Extending the predictive power of perturbative QCD

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

doi:10.1140/epjc/s10052-019-6704-9

“…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.…”

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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“…A way of using the PMC series together with the Padé approximation approach (PAA) [68][69][70] has been suggested in Ref. [71]. Some successful applications of this method can be found in Refs.…”

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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“…Conformal symmetry also leads to a rigorous way to eliminate the renormalization scale ambiguity [2][3][4] A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve precise fixed-order predictions for physical observables. The Principle of Maximal Conformality (PMC) provides a systematic way to set the renormalization scales order-by-order for any perturbative QCD process, eliminating the ambiguities associated with the conventional renormalization scale-setting procedure.…”

Section: Conformal Invariance Of Qcd and The Principle Of Maximum Conmentioning

confidence: 99%

Supersymmetric and Conformal Features of Hadron Physics

Brodsky

¹

2018

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The QCD Lagrangian is based on quark and gluonic fields—not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion q q ¯ eigenstate has zero mass for m q = 0 . A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: α s ( Q 2 ) ∝ e - Q 2 / 4 κ 2 , in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS 5 space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

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Extending the predictive power of perturbative QCD

Cited by 36 publications

References 54 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

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

Supersymmetric and Conformal Features of Hadron Physics

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