Explicit form of the <i>R-</i>ratio of electron–positron annihilation into hadrons

Нестеренко, А. В.

doi:10.1088/1361-6471/ab433e

Cited by 13 publications

(20 citation statements)

References 180 publications

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“…, see, e.g., Refs. [16,18], whereas at the higher-loop levels the corresponding RG relations for the coefficients Π j,k become quite cumbersome and can be found in Appendix A of Ref. [16].…”

Section: Resultsmentioning

confidence: 99%

“…At the same time, the higher-order coefficients Π j,k can also be expressed in terms of the coefficients Π i,0 and γ i (11). Specifically, for this purpose the obtained results should be supplemented by the relations [16] Π…”

Section: Resultsmentioning

confidence: 99%

“…( 8) on the renormalization scale was discussed in, e.g., Refs. [11][12][13][14][15][16]. It is worthwhile to mention here that a general choice of the renormalization scale µ 2 = c Q 2 (with c = 1 being a positive constant) keeps in the resulting expression for the Adler function D (ℓ) (Q 2 ) all the terms proportional to the higher-order coefficients Π j,k (0 ≤ j ≤ ℓ, 0 ≤ k ≤ j + 1) appearing on the right-hand side of Eq.…”

Section: Methodsmentioning

confidence: 99%

“…In particular, the direct calculation of discontinuity ( 6) of expression (8) with subsequent assignment of the renormalization scale µ 2 = |s| (that factually amounts to an incomplete RG summation in the timelike domain, see, e.g., Refs. [13,14,16,20]) yields…”

Section: Methodsmentioning

confidence: 99%

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Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients

Nesterenko

2020

Preprint

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The renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients are studied. The folded recurrent and unfolded explicit forms of such relations are obtained. The explicit expression for the coefficients, which incorporate the contributions of the π 2 -terms in the perturbative expansion of the R-ratio of electron-positron annihilation into hadrons, is derived at an arbitrary loop level.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients

Nesterenko

2020

Preprint

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“…In the case of the sum rules (9), the timelike squared energy σ m is in an intermediate range σ m ∼ m 2 τ ∼ 1 GeV 2 (we have here σ m = 2.8 GeV 2 ). There exist several other timelike quantities in form of integrals of D(Q 2 ) that are phenomenologically important [41], among them: (a) the production ratio for e + e − → hadrons, R(s) [42,43], where the squared energy |Q 2 | = s > 0 is in principle not constrained; (b) the leading order hadronic vacuum polarisation contribution to the anomalous magnetic moment of μ lepton, (g μ /2 − 1) had (1) [ 45,46], where the dominant momenta [47,48].…”

Section: Sum Rules and Adler Functionmentioning

confidence: 99%

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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Novel method to reliably determine the QCD coupling from Ruds measurements and its effects to muon g − 2 and $$ \alpha \left({M}_Z^2\right) $$ within the tau-charm energy region

Shen

Bing-Hai

Jiang

et al. 2023

J. High Energ. Phys.

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We present a novel method for precisely determining the QCD running coupling from Ruds measurements in electron-positron annihilation. When calculating the fixed-order perturbative QCD (pQCD) approximant of Ruds, its effective coupling constant $$ {\alpha}_s\left({Q}_{\ast}^2\right) $$ α s Q ∗ 2 is determined by using the principle of maximum conformality, a systematic scale-setting method for gauge theories, whose resultant pQCD series satisfies all the requirements of renormalization group. Contribution due to the uncalculated higher-order (UHO) terms is estimated by using the Bayesian analysis. Using Ruds data measured by the KEDR detector at 22 centre-of-mass energies between 1.84 GeV and 3.72 GeV, we obtain $$ {\alpha}_s\left({M}_Z^2\right) $$ α s M Z 2 = $$ {0.1227}_{-0.0132}^{+0.0117}\left(\exp .\right)\pm 0.0016\left(\textrm{the}.\right) $$ 0.1227 − 0.0132 + 0.0117 exp . ± 0.0016 the . , where the theoretical uncertainty (the.) is negligible compared to the experimental one (exp.). Numerical analyses confirm that the new method for calculating Ruds removes conventional renormalization scale ambiguity, and the residual scale dependence due to the UHO-terms will also be highly suppressed due to a more convergent pQCD series. This leads to a significant stabilization of the perturbative series, and a significant reduction of theoretical uncertainty. It thus provides a reliable theoretical basis for precise determination of the QCD running coupling from Ruds measurements at future Tau-Charm Facility. It can also be applied for the precise determination of the hadronic contributions to muon g − 2 and QED coupling $$ \alpha \left({M}_Z^2\right) $$ α M Z 2 within the tau-charm energy range.

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Explicit form of the R-ratio of electron–positron annihilation into hadrons

Cited by 13 publications

References 180 publications

Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients

Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients

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

Novel method to reliably determine the QCD coupling from Ruds measurements and its effects to muon g − 2 and $$ \alpha \left({M}_Z^2\right) $$ within the tau-charm energy region

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