Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the 
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-scheme coupling

Wu, Xing-Gang; Shen, Jian-Ming; Du, Bo-Lun; Brodsky, Stanley J.

doi:10.1103/physrevd.97.094030

Cited by 41 publications

(41 citation statements)

References 49 publications

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“…Moreover, the PMC procedure reduces in the N C → 0 Abelian limit to the Gell-Mann-Low method [19]. Thus the PMC eliminates renormalization scale-and-scheme ambiguities simultaneously, satisfying the principles of renormalization group invariance [20,21]. In addition, since the {β i }-terms have been removed, the divergent renormalon terms like α n s β n 0 n!…”

Section: Introductionmentioning

confidence: 99%

Scale-fixed predictions for γ + ηc production in electron-positron collisions at NNLO in perturbative QCD

Sang

Huang

et al. 2021

J. High Energ. Phys.

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In the paper, we present QCD predictions for γ + ηc production at an electron-positron collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for e+ + e− → γ + ηc using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the e+e− center-of-mass collision energy $$ \sqrt{s} $$ s . The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal β contributions into the QCD coupling αs(Q2). The renormalization group equation then sets the value of αs for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a renormalization scale-and-scheme independent prediction, σ|NNLO,PMC ≃ 41.18 fb for $$ \sqrt{s} $$ s =10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large K factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the Padé approximation approach, we predict σ|NNNLO,PMC+Pade ≃ 18.99 fb, which is consistent with the recent BELLE measurement $$ {\sigma}^{\mathrm{obs}}={16.58}_{-9.93}^{+10.51} $$ σ obs = 16.58 − 9.93 + 10.51 fb at $$ \sqrt{s} $$ s ≃ 10.6 GeV. This procedure also provides a first estimate of the NNNLO contribution.

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Section: Introductionmentioning

confidence: 99%

Scale-fixed predictions for γ + ηc production in electron-positron collisions at NNLO in perturbative QCD

Sang

Huang

et al. 2021

J. High Energ. Phys.

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“…The PMC-s approach fixes the renormalization scale by directly requiring all the RG-dependent nonconformal terms up to a given order to vanish; thus it inherits most of the features of the PMC standard multiscale approach. Its predictions are also scheme independent due to the resulting conformal series [33]. Thus, in order to eliminate the scale dependence from the last NNLO-term and ensure the renormalization scheme independence, we adopt the PMC-s approach to do the scalesetting for the asymmetry A FB , we then obtain…”

Section: Pmc Scale-setting For the B Quark Forward-backward Asymmetrymentioning

confidence: 99%

Revisiting the bottom quark forward–backward asymmetry $$A_\mathrm{{FB}}$$ in electron–positron collisions

Wang

Meng

et al. 2020

Eur. Phys. J. C

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The bottom quark forward–backward asymmetry $$A_\mathrm{{FB}}$$AFB is a key observable in electron–positron collisions at the $$Z^{0}$$Z0 peak. In this paper, we employ the Principle of Maximum Conformality (PMC) to fix the $$\alpha _s$$αs-running behavior of the next-to-next-to-leading order QCD corrections to $$A_\mathrm{{FB}}$$AFB. The resulting PMC scale for this $$A_\mathrm{{FB}}$$AFB is an order of magnitude smaller than the conventional choice $$\mu _r=M_Z$$μr=MZ. This scale has the physically reasonable behavior and reflects the virtuality of its QCD dynamics, which is independent to the choice of renormalization scale. Our analyses show that the effective momentum flow for the bottom quark forward–backward asymmetry should be $$\mu _r\ll M_Z$$μr≪MZ other than the conventionally suggested $$\mu _r=M_Z$$μr=MZ. Moreover, the convergence of perturbative QCD series for $$A_\mathrm{{FB}}$$AFB is greatly improved using the PMC. Our prediction for the bare bottom quark forward–backward asymmetry is refined to be $$A^{0,b}_\mathrm{FB}=0.1004\pm 0.0016$$AFB0,b=0.1004±0.0016, which diminishes the well known tension between the experimental determination for this (pseudo) observable and the respective Standard Model fit to $$2.1\sigma $$2.1σ.

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“…A recent demonstration of renormalization scale-andscheme independence of PMC prediction has been given in Refs. [51,52], where by using the C-scheme coupling [53], it has been proven that the PMC prediction is independent of the choice of renormalization scale and scheme up to any fixed order. Generally, the convergence of the pQCD series can be improved due to the elimination of the divergent renormalon terms like n!β n 0 α n s or n!β n 0 α n+1 s [54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Z-boson hadronic decay width up to $${{\mathcal {O}}}(\alpha _s^4)$$-order QCD corrections using the single-scale approach of the principle of maximum conformality

Huang

Zheng

et al. 2021

Eur. Phys. J. C

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In the paper, we study the properties of the Z-boson hadronic decay width by using the $$\mathcal {O}(\alpha _s^4)$$ O ( α s 4 ) -order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the Z-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown $$\mathcal {O}(\alpha _s^5)$$ O ( α s 5 ) -order terms are highly suppressed, e.g. conservatively, we have $$\Delta \Gamma _{\mathrm{Z}}^{\mathrm{had}}|^{{{\mathcal {O}}}(\alpha _s^5)}_{\mathrm{PMC}}\simeq \pm 0.004$$ Δ Γ Z had | PMC O ( α s 5 ) ≃ ± 0.004 MeV. In combination with the known electro-weak (EW) corrections, QED corrections, EW–QCD mixed corrections, and QED–QCD mixed corrections, our final prediction of the hadronic Z decay width is $$\Gamma _{\mathrm{Z}}^{\mathrm{had}}=1744.439^{+1.390}_{-1.433}$$ Γ Z had = 1744 . 439 - 1.433 + 1.390 MeV, which agrees with the PDG global fit of experimental measurements, $$1744.4\pm 2.0$$ 1744.4 ± 2.0 MeV.

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Novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the C -scheme coupling

Cited by 41 publications

References 49 publications

Scale-fixed predictions for γ + ηc production in electron-positron collisions at NNLO in perturbative QCD

Scale-fixed predictions for γ + ηc production in electron-positron collisions at NNLO in perturbative QCD

Revisiting the bottom quark forward–backward asymmetry $$A_\mathrm{{FB}}$$ in electron–positron collisions

Z-boson hadronic decay width up to $${{\mathcal {O}}}(\alpha _s^4)$$-order QCD corrections using the single-scale approach of the principle of maximum conformality

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