Expansions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math>hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

Abbas, Gauhar; Ananthanarayan, B.; Caprini, I.; Fischer, Ján

doi:10.1103/physrevd.88.034026

Cited by 40 publications

(43 citation statements)

References 60 publications

(402 reference statements)

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“…2 In this framework, the Borel transform of the moments can be calculated exactly in terms of the Borel transform of the Adler function -which is one of the main results of this paper, Eq. (41). The parallel with the large-β 0 limit is apparent and the results are formally identical.…”

Section: Introductionmentioning

confidence: 59%

“…Using the C scheme and a modified Borel transform we have been able to show, in Eq. (41), that the relation between Borel transformed moments and the Borel transformed Adler function is the same in QCD and in large-β 0 . In Eq.…”

Section: Discussionmentioning

confidence: 87%

“…Finally, moments with bad perturbative behaviour do not improve in any significant way when we apply the optimization described here. A more stable perturbative expansion for these moments can be achieved with the method of conformal mappings, making use of the information about the location of the renormalon singularities [40][41][42][43]. Even with this technique, in some cases, the series approaches the true value only at high orders.…”

Section: Optimal Truncation With Scheme Variationsmentioning

confidence: 99%

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Renormalons in integrated spectral function moments and αs extractions

Boito

Oliani

2020

Phys. Rev. D

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Precise extractions of α s from τ → (hadrons) + ν τ and from e + e − → (hadrons) below the charm threshold rely on finite energy sum rules (FESR) where the experimental side is given by integrated spectral function moments. Here we study the renormalons that appear in the Borel transform of polynomial moments in the large-β 0 limit and in full QCD. In large-β 0 , we establish a direct connection between the renormalons and the perturbative behaviour of moments often employed in the literature. The leading IR singularity is particularly prominent and is behind the fate of moments whose perturbative series are unstable, while those with good perturbative behaviour benefit from partial cancellations of renormalon singularities. The conclusions can be extended to QCD through a convenient scheme transformation to the C-scheme together with the use of a modified Borel transform which make the results particularly simple; the leading IR singularity becomes a simple pole, as in large-β 0 . Finally, for the moments that display good perturbative behaviour, we discuss an optimized truncation based on renormalisation scheme (or scale) variation. Our results allow for a deeper understanding of the perturbative behaviour of integrated spectral function moments and provide theoretical support for low-Q 2 α s determinations.

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Section: Introductionmentioning

confidence: 59%

Section: Discussionmentioning

confidence: 87%

Section: Optimal Truncation With Scheme Variationsmentioning

confidence: 99%

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Renormalons in integrated spectral function moments and αs extractions

Boito

Oliani

2020

Phys. Rev. D

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“…For the use of hadronic τ decays for the determination of the strong coupling α s , see Refs. [9,10,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Functional-analysis based tool for testing quark-hadron duality

2014

Self Cite

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Quark-hadron duality is a key concept in QCD, allowing for the description of physical hadronic observables in terms of quark-gluon degrees of freedom. The modern theoretical framework for its implementation is Wilson's operator product expansion (OPE), supplemented by analytic extrapolation from large Euclidean momenta, where the OPE is defined, to the Minkowski axis, where observable quantities are defined. Recently, the importance of additional terms in the expansion of QCD correlators near the Minkowski axis, responsible for quark-hadron duality violations (DVs), was emphasized. In this paper we introduce a mathematical tool that might be useful for the study of DVs in QCD. It is based on finding the minimal distance, measured in the $L^\infty$ norm along a contour in the complex momentum plane, between a class of admissible functions containing the physical amplitude and the asymptotic expansion predicted by the OPE. This minimal distance is given by the norm of a Hankel matrix that can be calculated exactly, using as input the experimental spectral function on a finite interval of the timelike axis. We also comment on the relation between the new functional tool and the more commonly used $\chi^2$-based analysis. The approach is illustrated on a toy model for the QCD polarization function recently proposed in the literature.Comment: 10 pages, 7 figure

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“…It has been previously used to extract the strong coupling constant α s from τ -decay in Refs. [28][29][30][31] and in Ref. [32] it was applied to reduce renormalization scale dependence due to higher order QCD corrections in Higgs boson production.…”

Section: Introductionmentioning

confidence: 99%

Optimal renormalization and the extraction of the strange quark mass from moments of the τ -decay spectral function

Ananthanarayan

Das

2016

Phys. Rev. D

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We introduce an optimal renormalization group analysis pertinent to the analysis of polarization functions associated with the s-quark mass relevant in τ -decay. The technique is based on the renormalization group invariance constraints which lead to closed form summation of all the leading and next-to-leading logarithms at each order in perturbation theory. The new perturbation series exhibits reduced sensitivity to the renormalization scale and improved behavior in the complex plane along the integration contour. Using improved experimental and theory inputs, we have extracted the value of the strange quark mass ms(2GeV) = 106.70 ± 9.36 MeV and ms(2GeV) = 74.47 ± 7.77 MeV from presently available ALEPH and OPAL data respectively. These determinations are in agreement with the determinations in other phenomenological methods and from the lattice.

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Expansions ofτhadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

Cited by 40 publications

References 60 publications

Renormalons in integrated spectral function moments and αs extractions

Renormalons in integrated spectral function moments and αs extractions

Functional-analysis based tool for testing quark-hadron duality

Optimal renormalization and the extraction of the strange quark mass from moments of the τ -decay spectral function

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