${\mathcal O}(\alpha_s v^2)$ correction to $J/\psi$ plus $\eta_c$ production in $e^+e^-$ annihilation at $\sqrt{s}=10.6GeV

TL;DR

This paper calculates the mixed order ${ m O}(\a_s v^2)$ corrections to $J/$ plus $$ production in electron-positron collisions, showing these corrections are small and confirming the convergence of the perturbative series.

Contribution

It provides the first detailed calculation of ${ m O}(\a_s v^2)$ corrections in this process, confirming the perturbative expansion's convergence and aligning with previous results.

Findings

Corrections at ${ m O}(\a_s v^2)$ are only a few percent.

Perturbative series shows good convergence.

Results agree with previous studies.

Abstract

Based on the nonrelativistic QCD factorization approach, ${\mathcal O}(\alpha_s v^2)$ corrections to $\jpsi$ plus $\eta_c$ production in $e^+e^-$ annihilation at $\sqrt{s}=10.6 \gev$ is calculated in this work. The numerical results show that the correction at $\alpha_s v^2$ order is only about a few percent for the total theoretical result. It indicates that the perturbative expansions for the theoretical prediction become convergence and higher order correction will be smaller. The uncertainties from the long-distance matrix elements, renormalization scale and the measurement in experiment are also discussed. Our result is in agreement with previous result in ref [1].