Exclusive production of $J/\psi +{\eta }_c$ at the $B$ factories Belle and Babar using the principle of maximum conformality

Abstract

We predict the rate for exclusive double-charmonium production in electron-positron annihilation $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ using perturbative quantum chromodynamics and the NRQCD framework for hard, heavy-quarkonium exclusive processes. The cross sections measured at the $B$-factories Belle and Babar at $\sqrt{s}=10.6$ GeV disagree with the pQCD leading-order predictions by an order of magnitude. The predictions at next-to-leading order are, however, very sensitive to the choice of the renormalization scale, resulting in an apparent discrepancy between the theoretical prediction and the data. We show that this discrepancy can in fact be eliminated by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. ... By carefully applying the PMC to different topologies of the annihilation process, one achieves precise pQCD predictions, together with improved perturbative convergence. We also observe that the single-photon-fragmentation QED correction is important, an effect which increases the total cross-section by about $10\%$. The scale-fixed, scheme-independent cross-section predicted by the PMC is ${\sigma }_{\mathrm{tot}}{|}_{\mathrm{PMC}}=20.35_{-3.8}^{+3.5}$ fb, where the uncertainties come from the squared average of the errors due to the value of the charm mass and the uncertainty from the quarkonium wavefunctions at the origin. We find that the typical momentum flow of the process is $2.30$ GeV, which explains the guessed choice of $2-3$ GeV using conventional scale-setting. The scale-fixed $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ cross-section predicted by the PMC shows excellent agreement with the Belle and Babar measurements, emphasizing the importance of a rigorous renormalization scale-setting procedure.

arXiv comment5 pages, 3 figures. Accepted for publication in PRD

References in corpus (32)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• J/psi polarization at hadron colliders in nonrelativistic QCD
• Observation of Double cc bar Production in e+ e- Annihilation at sqrt{s} ~ 10.6 GeV
• Exclusive Double-Charmonium Production from e^+ e^- Annihilation into a Virtual Photon
• A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
• Commensurate Scale Relations in Quantum Chromodynamics
• Measurement of Double Charmonium Production in $e^{+}{e}^{-}$ Annihilations at $\sqrt{s}=10.6$ GeV
• Next-to-Leading Order QCD Correction to ${\mathbf{e}}^{+}{\mathbf{e}}^{-}\to \mathbf{J}/\mathbf{\psi }+{\mathbf{\eta }}_{\mathbf{c}}$ at $\sqrt{s}=10.6$GeV}
• Fragmentation contributions to J/psi production at the Tevatron and the LHC
• Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations
• Problems of Double Charm Production in $e^{+}{e}^{-}$ Annihilation at $\sqrt{s}=10.6$ GeV
• Is the BELLE result for the cross section e+e- -> J/psi+eta_c a real difficulty for 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
• Study of double charmonium production in e^+ e^- annihilation at \sqrt{s} ~ 10.6 GeV
• Progress in FDC Project
• Exclusive J/ψProductions at e^+ e^- Colliders
• QCD corrections to J/psi plus eta_c production in e+e- annihilation at sqrt{s}=10.6 GeV
• Impact of ${\eta }_c$ hadroproduction data on charmonium production and polarization within NRQCD framework
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• Reconciling the light-cone and nonrelativistic QCD approaches to calculating e+ e- -> J/psi + eta_c
• Predictions for $e^{+}{e}^{-}\to J/\psi {\eta }_c$ with Light-Cone Wave-Functions
• Excited charmonium mesons production in e^+e^- annihilation at \sqrt{s}=10.6 GeV
• Search for excited charmonium states in $e^{+}{e}^{-}$ Annihilation at $\sqrt{s}=10.6$ GeV
• A novel demonstration of the renormalization group invariance of the fixed-order predictions using the principle of maximum conformality and the $C$-scheme coupling
• The cross section of the process $e^{+}+e^{-}\to J/\psi +{\eta }_c$ within the QCD light-cone sum rules
• QCD leading order study of the $J/\psi$ leptoproduction at HERA within the nonrelativistic QCD framework
• QCD Corrections to the Color-singlet $J/\psi$ Production in Deeply Inelastic Scattering at HERA
• Reconciling charmonium production and polarization data within the nonrelativistic QCD framework
• Is the colour-octet mechanism consistent with the double $J/\psi$ production measurement at B-factories?

Cited by in corpus (12)

• Next-to-next-to-leading-order QCD corrections to $J/\psi$ plus ${\eta }_c$ production at the $B$ factories
• Next-to-leading-order study of $J/\psi$ angular distributions in $e^{+}{e}^{-}\to J/\psi +{\eta }_c,{\chi }_{cJ}$ at $\sqrt{s}\approx 10.6$ GeV
• Next-to-leading-order QCD corrections to the decay of $Z$ boson into ${\chi }_c({\chi }_b)$
• One-loop corrections to the processes $e^{+}{e}^{-}\to \gamma ,Z\to J/\psi {\eta }_c$ and $e^{+}{e}^{-}\to Z\to J/\psi J/\psi$
• Analysis of double-$J/\psi$ production in $Z$ decay at next-to-leading-order QCD accuracy
• Associated charmonium-bottomonium production in a single boson $e^{+}{e}^{-}$ annihilation
• Revisiting the production of $J/\psi +{\eta }_c$ via the $e^{+}{e}^{-}$ annihilation within the QCD light-cone sum rules
• Comprehensive studies of ${\rm Y}$ inclusive production in $Z$ boson decay
• The studies on $Z\to {\rm Y}(1S)+g+g$ at the next-to-leading-order QCD accuracy
• Revisiting the Bottom Quark Forward-Backward Asymmetry $A_{\mathrm{FB}}$ in Electron-Positron Collisions
• Elimination of QCD Renormalization Scale and Scheme Ambiguities
• Two loop QCD corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ in asymptotic expansion