Inclusive $J/ψ$ and $η_c$ production in $Υ$ decay at $\mathcal{O}(α_s^5)$ in nonrelativistic QCD factorization

Abstract

We study $J/ψ$ and $η_c$ 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 $h_c$ feed-down contribution. We calculate the short distance coefficients completely through $\mathcal{O}(α_s^5)$. The NRQCD predictions for the branching fraction $\mathcal{B}(Υ\to J/ψ+X)$ 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 $η_c$ and $h_c$ LDMEs obtained from $J/ψ$ and $χ_c$ ones via heavy-quark spin symmetry, we find that the bulk of $\mathcal{B}(Υ\toη_c+X)$ via prompt production arises from the $c\bar{c}({}^3\!S_1^{[8]})$ 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.