. It is obvious from both figures that knowledge of the ln N(α s ln N) n and (α s ln N) n terms [1,2] alone is not sufficient for reliably determining the functions G N P and their impact after convolution even for rather moderate values of N and x (often denoted τ in the DY case).…”

mentioning

confidence: 70%

“…The exact expression for P (2) qq (x) has not been completed yet. However, recently rather accurate approximations have been derived [6] from the available partial results, most notably the lowest integer-N moments [7,8]. Together with the exact N 2 f term determined in ref.…”

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confidence: 99%

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Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell–Yan process

2001

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The soft-gluon resummation exponents G N in moment space are investigated for the quark coefficient functions in deep-inelastic structure functions and the quark-antiquark contribution to the Drell-Yan cross section dσ/dM. Employing results from two-and three-loop calculations we obtain the next-to-next-to-leading logarithmic terms α s (α s ln N) n of G N to all orders in the strong coupling constant α s . These new contributions facilitate a reliable assessment of the numerical effect and the stability of the large-N expansion.

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supporting

confidence: 62%

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confidence: 70%

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Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell–Yan process

2001

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“…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.…”

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confidence: 99%

Improved approximations for the three-loop splitting functions in QCD

2000

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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...

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“…Ref. [25]) it is possible to factorize a flavour number independent coefficient function for which we use the standard notation C ns .…”

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confidence: 99%

The αS3 approximation of quantum chromodynamics to the Ellis-Jaffe sum rule

1997

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The αs3 correction to Γ(Z0 → hadrons

Abstract: We present the α 3 s correction to the Z 0 decay rate into hadrons in the limit m top >> m Z .

Cited by 172 publications

References 32 publications

Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell–Yan process

Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell–Yan process

Improved approximations for the three-loop splitting functions in QCD

The αS3 approximation of quantum chromodynamics to the Ellis-Jaffe sum rule

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