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 ${\rm Y}(4S)$, 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. For the central LDME choice, including $\psi (2S)$ feed-down further amplifies the NRQCD prediction by about $40\%$ at ${\rm Y}(4S)$. With Belle's reconstruction of $J/\psi \to {\mu }^{+}{\mu }^{-}$ and six ${\eta }_c$ decay channels, the process shows promising potential for observation.

arXiv comment23 pages, 7 figures, and 2 tables; accepted for publication in JHEP