ηb decay into charmonium in association with c(c) pair

We calculate the inclusive decay rates of ηb into charmonium via double cc pairs for S- and P-wave states ηc, J/ψ and χcJ within the framework of non-relativistic QCD (NRQCD) factorization at leading order in αs. Besides calculating the contributions of the color-singlet channels ηb→c(c)2S+1Sl(1)]+c(c), the effects of c(c) pair in the color-octet configurations are also considered. We find that ηb→c(c)3S1(8)]+c(c) make a small contribution to Br(ηb→J/ψ(ηc)+c(c)). While in ther ηb→χcJ+c(c) case, the color octet contributions are significant, for they are of the same αs4vc5 order as the color-singlet processes. We predict Br(ηb → J/ψ(ηc)+c(c)) = 2.99(2.75) × 10-5 for S-vrave states J/ψ and ηc, and Br(ηb→χcJ +c(c))= (4.37,3.40,2.83)×10-5 (for J = 0,1,2) for P-wave states χcJ. In the end, we also find Br(ηb → c(c)c(c)) is almost saturated by ηb decay into charmonium in association with cc pair from the point of view of duality.