Exclusive decay of $\Upsilon$ into $J/\psi+\chi_{c0,1,2}$

We study the $\Upsilon$ exclusive decay into double charmonium, specifically, the $S$-wave charmonium $J/\psi$ plus the $P$-wave charmonium $\chi_{c0,1,2}$ in the NRQCD factorization framework. Three distinct decay mechanisms, i.e., the strong, electromagnetic and radiative decay channels are included and their interference effects are investigated. The decay processes $\Upsilon(1S,2S,3S)\to J/\psi+\chi_{c1,0}$ are predicted to have the branching fractions of order $10^{-6}$, which should be observed in the prospective Super $B$ factory.