Inclusive $J/\psi$ and $\eta_c$ production in $\Upsilon$ decay at $\mathcal{O}(\alpha_s^5)$ in non-relativistic QCD factorization

We study J/ψ and ηc inclusive production in ϒ decay within the framework of nonrelativistic-QCD (NRQCD) factorization. In the latter case, for which no experimental data exist so far, we also include the hc feed-down contribution. We calculate the short-distance coefficients completely through O(αs5). The NRQCD predictions for the branching fraction B(ϒ→J/ψ+X) via direct production, evaluated with different sets of long-distance matrix elements (LDMEs), all agree with the experimental data in a reasonable range of renormalization scale. Using ηc and hc LDMEs obtained from J/ψ and χc ones via heavy-quark spin symmetry, we find that the bulk of B(ϒ→ηc+X) via prompt production arises from the cc¯(S31[8]) Fock state. The experimental study of this decay process would, therefore, provide a particularly clean probe of the color octet mechanism of heavy-quarkonium production