The heavy quarkonium inclusive decays using the principle of maximum conformality

Abstract

The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium ${\eta }_Q$ ($Q$ being $c$ or $b$) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the NNLO decay width still has large conventional renormalization scale dependence due to its weaker pQCD convergence, e.g. about ${(}_{-34\%}^{+4\%})$ for ${\eta }_c$ and ${(}_{-9\%}^{+0.0})$ for ${\eta }_b$, by varying the scale within the range of $[m_Q,4m_Q]$. The principle of maximum conformality (PMC) provides a systematic way to fix the ${\alpha }_s$-running behavior of the process, which satisfies the requirements of renormalization group invariance and eliminates the conventional renormalization scheme and scale ambiguities. Using the PMC single-scale method, we show that the resultant PMC conformal series is renormalization scale independent, and the precision of the ${\eta }_Q$ inclusive decay width can be greatly improved. Taking the relativistic correction $\mathcal{O}({\alpha }_s{v}^2)$ into consideration, the ratios of the ${\eta }_Q$ decays to light hadrons or $\gamma \gamma$ are: $R_{{\eta }_c}^{\mathrm{NNLO}}{|}_{\mathrm{PMC}}=(3.93_{-0.24}^{+0.26})\times 10^3$ and $R_{{\eta }_b}^{\mathrm{NNLO}}{|}_{\mathrm{PMC}}=(22.85_{-0.87}^{+0.90})\times 10^3$, respectively. Here the errors are for $\Delta {\alpha }_s(M_Z)=\pm 0.0011$. As a step forward, by applying the Pad$\acute{e}$ approximation approach (PAA) over the PMC conformal series, we obtain approximate NNNLO predictions for those two ratios, e.g. $R_{{\eta }_c}^{\mathrm{NNNLO}}{|}_{\mathrm{PAA}+\mathrm{PMC}}=(5.66_{-0.55}^{+0.65})\times 10^3$ and $R_{{\eta }_b}^{\mathrm{NNNLO}}{|}_{\mathrm{PAA}+\mathrm{PMC}}=(26.02_{-1.17}^{+1.24})\times 10^3$. The $R_{{\eta }_c}^{\mathrm{NNNLO}}{|}_{\mathrm{PAA}+\mathrm{PMC}}$ ratio agrees with the latest PDG value $R_{{\eta }_c}^{\exp }=(5.3_{-1.4}^{+2.4})\times 10^3$, indicating the necessity of a strict calculation of NNNLO terms.

arXiv comment10 pages, 4 figures

References in corpus (42)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• The four-loop beta-function in Quantum Chromodynamics
• The three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• Naive nonabelianization and resummation of fermion bubble chains
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Order-v^4 Corrections to S-wave Quarkonium Decay
• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• The strong coupling and its running to four loops in a minimal MOM scheme
• The Renormalization Scale-Setting Problem in QCD
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• Asymptotic Pade Approximant Predictions: up to Five Loops in QCD and SQCD
• The QCD Renormalization Group Equation and the Elimination of Fixed-Order Scheme-and-Scale Ambiguities Using the Principle of Maximum Conformality
• The Form Factors of the Gauge-Invariant Three-Gluon Vertex
• Charmonium decays: J/psi --> e+e- and eta_c --> gamma gamma
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• Can NRQCD explain the $\gamma {\gamma }^{\ast }\to {\eta }_c$ transition form factor data?
• Higher-order QCD corrections to hadronic $\tau$ decays from Padé approximants
• Novel All-Orders Single-Scale Approach to QCD Renormalization Scale-Setting
• NRQCD matrix elements for S-wave bottomonia and Gamma[eta_b(nS) -> gamma gamma] with relativistic corrections
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy
• A Prediction for the 4-Loop βFunction
• $O({\alpha }_s{v}^2)$ Corrections to Hadronic and Electromagnetic Decays of ${}^1{S}_0$ Heavy Quarkonium
• Degeneracy Relations in QCD and the Equivalence of Two Systematic All-Orders Methods for Setting the Renormalization Scale
• Next-to-next-to-leading-order QCD corrections to hadronic width of pseudoscalar quarkonium
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• Extending the Predictive Power of Perturbative QCD
• $O({\alpha }_s{v}^2)$ correction to pseudoscalar quarkonium decay to two photons
• Improvement of the method of diagonal Pade approximants for perturbative series in gauge theories
• Inclusive decays of ${\eta }_c$ and ${\eta }_b$ at NNLO with large $n_f$ resummation
• Ambiguities of the principle of maximum conformality procedure for hadron collider processes
• Reanalysis of the Higgs-boson decay $H\to gg$ up to ${\alpha }_s^6$-order level using the principle of maximum conformality
• Application of Pade Approximants to Determination of alpha_s(M_Z^2) from Hadronic Event Shape Observables in e+e- Annihilation
• Reconsideration of the QCD corrections to the ${\eta }_c$ decays into light hadrons using the principle of maximum conformality

Cited by in corpus (11)

• A novel determination of non-perturbative contributions to Bjorken sum rule
• Determination of the top-quark $\overline{\mathrm{MS}}$ running mass via its perturbative relation to the on-shell mass with the help of principle of maximum conformality
• Scale-Fixed Predictions for $\gamma +{\eta }_c$ production in electron-positron collisions at NNLO in perturbative QCD
• Detailed Comparison of Renormalization Scale-Setting Procedures based on the Principle of Maximum Conformality
• Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders
• $Z$-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
• Observation of the charmonium decay ${\eta }_c\to \gamma \gamma$ in $J/\psi \to \gamma {\eta }_c$
• Self-consistent analysis for the ${\eta }_c\to \gamma \gamma$ process
• Precise determination of the top-quark on-shell mass $M_t$ via its scale-invariant perturbative relation to the top-quark $\overline{\mathrm{MS}}$ mass ${\overline{m}}_t({\overline{m}}_t)$
• A new analysis of the pQCD contributions to the electroweak parameter $\rho$ using the single-scale approach of principle of maximum conformality
• Study of the Magnetic Dipole Transition of $J/\psi \to \gamma {\eta }_c$ via ${\eta }_c\to p\bar{p}$