Novel Method to Reliably Determine the QCD Coupling from $R_{\mathrm{uds}}$ Measurements and its effects to Muon $g-2$ and $\alpha (M_Z^2)$ within the Tau-Charm Energy Region

Abstract

We present a novel method for precisely determining the QCD running coupling from $R_{\mathrm{uds}}$ measurements in electron-positron annihilation. When calculating the fixed-order perturbative QCD (pQCD) approximant of $R_{\mathrm{uds}}$, its effective coupling constant ${\alpha }_s(Q_{\ast }^2)$ 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 $R_{\mathrm{uds}}$ data measured by the KEDR detector at $22$ centre-of-mass energies between $1.84$ GeV and $3.72$ GeV, we obtain ${\alpha }_s(M_Z^2)=0.1227_{-0.0132}^{+0.0117}(exp.)\pm 0.0016(the.)$, where the theoretical uncertainty (the.) is negligible compared to the experimental one (exp.). Numerical analyses confirm that the new method for calculating $R_{\mathrm{uds}}$ 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 $R_{\mathrm{uds}}$ 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 $\alpha (M_Z^2)$ within the tau-charm energy range.

arXiv comment22 pages, 8 figures. To be published in JHEP

References in corpus (52)

• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• The global electroweak fit at NNLO and prospects for the LHC and ILC
• Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes
• Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks
• Three-Loop Polarization Function and $\mathcal{O}({\alpha }_s^2)$ Corrections to the Production of Heavy Quarks
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• The Physics of Hadronic Tau Decays
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Estimates of the higher-order QCD corrections to R(s), R_τ and deep-inelasstic scattering sum rules
• QCD Corrections to the $e^{+}{e}^{-}$ Cross Section and the $Z$ Boson Decay Rate
• New Results on the Hadronic Contributions to alpha(M_Z) and to (g-2)_mu
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Update of the ALEPH non-strange spectral functions from hadronic $\tau$ decays
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• On the running coupling constant in QCD
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• The Renormalization Scale-Setting Problem in QCD
• Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
• Improved Determination of alpha_QED(M_Z^2) and the Anomalous Magnetic Moment of the Muon
• Improved Determination of $\alpha (M_{\mathrm{Z}}^2$) and the Anomalous Magnetic Moment of the Muon
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• Vector Correlator in Massless QCD at Order O(alpha_s^4) and the QED beta-function at five loop
• Heavy Quark Vacuum Polarisation to Three Loops
• Reconstruction of heavy quark current correlators at O(α_s^3)
• Meaningful characterisation of perturbative theoretical uncertainties
• The strong coupling from the revised ALEPH data for hadronic $\tau$ decays
• A theory driven analysis of the effective QED coupling at $M_Z$
• Complete QCD Corrections to Hadronic $Z$--Decays in Order ${\alpha }_s^4$
• Determination of the QCD Coupling from ALEPH $\tau$ Decay Data
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD
• Nonfactorizable QCD and Electroweak Corrections to the Hadronic Z Boson Decay Rate
• Perturbative expansion of tau hadronic spectral function moments and alpha_s extractions
• Quartic Mass Corrections to $R_{had}$
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting
• Probabilistic definition of the perturbative theoretical uncertainty from missing higher orders
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• The strong coupling from $e^{+}{e}^{-}\to$ hadrons below charm
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• Modified Contour-Improved Perturbation Theory
• Electron-positron annihilation into hadrons at the higher-loop levels
• Violations of Quark-Hadron Duality in Low-Energy Determinations of ${\alpha }_s$
• Precise perturbative predictions from fixed-order calculations
• Extending the Predictive Power of Perturbative QCD Using the Principle of Maximum Conformality and Bayesian Analysis
• Explicit form of the R-ratio of electron-positron annihilation into hadrons
• Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $\tau$ decay data, and determination of pQCD coupling
• Recurrent form of the renormalization group relations for the higher-order hadronic vacuum polarization function perturbative expansion coefficients
• The R ratio in e+ e-, the determination of alpha(Mz^2) and a possible non-perturbative gluonic contribution

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• Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\mathrm{MS}}$-scheme running mass
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator
• Perturbative QCD fitting of KEDR and BESIII $e^{+}{e}^{-}$ data for R(s) and ${\alpha }_s$ determination
• Determination of the Strong Coupling Constant ${\alpha }_s$ from Inclusive Semi-leptonic $B$ Meson Decays