Dispersive Approach to QCD

Нестеренко, А. В.

doi:10.1016/b978-0-12-803439-2.00004-1

Cited by 3 publications

(10 citation statements)

References 82 publications

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“…(11) hereinafter, which makes Eq. (10) identical to that of both the foregoing DPT [31][32][33][34] and the so-called analytic perturbation theory 2 (APT) [54][55][56][57]. It has to be noted that, in general, the perturbative spectral function at small values of its argument may be altered by the terms of an intrinsically nonperturbative nature.…”

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

“…In particular, the DPT enables one to overcome some intrinsic difficulties of the QCD perturbation theory and to extend its applicability range towards the infrared domain; see Ref. [31] and the references therein for the details.…”

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

“…[115][116][117], this prescription yields a misleading result, which differs from the proper one (10) even in the deep ultraviolet asymptotic, see also Refs. [42,118,119] as well as [31] and the references therein.…”

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

“…In turn, the relations (2)-(7) impose a number of strict physical inherently nonperturbative constraints on the functions Π(q 2 ), R(s), and D(Q 2 ), which should definitely be taken into account when one intends to go beyond the limits of applicability of the QCD perturbation theory. It is worthwhile to note that these nonperturbative restrictions have been merged with the corresponding perturbative input in the framework of dispersively improved perturbation theory (DPT) [31][32][33][34] (its preliminary formulation was discussed in Refs. [35][36][37][38]).…”

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

“…For this purpose the effects due to the masses of the involved particles can be safely neglected (a discussion of the impact of such effects 1 on the low-energy behavior of the functions Π(q 2 ), R(s), and D(Q 2 ) can be found in, e.g., Refs. [31][32][33][34][45][46][47][48][49][50][51][52][53]). Additionally, for the schemedependent perturbative coefficients β j and d j the MS-scheme will be assumed and for the uncalculated yet five-loop coefficient d 5 its numerical estimation [42] will be employed.…”

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

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Electron–positron annihilation into hadrons at the higher-loop levels

Нестеренко

2017

Eur. Phys. J. C

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The strong corrections to the R-ratio of electronpositron annihilation into hadrons are studied at the higherloop levels. Specifically, the derivation of a general form of the commonly employed approximate expression for the Rratio (which constitutes its truncated re-expansion at high energies) is delineated, the appearance of the pertinent π 2 -terms is expounded, and their basic features are examined. It is demonstrated that the validity range of such approximation is strictly limited to √ s/Λ > exp(π/2) 4.81 and that it converges rather slowly when the energy scale approaches this value. The spectral function required for the proper calculation of the R-ratio is explicitly derived and its properties at the higher-loop levels are studied. The developed method of calculation of the spectral function enables one to obtain the explicit expression for the latter at an arbitrary loop level. By making use of the derived spectral function the proper expression for the R-ratio is calculated up to the five-loop level and its properties are examined. It is shown that the loop convergence of the proper expression for the R-ratio is better than that of its commonly employed approximation. The impact of the omitted higher-order π 2 -terms on the latter is also discussed.

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Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

Section: R-ratio Of Electron-positron Annihilation Into Hadronsmentioning

confidence: 99%

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Electron–positron annihilation into hadrons at the higher-loop levels

Нестеренко

2017

Eur. Phys. J. C

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Perturbative contributions to $$ \Delta {\alpha}^{(5)}\left({M}_Z^2\right) $$

Erler,

Ferro-Hernández

2023

J. High Energ. Phys.

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We compute a theoretically driven prediction for the hadronic contribution to the electromagnetic running coupling at the Z scale using lattice QCD and state-of-the-art perturbative QCD. We obtain$$ {\displaystyle \begin{array}{cc}\Delta {\alpha}^{(5)}\left({M}_Z^2\right)=\left[279.5\pm 0.9\pm 0.59\right]\times {10}^{-4}& \left(\textrm{Mainz}\ \textrm{Collaboration}\right)\\ {}\Delta {\alpha}^{(5)}\left({M}_Z^2\right)=\left[278.42\pm 0.22\pm 0.59\right]\times {10}^{-4}& \left(\textrm{BMW}\ \textrm{Collaboration}\right),\end{array}} $$ Δ α 5 M Z 2 = 279.5 ± 0.9 ± 0.59 × 10 − 4 Mainz Collaboration Δ α 5 M Z 2 = 278.42 ± 0.22 ± 0.59 × 10 − 4 BMW Collaboration , where the first error is the quoted lattice uncertainty. The second is due to perturbative QCD, and is dominated by the parametric uncertainty on $$ {\hat{\alpha}}_s $$ α ̂ s , which is based on a rather conservative error. Using instead the PDG average, we find a total error on $$ \Delta {\alpha}^{(5)}\left({M}_Z^2\right) $$ Δ α 5 M Z 2 of 0.4 × 10−4. Furthermore, with a particular emphasis on the charm quark contributions, we also update $$ \Delta {\alpha}^{(5)}\left({M}_Z^2\right) $$ Δ α 5 M Z 2 when low-energy cross-section data is used as an input, obtaining $$ \Delta {\alpha}^{(5)}\left({M}_Z^2\right) $$ Δ α 5 M Z 2 = [276.29 ± 0.38 ± 0.62] × 10−4. The difference between lattice QCD and cross-section-driven results reflects the known tension between both methods in the computation of the anomalous magnetic moment of the muon. Our results are expressed in a way that will allow straightforward modifications and an easy implementation in electroweak global fits.

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Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

2021

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We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $$\tau $$ τ -decay data. The determination involves the double-pinched Borel–Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value of the Borel resummation (PV). All the methods involve truncations in the order of the coupling. In contrast to the truncated CIPT method, the truncated FOPT and PV methods account correctly for the suppression of various renormalon contributions of the Adler function in the mentioned sum rules. The extracted value of the $${\overline{\mathrm{MS}}}$$ MS ¯ coupling is $$\alpha _s(m_{\tau }^2) = 0.3116 \pm 0.0073$$ α s ( m τ 2 ) = 0.3116 ± 0.0073 [$$\alpha _s(M_Z^2)=0.1176 \pm 0.0010$$ α s ( M Z 2 ) = 0.1176 ± 0.0010 ] for the average of the FOPT and PV methods, which we regard as our main result. On the other hand, if we include in the average also the CIPT method, the resulting values are significantly higher, $$\alpha _s(m_{\tau }^2) = 0.3194 \pm 0.0167$$ α s ( m τ 2 ) = 0.3194 ± 0.0167 [$$\alpha _s(M_Z^2)=0.1186 \pm 0.0021$$ α s ( M Z 2 ) = 0.1186 ± 0.0021 ].

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Dispersive Approach to QCD

Cited by 3 publications

References 82 publications

Electron–positron annihilation into hadrons at the higher-loop levels

Electron–positron annihilation into hadrons at the higher-loop levels

Perturbative contributions to $$ \Delta {\alpha}^{(5)}\left({M}_Z^2\right) $$

Determination of perturbative QCD coupling from ALEPH $$\tau $$ decay data using pinched Borel–Laplace and Finite Energy Sum Rules

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