η_b decay into charmonium in association with c 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 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2S+1SL(1)]+c,the effects of c pair in the color-octet configurations are also considered.We find that ηb→c3S1(8)]+c make a small contribution to Br(ηb→J/ψ(ηc)+c).While in the ηb→χcJ+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)=2.99(2.75)×10-5 for S-wave states J/ψ and ηc,and Br(ηb→χcJ+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) is almost saturated by ηb decay into charmonium in association with c pair from the point of view of duality.