Next-to-next-to-leading-order QCD corrections to $J/ψ$ plus $η_c$ production at the $B$ factories

Abstract

In this paper, we calculate the next-to-next-to-leading-order (NNLO) QCD corrections to $e^+e^- \to J/ψ+η_c$ at the $B$ factories. After including the NNLO corrections, the cross section of $e^+e^- \to J/ψ+η_c$ 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 $α_s^3$-order, which is about $2.4\%$ of the total prediction. The renormalization scale $μ_R$ 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 $μ_R$, charm quark mass $m_c$ and the NRQCD factorization scale $μ_Λ$, our prediction shows agreement with the BABAR and BELLE measurements within errors.