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 b(b-bar)(3PJ, 1) → c(c-bar)(3S1, 8) + c +c-bar, b(b-bar)(3S1, 8) → c(c-bar)(3S1, 1) + g + g, b(b-bar)(3S1, 8) → c(c-bar)(3S1, 1) + c +c-bar and b(b-bar)(3S1, 8) → c(c-bar)(3S1, 8) + g. 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. (authors)