# Perturbative QCD for $J/\psi$ Inclusive Production Via Initial State Radiation at $e^+e^-$ collider

## TL;DR

This paper calculates the NLO QCD predictions for inclusive $J/ar{J}$ production in $e^+e^-$ collisions across various energies, compares with experimental data, and discusses the limitations of perturbative QCD at lower energies.

## Contribution

It provides the first NLO QCD calculations including initial state radiation effects for $J/\psi$ production at different energies, offering a new method to test perturbative QCD validity.

## Key findings

- Results agree with Belle at 10.6 GeV
- Predictions underestimate BESIII data at lower energies
- Initial state radiation effects are quantified for future tests

## Abstract

Up to the next-leading order (NLO) of quantum chromodynamics (QCD), the process $e^+e^-\to J/\psi +X$ with the center-of-mass (CM) energy range from 3.7 to 10.6 GeV is calculated. At 10.6 GeV, the results is consistent with the experiment results at the Belle. However, the predictions are much smaller than the measurement at BESIII at low CM energy range from 3.7 to 4.6 GeV. This indicates that the convergence of QCD perturbative expansion becomes worse as the CM energy becomes lower and closer to the inclusive $J/\psi$ production threshold. For a further study of the QCD mechanism on $J/\psi$ production at $e^+e^-$ collider with different CM energy, the initial state radiation effect of $e^+e^-\to J/\psi+gg$ and $e^+e^-\to J/\psi+c \bar{c}$ are calculated at the QCD NLO. The results are plotted and the numbers of events for different CM energy bins are provided for the designed SuperKEKB. This provides a method to precisely test the validity of perturbative prediction on $J/\psi$ production in future measurements.