Inclusive productions of $J/\psi+\eta_c$ in $e^{+}e^{-}$ annihilation at Belle

Abstract

We study $e^{+}e^{-} \to J/\psi+\eta_c+X$ at next-to-leading order (NLO) in $\alpha_s$ within the nonrelativistic QCD (NRQCD) framework to assess the color-octet (CO) mechanism at low energies. QCD corrections significantly enhance both color-singlet (CS) and CO leading-order results, with non-negligible QED-diagram contributions to the CS channel. At $\Upsilon(4S)$, CO terms increase the inclusive cross section by $20\%$--$30\%$, and the enhancement grows rapidly with $\sqrt{s}$, yielding an energy dependence distinct from CS predictions and providing a sensitive test of NRQCD. Including $\psi(2S)$ feed-down further amplifies the NRQCD prediction by about $40\%$ at $\Upsilon(4S)$. With Belle's reconstruction of $J/\psi \to \mu^+\mu^-$ and six $\eta_c$ decay channels, the process shows promising potential for observation.