Next-to-next-to-leading-order QCD corrections to $J/\psi$ plus ${\eta }_c$ production at the $B$ factories

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.

Comments: 13 pages, 3 figures. Published version