Next-to-Leading-Order QCD Corrections to e+ e- --> J/psi c c_bar at the B Factories

TL;DR

This work tackles the discrepancy between LO NRQCD predictions and experimental measurements of J/psi production in e^+e^- annihilation at B factories by performing a full NLO QCD calculation of e^+e^- → J/psi c cbar within the NRQCD framework. It reports virtual and real corrections, uses a two-cutoff phase-space slicing method, and applies a Brodsky–Lepage–Mackenzie scale setting to improve perturbative convergence, including psi' feed-down to match Belle data. The results show that the NLO cross section rises and, with psi' feed-down, can reproduce the Belle measurements, while angular distributions from individual channels remain at odds with data; J/psi polarization also presents a puzzle that requires further measurements. The work improves theoretical control over heavy-quarkonium production at e^+e^- colliders and highlights scale-setting as a crucial ingredient in matching precision data, pointing to potential nonperturbative effects or experimental issues that need resolution.

Abstract

We calculate the next-to-leading-order (NLO) QCD correction to $e^+e^-\to J/ψc \bar{c}$ at the B factories, and present theoretical predictions on the momentum and production angular distribution for $J/ψ$ production, and momentum distribution for $J/ψ$ polarization at NLO for the first time. By applying Brodsky, Lepage and Mackenzie scale setting for the renormalization scale, it is found that the QCD perturbative expansion is significantly improved with the unique scale choice $μ^*=1.65$GeV. Together with the $ψ^\prime$ feed-down contribution, the total cross section and momentum distribution can account for the recent experimental measurement by the Belle collaboration. The total cross section and momentum distribution are also found to be consistent with the experimental measurement in the previous study on $e^+e^-\to J/ψgg$. However, the production angular distribution of $J/ψ$ production for either the $J/ψc\bar{c}$ or the $J/ψgg$ channel has a quite different shape in contrast with the new experimental data, although it fits with the experimental data when the two channels are added together. This situation is difficult to explain. To clarify the puzzle of $J/ψ$ polarization, further experimental measurements are strongly expected to testify our predictions on the momentum distribution for $J/ψ$ polarization. Our total cross section agrees with that given in the previous study of Zhang and Chao by using their renormalization scheme and input parameters.

Figures (15)

• Figure 1: Typical Feynman diagrams at LO.
• Figure 2: Typical Feynman diagrams for virtual corrections. Groups $(a_1)-(a_4)$ are the counter-term diagrams, including corresponding loop diagrams. More diagrams can be obtained by reversing the arrows of the quark lines, and exchanging the places of the $J/\psi$ and open charm pairs in groups $(a)$ and $(b)$.
• Figure 3: Typical Feynman diagrams for real correction process $e^+e^-\rightarrow {J/\psi} c\overline{c}g$. $(a)$: Diagrams obtained by adding a gluon to LO diagrams. This type contains 24 diagrams; $(b)$: Diagrams with two quark lines. This type contains six diagrams.
• Figure 4: Cross sections of $e^+e^-\rightarrow {J/\psi} c\bar{c}$ as a function of the renormalization scale $\mu$. The mass of charm quark is chosen as 1.4, 1.5 and 1.6 GeV, respectively.
• Figure 5: Cross sections for ${J/\psi} c\bar{c}$, ${J/\psi} gg$ and total, as a function of the renormalization scale $\mu$.