J/Ψ inclusive production in χbJ(nP) decays

We study J/Ψ inclusive production in the decays of P-wave bottomonium χbJ(1P, 2P) for J = 0,1,2. Within the framework of the non-relativistic QCD (NRQCD) factorization method we calculate the contributions coming from four relevant processes including one color-singlet process and three color-octet ones, which are and . Our calculation shows that the color-octet processes, especially the gluon fragmentation one, contribute the most in the decays of χb0 and χb1. However, the J/Ψ production in the χb2 decay is dominated by the color-singlet process. Furthermore, the gluon fragmentation process gives a δ function in the energy fraction distribution of J/Ψ, which can be considered to be another characteristic for its identification. From our estimation the branching ratio for these processes is about 10−4 – 10−5, which indicates that J/Ψ inclusive production is detectable at B-factories. Studying these processes would help us to gain a deeper understanding of the color-octet mechanism.