Inclusive decays of ηb into S- and P-wave charmonium states

Inclusive S- and P-wave charmonium productions in the bottomonium ground state ηb decay are calculated at the leading order in the strong coupling constant αs and quarkonium internal relative velocity v in the framework of the NRQCD factorization approach. We find the contribution of ηb→χcJ+gg followed by χcJ→J/ψ+γ is also very important to inclusive J/ψ production in the ηb decays, which maybe helpful to the investigation of the color-octet mechanism in the inclusive J/ψ production in the ηb decays in the forthcoming LHCb and SuperB. As a complementary work, we also study the inclusive production of ηc, and χcJ in the ηb decays, which may help us understand the X(3940) and X(3872) states.