Inclusive decays of $η_{b}$ into $S$- and $P$-wave charmonium states

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

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