ηb decay into charmonium in association with cc pair

We calculate the inclusive decay rates of ηb into charmonium via double c~ pairs for S- and P-wave states ηc, J/ψ and XcJ within the framework of non-relativistic QCD （NRQCD） factorization at leading order in αs. Besides calculating the contributions of the color-singlet channels ηb → cc[2s＋1SL^（1）]＋cc, the effects of cc pair in the color-octet configurations are also considered. We find that ηb → cc[3S1^（8）] ＋cc make a small contribution to Br（ηb →J/ψ（ηc）＋cc）. While in the ηb →XcJ ＋cc case, the color octet contributions are significant, for they are of the same a 5 order as the color-singlet processes. We predict Br（ηb →J/ψ（ηc）＋cc） = 2.99（2.75） × 10^-5 Vc for S-wave states J/ψ and ηc, and Br（ηb → XcJ ＋cc） = （4.37, 3.40, 2.83） × 10^-5 （for J = 0,1, 2） for P-wave states XcJ. In the end, we also find Br（ηb → cccc） is almost saturated by ηb decay into charmonium in association with cc pair from the point of view of duality.