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In this work, we study the exclusive decay of $\Upsilon$ into $J/\psi$ inassociation with $\eta_c$ ($\chi_{c0,1,2}$). The decay widths for differenthelicity configurations are evaluated up to QCD next-to-leading order withinthe nonrelativistic QCD framework. We find that the QCD corrections notablymitigate the renormalization scale dependence of the decay widths for all theprocesses. The branching fraction of $\Upsilon\rightarrow J/\psi+\chi_{c1}$ isobtained as $3.73^{+5.10+0.10}_{-2.06-1.19}\times 10^{-6}$, which agrees wellwith the Belle measurement, i.e., ${\rm Br}(\Upsilon\rightarrowJ/\psi+\chi_{c1})=(3.90\pm1.21\pm0.23)\times10^{-6}$. For the other processes,our results of the branching fractions are compatible with the upper limitsgiven by the Belle experiments, except for $\Upsilon(2S)\to J/\psi +\chi_{c1}$,where some tension exists between theory and experiment. Having the polarizeddecay widths, we study the $J/\psi$ polarization, which turn out to beindependent of any nonperturbative parameters. Further, according to ourcalculation, it is promising to measure all the processes at Super B factorythanks to the high luminosity.

Higher-order QCD corrections to $\Upsilon$ decay into double charmonia