Next-to-next-to-leading-order QCD corrections to $J/\psi$ plus $\eta_c$ production at the $B$ factories

TL;DR

This paper computes NNLO QCD corrections to $J/ au_c$ production at B factories, showing a 17% cross section increase, improved convergence, and better agreement with experimental data.

Contribution

It provides the first NNLO QCD correction calculation for $J/ au_c$ production at B factories, enhancing theoretical precision.

Findings

Cross section increased by about 17% after NNLO corrections.

Perturbative series exhibits convergent behavior at NNLO.

Prediction aligns with BABAR and BELLE measurements within uncertainties.

Abstract

In this paper, we calculate the next-to-next-to-leading-order (NNLO) QCD corrections to $e^+e^- \to J/\psi+\eta_c$ at the $B$ factories. After including the NNLO corrections, the cross section of $e^+e^- \to J/\psi+\eta_c$ is enhanced by about $17\%$, and the perturbative series of the prediction shows the convergent behavior. It is also found that the contribution from bottom quark starts at the $\alpha_s^3$-order, which is about $2.4\%$ of the total prediction. The renormalization scale $\mu_R$ dependence of the cross section is reduced at the NNLO level, but the prediction is sensitive to the charm quark mass $m_c$. By considering the uncertainties caused by renormalization scale $\mu_R$, charm quark mass $m_c$ and the NRQCD factorization scale $\mu_\Lambda$, our prediction shows agreement with the BABAR and BELLE measurements within errors.