The heavy quarkonium inclusive decays using the principle of maximum conformality

Wu, Xing-Gang; Zeng, Jun; Huang, Xu-Dong; Yu, Huai-Min

doi:10.1140/epjc/s10052-020-7967-x

“…If one has a renormalization-scale independent conformal series, one can often obtain a reliable prediction of unknown higher-order contributions [44] with the help of the Padé JHEP01(2021)131 resummation [45][46][47]. The diagonal [1/1]-type Padé series is generally preferable for estimating the unknown contributions from a poor pQCD convergent series [48][49][50]; and for the present process, the poor convergence of PMC series is due to large conformal coefficients. Detailed procedures for obtaining a combined Padé +PMC prediction can be found in ref.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Detailed procedures for obtaining a combined Padé +PMC prediction can be found in ref. [50]. By using the diagonal [1/1]-type PAA approximant, the predicted coefficient of the N 3 LO term is -2713.77, which results in an extra 38% suppression from the LO cross-section, leading to a NNNLO prediction in better agreement with the data; i.e., where µ Λ = 1 GeV and the other parameters are set to their central values.…”

Section: Numerical Resultsmentioning

confidence: 99%

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

Yu

¹

,

Sang

²

,

Huang

³

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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“…Moreover, due to the independence on the renormalization scheme and scale, the resulting conformal series not only provides precise pQCD predictions; it also can reliably estimate the contributions from the unknown higher-order terms. The PMCs has been successfully applied to several high-energy processes [37][38][39][40][41][42][43], where the contributions from unknown higher-order terms have been estimated by using the Padé approximation approach [44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality

Huang¹,

Jiang²,

Ma³

et al. 2021

Preprint

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It has become conventional to simply guess the renormalization scale and choose an arbitrary range of uncertainty when making perturbative QCD (pQCD) predictions. However, this ad hoc assignment of the renormalization scale and the estimate of the size of the resulting uncertainty leads to anomalous renormalization scheme-and-scale dependences. In fact, relations between physical observables must be independent of the theorist's choice of the renormalization scheme, and the renormalization scale in any given scheme at any given order of pQCD is not ambiguous. The Principle of Maximum Conformality (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for observables consistent with the principles of the renormalization group. The renormalization scale in the PMC is fixed such that all β terms are eliminated from the perturbative series and resumed into the running coupling; this procedure results in a convergent, scheme-independent conformal series without factorial renormalon divergences. The resulting relations between physical observables, such as commensurate scale relations, are independent of the choice of renormalization scheme. Although conventional renormalization scheme and scale ambiguities do not appear, a PMC prediction will of course still have some residual scale uncertainty arising from uncalculated higher-order terms. If the resulting PMC conformal series does not have sufficient convergence, the residual scale uncertainty from the unknown higher order pQCD contributions could be significant. Several variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, such as the multi-scale-setting approach (PMC), the single-scale-setting approach (PMCs), and the procedures based on "intrinsic conformality" (PMC∞). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities R e + e − , Rτ , and Γ(H → b b) up to four-loop pQCD corrections. The PMC approach also determines an overall effective running coupling αs(Q) by the recursive use of the renormalization group equation, whose argument Q represents the actual momentum flow of the process. Our numerical results show that the single-scale PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with less residual scale dependence.

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“…Some successful applications of this method can be found in Refs. [72][73][74][75]. We shall adopt this method to estimate the magnitude of the unknown O(α 5 s )-terms of E ns (Q 2 ), and in the following, we give a brief introduction of PAA.…”

Section: Perturbative Series Of the Leading-twist Termsmentioning

confidence: 99%

A novel determination of non-perturbative contributions to Bjorken sum rule

Wu

¹

,

Zhou

²

,

Huang

³

2021

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Based on the operator product expansion, the perturbative and nonperturbative contributions to the polarized Bjorken sum rule (BSR) can be separated conveniently, and the nonperturbative one can be fitted via a proper comparison with the experimental data. In the paper, we first give a detailed study on the pQCD corrections to the leading-twist part of BSR. Basing on the accurate pQCD prediction of BSR, we then give a novel fit of the non-perturbative high-twist contributions by comparing with JLab data. Previous pQCD corrections to the leading-twist part derived under conventional scale-setting approach still show strong renormalization scale dependence. The principle of maximum conformality (PMC) provides a systematic and strict way to eliminate conventional renormalization scale-setting ambiguity by determining the accurate $$\alpha _s$$ α s -running behavior of the process with the help of renormalization group equation. Our calculation confirms the PMC prediction satisfies the standard renormalization group invariance, e.g. its fixed-order prediction does scheme-and-scale independent. In low $$Q^2$$ Q 2 -region, the effective momentum of the process is small and in order to derive a reliable prediction, we adopt four low-energy $$\alpha _s$$ α s models to do the analysis, i.e. the model based on the analytic perturbative theory (APT), the Webber model (WEB), the massive pQCD model (MPT) and the model under continuum QCD theory (CON). Our predictions show that even though the high-twist terms are generally power suppressed in high $$Q^2$$ Q 2 -region, they shall have sizable contributions in low and intermediate $$Q^2$$ Q 2 domain. Based on the more accurate scheme-and-scale independent pQCD prediction, our newly fitted results for the high-twist corrections at $$Q^2=1\;\mathrm{GeV}^2$$ Q 2 = 1 GeV 2 are, $$f_2^{p-n}|_{\mathrm{APT}}=-0.120\pm 0.013$$ f 2 p - n | APT = - 0.120 ± 0.013 , $$f_2^{p-n}|_\mathrm{WEB}=-0.081\pm 0.013$$ f 2 p - n | WEB = - 0.081 ± 0.013 , $$f_2^{p-n}|_{\mathrm{MPT}}=-0.128\pm 0.013$$ f 2 p - n | MPT = - 0.128 ± 0.013 and $$f_2^{p-n}|_{\mathrm{CON}}=-0.139\pm 0.013$$ f 2 p - n | CON = - 0.139 ± 0.013 ; $$\mu _6|_\mathrm{APT}=0.003\pm 0.000$$ μ 6 | APT = 0.003 ± 0.000 , $$\mu _6|_{\mathrm{WEB}}=0.001\pm 0.000$$ μ 6 | WEB = 0.001 ± 0.000 , $$\mu _6|_\mathrm{MPT}=0.003\pm 0.000$$ μ 6 | MPT = 0.003 ± 0.000 and $$\mu _6|_{\mathrm{CON}}=0.002\pm 0.000$$ μ 6 | CON = 0.002 ± 0.000 , respectively, where the errors are squared averages of those from the statistical and systematic errors from the measured data.

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The heavy quarkonium inclusive decays using the principle of maximum conformality

Cited by 15 publications

References 55 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

Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality

A novel determination of non-perturbative contributions to Bjorken sum rule

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