Inclusive $J/\psi$ and ${\eta }_c$ production in ${\rm Y}$ decay at $\mathcal{O}({\alpha }_s^5)$ in nonrelativistic QCD factorization

Abstract

We study $J/\psi$ and ${\eta }_c$ inclusive production in ${\rm Y}$ 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 $\mathcal{O}({\alpha }_s^5)$. The NRQCD predictions for the branching fraction $\mathcal{B}({\rm Y}\to J/\psi +X)$ 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 ${\eta }_c$ and $h_c$ LDMEs obtained from $J/\psi$ and ${\chi }_c$ ones via heavy-quark spin symmetry, we find that the bulk of $\mathcal{B}({\rm Y}\to {\eta }_c+X)$ 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.

Comments: 9 pages, 6 figures, 5 tables; text, appendix and reference added, typos corrected; matches journal version