Inclusive $J/ψ$ Productions at $e^+ e^-$ Colliders

TL;DR

The paper investigates inclusive J/psi production in e+e- collisions at B-factory energies within NRQCD, focusing on reconciling Belle measurements with naive color-singlet predictions. It computes LO contributions from J/psi c cbar (QCD+QED) and J/psi gg, and finds a ccbar-to-gg ratio near 1:1.5; by introducing collinear suppression for gg and a large K factor (~4) for ccbar, the observed momentum spectra and J/psi c cbar fractions can be reproduced without invoking color-octet contributions. A detailed spin-density-matrix analysis is presented, revealing distinct polarization and angular patterns for the different subprocesses and showing strong sensitivity of certain observables to the K factor. The work also discusses connections to exclusive double-charmonium production and outlines experimental observables to constrain subprocess normalizations, providing a coherent framework for interpreting current data and guiding future measurements.

Abstract

Inclusive $J/ψ$ productions in $e^+ e^-$ annihilation is studied in the framework of NRQCD. We first review the leading-order calculations of the cross sections for $e^+ e^- \to J/ψc \bar{c}$ and $e^+ e^- \to J/ψg g$ and find that their ratio is about 1:1.5 at $\sqrt{s}\simeq 10$\gev. This result is in conflict with the current measurements by the Belle Collaboration, which finds that the process $e^+e^- \to J/ψc\bar{c}$ accounts for about 2/3 of all the prompt $J/ψ$'s. We show that the discrepancy in the total rate as well as in the $J/ψ$ momentum distributions can be resolved by considering a large renormalization $K$ factor ($K\simeq 4$) for the $J/ψc \bar {c}$ cross section and by taking into account collinear suppression in the end-point energy region of $J/ψg g$ production. Detailed studies of the model predictions in terms of the density matrix are performed and various momentum and angular distributions are presented as functions of the $K$ factors. These distributions can be used to determine the normalizations of each subprocess provided that the production and decay angular distributions do not alter much by higher order corrections.

Figures (8)

• Figure 1: Feynman diagrams for the $J/\psi c {\bar{c}}$ productions from $e^+ + e^-$ annihilation: (a) the QCD production, (b) the $t$-channel QED production, (c) and (d) the $s$-channel QED productions.
• Figure 2: Feynman diagrams for the $J/\psi gg$ production from $e^+ + e^-$ annihilation.
• Figure 3: Momentum and angular distributions of $e^+ e^-\rightarrow J/\psi c{\bar{c}}$ and $J/\psi gg$ processes: (a) and (b) are for the total cross section, and (c) and (d) are for the fraction of the transversely polarized $J/\psi$ production. The solid, dashed and dotted lines correspond to the QCD $J/\psi c {\bar{c}}$, QED $J/\psi c {\bar{c}}$, and $J/\psi gg$ production, respectively.
• Figure 4: Momentum (a) and angular (b) distributions for the $J/\psi gg$ cross section. The dashed line is for the leading order calculation, while the solid line is for the calculation with the collinear suppression.
• Figure 5: Momentum and angular distributions: (a) and (b) are for the total cross section, and (c) and (d) are for the the fraction of the transversely polarized $J/\psi$, (e) and (f) are for the fraction of $\sigma_{+-}$. The solid, dashed and dotted lines correspond to the $J/\psi c {\bar{c}}$, $J/\psi gg$ and total inclusive productions respectively.