Nonanalyticity of the perturbation series for a physical quantity

Barclay, D.T.; Maxwell, C.J.

doi:10.1103/physrevd.45.1760

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…The large-order behaviour of the QCD perturbation expansion remains an open question. BARCLAY and MAXWELL [19] direct their attention at the remarkable agreement of the estimate ry'= -12.0 (see (3.4)) with the explicitly calculated value r7 = -12.8, as obtained…”

Section: Comments On Large-order Estimatessupporting

confidence: 55%

“…Recently two independent attempts, [19] and [20], have been made to obtain some information about the large-order behaviour of the perturbation expansion coefficients of certain physical quantities. Both of them arrive at the conclusion that QCD perturbation series are factorially divergent.…”

Section: (33)mentioning

confidence: 99%

“…Both of them arrive at the conclusion that QCD perturbation series are factorially divergent. Whereas the former approach [19] considers the special problem of particle fractions in the e+ e -annihilation, the procedure presented in [20] does explicitly use the information following from the general analytic properties of the corresponding Green functions and from the renormalization group equation. It is claimed in ref.…”

Section: (33)mentioning

confidence: 99%

“…For instance, rY(1; MS) = 16.3, but formula (3.4), beingnormalization scheme independent, yields the same value for the MS scheme as for the MS scheme. West's derivation was examined by several authors (see, for example, [16], [19] and [23]). We shall occasionally mention some points of these analyses, following basically the reasoning presented in ref.…”

Section: (33)mentioning

confidence: 99%

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Large-Order Estimates in Perturbative QCD and Non-Borel Summable Series

Fischer

1994

Fortschr. Phys.

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Basic facts about the summation of divergent power series are reviewed, both for series with non vanishing and for series with vanishing convergence radius. Particular attention is paid to the recent development that makes it possible, in the former case, to define summation in the whole Mittag-Lemer star and, in the latter case, to define summation when the point of expansion lies at the tip of a horn-shaped analyticity domain with zero opening angle. Relevance of these results to perturbative QCD is stressed in relation to current discussions concerning large-order estimates of perturbative QCD expansion coefficients. 665 667 668 668 669 670 612 674 614 676 678 679 679 68 1 682 684 685 685 686 681It is widely believed that perturbation series in quantum theory are mostly divergent. But the problem is not whether a power series is convergent or divergent, but rather whether

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Section: Comments On Large-order Estimatessupporting

confidence: 55%

Section: (33)mentioning

confidence: 99%

Section: (33)mentioning

confidence: 99%

Section: (33)mentioning

confidence: 99%

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Large-Order Estimates in Perturbative QCD and Non-Borel Summable Series

Fischer

1994

Fortschr. Phys.

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“…In fact the question of the possible divergence of QCD (as well as other field theories) perturbation expansions, which goes back to the original argument of Dyson [5], still defies definite and clear answer. The original conjecture that the divergence of perturbation expansions is directly related to the discontinuities of Green's functions in unphysical domains of the coupling constant [6] has been seriously questioned by several authors [7,8,9]. The knowledge of the discontinuity itself is simply insufficient for the determination of large order behaviour of perturbation theory coefficients and one needs much more detailed information on the behaviour of Green's functions in the vicinity of the corresponding cut in order to establish this relation.…”

Section: Introductionmentioning

confidence: 99%

On an asymptotic estimate of then-loop correction in perturbative QCD

1993

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A recently proposed method of estimating the asymptotic behavior of QCD perturbation theory coefficients is critically reviewed and shown to contain numerous invalid mathematical operations and unsubstantiated assumptions. We discuss in detail why this procedure, based solely on renormalization group considerations and analyticity constraints, cannot lead to such estimates. We stress the importance of the correct renormalization scheme dependence of any meaningful asymptotic estimate and argue that the unambiguous summation of QCD perturbation expansions for physical quantities requires information from outside of perturbation theory itself.

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Renormalization scheme-invariant large-order perturbation theory and infrared renormalons in QCD

Beneke

1993

Physics Letters B

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Nonanalyticity of the perturbation series for a physical quantity

Cited by 6 publications

References 22 publications

Large-Order Estimates in Perturbative QCD and Non-Borel Summable Series

Large-Order Estimates in Perturbative QCD and Non-Borel Summable Series

On an asymptotic estimate of then-loop correction in perturbative QCD

Renormalization scheme-invariant large-order perturbation theory and infrared renormalons in QCD

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