Exclusive decay of $\mathrm{{\rm Y}}$ into $J\mathrm{/}\psi +{\chi }_{c0,1,2}$

We study the $\mathrm{{\rm Y}}$ exclusive decay into double charmonium, specifically, the $S$-wave charmonium $J\mathrm{/}\psi$ 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 $\mathrm{{\rm Y}}(1S,2S,3S)\to J\mathrm{/}\psi +{\chi }_{c1,0}$ are predicted to have the branching fractions of order ${10}^{-6}$, which should be observed in the prospective Super $B$ factory.