ηb decay into charmonium in association with cc̄ pair

Abstract

We calculate the inclusive decay rates of ηb into charmonium via double cc̄ 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 → cc̄[2s+1SL(1)] + cc̄, the effects of cc̄ pair in the color-octet configurations are also considered. We find that ηb → cc̄[3S1(8)] + cc̄ make a small contribution to Br(ηb → J/ϕ(ηc) + cc̄). While in the ηb → χcj + cc̄ case, the color octet contributions are significant, for they are of the same α4Sν5c order as the color-singlet processes. We predict Br(ηb → J/ϕ(ηc) + cc̄) = 2.99(2.75) × 10−5 for S-wave states J/Ψ and ηc, and Br(ηb → χcj) + cc̄) = (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 → cc̄cc̄) + cc̄) is almost saturated by ηb decay into charmonium in association with cc̄ pair from the point of view of duality.